programming python Array in Python

Hướng dẫn how do you check if all elements of array are in another array python? - làm cách nào để kiểm tra xem tất cả các phần tử của mảng có nằm trong một mảng khác không python?

Tôi thích sử dụng index để xác định điểm bắt đầu. Với ví dụ nhỏ này, nó nhanh hơn các giải pháp lặp:

def foo[A,B]:
    n=-1
    while True:
        try:
            n = A.index[B[0],n+1]
        except ValueError:
            return False
        if A[n:n+len[B]]==B:
            return True

Thời gian với điều này khá ổn định bất kể B [dài, ngắn, hiện tại hay không]. Thời gian cho các giải pháp lặp khác nhau thay đổi với nơi B bắt đầu.

Để làm cho điều này mạnh mẽ hơn, tôi đã thử nghiệm chống lại

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]

đó là dài hơn, và lặp lại các giá trị.

Cho hai mảng: ARR1 [0..M-1] và ARR2 [0..N-1]. Tìm xem ARR2 [] là một tập hợp con của ARR1 [] hay không. Cả hai mảng không theo thứ tự sắp xếp. Có thể giả định rằng các yếu tố trong cả hai mảng là khác biệt.subset of arr1[] or not. Both the arrays are not in sorted order. It may be assumed that elements in both arrays are distinct.

Examples:  

Đầu vào: ARR1 [] = {11, 1, 13, 21, 3, 7}, ARR2 [] = {11, 3, 7, 1} & nbsp; đầu ra: ARR2 [] là một tập hợp con của ARR1 []: arr1[] = {11, 1, 13, 21, 3, 7}, arr2[] = {11, 3, 7, 1} 
Output: arr2[] is a subset of arr1[]

Đầu vào: ARR1 [] = {1, 2, 3, 4, 5, 6}, ARR2 [] = {1, 2, 4} & nbsp; đầu ra: ARR2 [] là một tập hợp con của ARR1 []: arr1[] = {1, 2, 3, 4, 5, 6}, arr2[] = {1, 2, 4} 
Output: arr2[] is a subset of arr1[]

Quảng cáo

Đầu vào: ARR1 [] = {10, 5, 2, 23, 19}, ARR2 [] = {19, 5, 3} & nbsp; đầu ra: ARR2 [] không phải là một tập hợp con của ARR1 [] & nbsp;: arr1[] = {10, 5, 2, 23, 19}, arr2[] = {19, 5, 3} 
Output: arr2[] is not a subset of arr1[] 

Cách tiếp cận ngây thơ để tìm xem một mảng có phải là tập hợp con của một mảng khác không

Sử dụng hai vòng: Vòng ngoài chọn tất cả các phần tử của ARR2 [] từng cái một. Các vòng lặp bên trong tìm kiếm tuyến tính cho phần tử được chọn bởi vòng ngoài. Nếu tất cả các phần tử được tìm thấy thì hãy trả về 1, khác sẽ trả về 0. two loops: The outer loop picks all the elements of arr2[] one by one. The inner loop linearly searches for the element picked by the outer loop. If all elements are found then return 1, else return 0.

Dưới đây là việc thực hiện phương pháp trên:

C++

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
4

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
9
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
2index2index3index4index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index2index3B1index5

arr2[] is subset of arr1[]
3B4B5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

C

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
00

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
4

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
9
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
2index2index3index4index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index2index3B1index5

arr2[] is subset of arr1[]
3B4B5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

C

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

Java

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
13
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
18
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
23
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
25

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
29
arr2[] is subset of arr1[]
9
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
51

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
91

arr2[] is subset of arr1[]
92
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
94index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
91

arr2[] is subset of arr1[]
92
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
03index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Python3

arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
15
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____323

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
15
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
22
arr2[] is subset of arr1[]
29

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
32
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
35

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
9

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
40
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
43

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
51
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
54
arr2[] is subset of arr1[]
55

Các

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
73
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
65
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
67__258____259
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
96

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
98index3index4
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
98index3B1
arr2[] is subset of arr1[]
01

C#

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
11

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3__

arr2[] is subset of arr1[]
24
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
40

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
29
arr2[] is subset of arr1[]
9
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
66

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
77

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
80

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
86

arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
89index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
95

arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
98index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

PHP

arr2[] is subset of arr1[]
03

arr2[] is subset of arr1[]
04 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
10
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
1212

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
17

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
19 
arr2[] is subset of arr1[]
17

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3______516

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
arr2[] is subset of arr1[]
19

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

Các

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
9
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index3
arr2[] is subset of arr1[]
19 
arr2[] is subset of arr1[]
67
arr2[] is subset of arr1[]
10
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
06 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
83

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
06index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
08__

Các

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index4
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 B1
arr2[] is subset of arr1[]
23

arr2[] is subset of arr1[]
24

JavaScript

arr2[] is subset of arr1[]
25

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
28

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
32

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
34

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
40

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
29
arr2[] is subset of arr1[]
9
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
63

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
65

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
69

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
66

arr2[] is subset of arr1[]
73
arr2[] is subset of arr1[]
74
arr2[] is subset of arr1[]
91

arr2[] is subset of arr1[]
76
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
94index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
73
arr2[] is subset of arr1[]
74
arr2[] is subset of arr1[]
91

arr2[] is subset of arr1[]
29
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
03index5

arr2[] is subset of arr1[]
89

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
77

arr2[] is subset of arr1[] 

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
80 O[m*n]
Auxiliary Space: O[1]

PHPSorting and Binary Search

Ý tưởng là sắp xếp mảng đã cho ARR1 [], và sau đó cho mỗi phần tử trong ARR2 [] thực hiện tìm kiếm nhị phân cho nó trong ARR1 được sắp xếp []. Nếu phần tử không được tìm thấy thì hãy trả về 0. Nếu tất cả các phần tử có mặt thì hãy trả về 1.not found then return 0. If all elements are present then return 1.

Illustration:

Cho mảng ARR1 [] = {11, 1, 13, 21, 3, 7} và ARR2 [] = {11, 3, 7, 1}.arr1[] = { 11, 1, 13, 21, 3, 7 } and arr2[] = { 11, 3, 7, 1 }.

Bước 1: Chúng tôi sẽ sắp xếp mảng ARR1 [] và có ARR1 [] = {1, 3, 7, 11, 13, 21}.We will sort the array arr1[], and have arr1[] = { 1, 3, 7, 11, 13, 21}.

Bước 2: Chúng tôi sẽ tìm kiếm từng phần tử trong ARR2 [] trong ARR1 [] bằng tìm kiếm nhị phân.We will look for each element in arr2[] in arr1[] using binary search.

  • ARR2 [] = {11, 3, 7, 1}, 11 có mặt trong ARR1 [] = {1, 3, 7, 11, 13, 21}11, 3, 7, 1 }, 11 is present in arr1[] = { 1, 3, 7, 11, 13, 21}
  • ARR2 [] = {11, 3, 7, 1}, 3 có mặt trong ARR1 [] = {1, 3, 7, 11, 13, 21}3, 7, 1 }, 3 is present in arr1[] = { 1, 3, 7, 11, 13, 21}
  • ARR2 [] = {11, 3, 7, 1}, 7 có mặt trong ARR1 [] = {1, 3, 7, 11, 13, 21}7, 1 }, 7 is present in arr1[] = { 1, 3, 7, 11, 13, 21}
  • ARR2 [] = {11, 3, 7, 1}, 1 có mặt trong ARR1 [] = {1, 3, 7, 11, 13, 21}1 }, 1 is present in arr1[] = { 1, 3, 7, 11, 13, 21}

Vì tất cả các yếu tố được tìm thấy, chúng ta có thể kết luận ARR2 [] là tập hợp con của ARR1 [].

Algorithm:

Thuật toán khá đơn giản. & NBSP;

  • Sắp xếp mảng đầu tiên ARR1 [].
  • Tìm các phần tử của ARR2 [] trong ARR1 được sắp xếp [].
  • Nếu chúng ta gặp phải một giá trị cụ thể có trong ARR2 [] nhưng không phải trong ARR1 [], mã sẽ chấm dứt, ARR2 [] không bao giờ có thể là tập hợp con của ARR1 [].
  • Other Arr2 [] là tập hợp con của ARR1 [].

Dưới đây là việc thực hiện mã của phương pháp trên:

C++

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
92 
arr2[] is subset of arr1[]
93

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
95
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
97
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
99__

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
05
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
07__

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
27

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
33

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
05
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
07__

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
56

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
62

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
64

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
79

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
84

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
87
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
89
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
91

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
95

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
97

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
99

arr2[] is subset of arr1[]
3index01

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index04
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index06
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
99
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index10

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index14

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index17

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index20

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index23

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index26

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
5index30

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3index36

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 index39

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
95
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index06
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
99
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index10

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index52

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index55

arr2[] is subset of arr1[]
2index57

arr2[] is subset of arr1[]
2index59

arr2[] is subset of arr1[]
2index61

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
2index92index4
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index92index99
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

C

B05

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
00

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
95
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
97
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
99__

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
05
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
07__

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
27

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
33

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
05
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
07__

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
56

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
62

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
64

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
79

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
84

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
87
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
89
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
91

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
95

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
97

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
99

arr2[] is subset of arr1[]
3index01

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index04
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index06
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
99
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index10

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index14

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index17

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index20

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index23

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index26

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
5index30

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3index36

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 index39

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
95
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index06
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
99
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index10

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index52

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index55

arr2[] is subset of arr1[]
2index57

arr2[] is subset of arr1[]
2index59

arr2[] is subset of arr1[]
2index61

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
2index2index3index4index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index2index3index99index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

Java

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
121

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
143
arr2[] is subset of arr1[]
09
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
145
arr2[] is subset of arr1[]
59index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
18
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
155
arr2[] is subset of arr1[]
09
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
145
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
159
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03__

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
52

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
18
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
155
arr2[] is subset of arr1[]
09
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
145
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
159
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
64

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03__

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
218
arr2[] is subset of arr1[]
11

arr2[] is subset of arr1[]
5index7

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
52

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
56

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
194
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
195
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
199
arr2[] is subset of arr1[]
09 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
201
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
57

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
215
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
217

arr2[] is subset of arr1[]
8index28

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
224
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
226

arr2[] is subset of arr1[]
8
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
270

arr2[] is subset of arr1[]
8
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
272

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
283
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
285

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index04__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
250

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
253
arr2[] is subset of arr1[]
59index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
260

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
263

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
314
arr2[] is subset of arr1[]
59index5

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
318
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
320

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
8
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
268

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
279
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
281

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
287

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
290
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
298__

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
309

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
90index4index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
90

arr2[] is subset of arr1[]
8B1index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Python3

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
312

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
51

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
388
arr2[] is subset of arr1[]
09
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
390
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
56
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
71
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
09

Các

Các

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
453

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
455
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
456

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
459
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430 
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
462

arr2[] is subset of arr1[]
2index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
468
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231 
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
471

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
08 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
477

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
479
arr2[] is subset of arr1[]
12 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
481

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
12 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
485
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
15
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
22
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
494

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
497
arr2[] is subset of arr1[]
12 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
499

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
11
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
506
arr2[] is subset of arr1[]
12 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
508

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
510
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430 
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
513
arr2[] is subset of arr1[]
12

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
521
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
08 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
526

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
529

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
531
arr2[] is subset of arr1[]
12 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
533

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
535
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
540
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430 
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
543

Is

Các

arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93

arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
96

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
98index3index4
arr2[] is subset of arr1[]
01

index7

arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
98index3index99
arr2[] is subset of arr1[]
01

C#

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
11

arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3__

arr2[] is subset of arr1[]
24
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
5

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
616

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
33

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
03__

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
52

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
56

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
62

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
64

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
670

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
218
arr2[] is subset of arr1[]
11

arr2[] is subset of arr1[]
5index7

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
79

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
84

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 index04__

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
250

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
702

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
705

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
260

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
263

arr2[] is subset of arr1[]
8index28

arr2[] is subset of arr1[]
8
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
268

arr2[] is subset of arr1[]
8
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
270

arr2[] is subset of arr1[]
8
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
272

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
727

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
729

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
287

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
734

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
298__

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
309

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
312

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
756

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
758

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
66

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
77

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
80

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
786index4index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
786

arr2[] is subset of arr1[]
8B1index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

PHP

arr2[] is subset of arr1[]
03

arr2[] is subset of arr1[]
04 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
08
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
805

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
806
arr2[] is subset of arr1[]
10
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
17

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
95
arr2[] is subset of arr1[]
06
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
8181

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3______516

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
836
arr2[] is subset of arr1[]
06
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
818
arr2[] is subset of arr1[]
10 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
840

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
806
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
16
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
845

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
857
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
859
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
861
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
861 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
870
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
859
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
877 ____1859 
arr2[] is subset of arr1[]
93
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
861
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
881

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
884
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
886
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
888__

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
893
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
894
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
857
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876
arr2[] is subset of arr1[]
53
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863
arr2[] is subset of arr1[]
13

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
888__

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
857
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
805

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
920index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
923
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
861
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
03
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
857
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
805

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
920index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
923
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
861
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
920
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
859
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
937
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
939
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863index5

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
84

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
949
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
950
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
951
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
952
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
956 
arr2[] is subset of arr1[]
81
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
950
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
950 
arr2[] is subset of arr1[]
81
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
952
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
952 
arr2[] is subset of arr1[]
81
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
956
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
972
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
973
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
975
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
9777
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863 
arr2[] is subset of arr1[]
81
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
973
arr2[] is subset of arr1[]
59
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
9777__1281

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
16 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
989
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
975 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
991

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
973
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
013
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
16
arr2[] is subset of arr1[]
020

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3______519

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

Các

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
036
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
973
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
040__

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 index3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
049

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
0522____1973
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
975
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
9777
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

Các

Các

Các

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Các

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
06 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
83

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
06index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
05
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
10
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
13

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
08__

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index4
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
24

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index99
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
25

JavaScript

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
32

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
616

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0
arr2[] is subset of arr1[]
153

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
28

arr2[] is subset of arr1[]
24
arr2[] is subset of arr1[]
160

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
158

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
173

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
181

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
177

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
186

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
184

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
71

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
920
arr2[] is subset of arr1[]
198

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
196

arr2[] is subset of arr1[]
204
arr2[] is subset of arr1[]
205

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
920
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
859
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
937
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
876 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
939
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
863index5

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
84

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
216

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
218

arr2[] is subset of arr1[]
04 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
949
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
950
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
951
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
952
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
956 
arr2[] is subset of arr1[]
81
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
950
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
232

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
270

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
272

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
242

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
729

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
287

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
734

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
252

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
256

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
260

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
756

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
758

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
63

arr2[] is subset of arr1[]
65

arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
69

arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74index4index5

index7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74B1index5

arr2[] is subset of arr1[]
89

Đầu ra

arr2[] is subset of arr1[]

Độ phức tạp về thời gian: O [mlog [m] + nlog [m]]. O [mlog [m]] để sắp xếp và o [nlog [m]] để tìm kiếm nhị phân mỗi phần tử của một mảng trong một mảng khác. Trong mã trên, loại nhanh được sử dụng và độ phức tạp trong trường hợp xấu nhất của loại nhanh là O [M2] .AUXILIARY SPACE: O [N] O[mLog[m] + nlog[m]]. O[mLog[m]] for sorting and O[nlog[m]] for binary searching each element of one array in another. In the above code, Quick Sort is used and the worst-case time complexity of Quick Sort is O[m2].
Auxiliary Space: O[n]

Tìm xem một mảng có phải là tập hợp con của một mảng khác bằng cách sử dụng sắp xếp và hợp nhất khôngSorting and Merging

Ý tưởng là sắp xếp hai mảng và sau đó lặp lại trên mảng thứ hai tìm kiếm cùng một giá trị trên mảng thứ nhất bằng hai con trỏ. Bất cứ khi nào chúng ta gặp phải cùng một giá trị, chúng ta sẽ tăng cả con trỏ và nếu chúng ta gặp bất kỳ giá trị nào ít hơn so với mảng thứ hai, chúng ta sẽ tăng giá trị của con trỏ trỏ đến mảng thứ nhất. Nếu giá trị lớn hơn giá trị của mảng thứ hai, chúng ta biết mảng thứ hai không phải là tập hợp con của mảng thứ nhất.

Illustration:

Algorithm:

Bước ban đầu sẽ là sắp xếp hai mảng.

  • Đặt hai con trỏ J và I hoặc ARR1 [] và ARR2 [] tương ứng.
  • Nếu ARR1 [J] ARR2 [i], chúng ta sẽ chấm dứt dưới dạng ARR2 [] không phải là tập hợp con của ARR1 [].

Dưới đây là việc thực hiện phương pháp trên: & nbsp;

C++

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
92 
arr2[] is subset of arr1[]
93

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
301

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
304

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
309

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
311

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
314

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
317

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
333

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
341
arr2[] is subset of arr1[]
37 
arr2[] is subset of arr1[]
343
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
2index2index3index4index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index2index3index99index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

C

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
00

arr2[] is subset of arr1[]
390

arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
392

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
404

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
407

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
410

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
413

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
416

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
418

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
421

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
423

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
425

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
427

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
429

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
432

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
435

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
437

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
446

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
452

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
457

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
437

arr2[] is subset of arr1[]
2index28

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
452

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
468

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
446

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
452

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
50 ____2479
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
05
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
489

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
492

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
494

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
496

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
498

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
301

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
304

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
523

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
525

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
314

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
317

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
333

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
341
arr2[] is subset of arr1[]
37 
arr2[] is subset of arr1[]
343
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
2index2index3index4index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index2index3index99index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

Java

arr2[] is subset of arr1[]
599 
arr2[] is subset of arr1[]
600

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
6222

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
304

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
633

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
635

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
314

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
317

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
8index28

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
333

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
666

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
314

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
317

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
333

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
666

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722
arr2[] is subset of arr1[]
723index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
730index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Python3

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
683

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
56
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
71
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
752

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
754

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
15
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
15
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
747

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
09

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
757
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
446 
arr2[] is subset of arr1[]
759

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
762

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
15
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
455 
arr2[] is subset of arr1[]
770
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
773

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
11
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
455 
arr2[] is subset of arr1[]
786

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
98index3
arr2[] is subset of arr1[]
840
arr2[] is subset of arr1[]
01

index7

arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
845
arr2[] is subset of arr1[]
846
arr2[] is subset of arr1[]
01

C#

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
09

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
6222

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
304

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
878

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
880

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
314

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
317

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
8index28

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
333

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
666

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
313 
arr2[] is subset of arr1[]
314

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
317

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
323

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
333

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
786
arr2[] is subset of arr1[]
723index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
786
arr2[] is subset of arr1[]
730index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
683

arr2[] is subset of arr1[]
03

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
56
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
25
arr2[] is subset of arr1[]
19 
arr2[] is subset of arr1[]
17

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 index3
arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
27__51212

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
298
arr2[] is subset of arr1[]
06index5

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
298
arr2[] is subset of arr1[]
08index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 index3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
27
arr2[] is subset of arr1[]
12

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

Các

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
020

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
009
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
53
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
16____
arr2[] is subset of arr1[]
017

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
020

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
16
arr2[] is subset of arr1[]
020

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
009
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
050
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
16
arr2[] is subset of arr1[]
017

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 index3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
27
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
066

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
06 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
83

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
06index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
08__

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
05
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
10
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
13

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index4
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index99
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
24

JavaScript

arr2[] is subset of arr1[]
25

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
28

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
119

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
304

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
127

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
129

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
313 index3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
27
arr2[] is subset of arr1[]
12

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

Các

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
009
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
53
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
16____
arr2[] is subset of arr1[]
017

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
319

arr2[] is subset of arr1[]
5index28

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
009
arr2[] is subset of arr1[]
06
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
19
arr2[] is subset of arr1[]
050
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
16
arr2[] is subset of arr1[]
017

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 index3
arr2[] is subset of arr1[]
16 
arr2[] is subset of arr1[]
27
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
066

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
63

arr2[] is subset of arr1[]
65

arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
69

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
06 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
83

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74index4index5

index7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74index99index5

arr2[] is subset of arr1[]
89

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
82
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[] 

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
06index5 O[mLog[m] + nLog[n]] which is better than approach 2.
Auxiliary Space: O[1]

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
92index3
arr2[] is subset of arr1[]
08__Parthsarthi for suggesting this method.

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index4
arr2[] is subset of arr1[]
0Hashing

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
15 index99
arr2[] is subset of arr1[]
0

Illustration:

JavaScriptarr1[] = { 11, 1, 13, 21, 3, 7 } and arr2[] = { 11, 3, 7, 1 }.

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
28We will storethe array arr1[] elements in HashSet

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
304We will look for each element in arr2[] in arr1[] using binary search.

  • arr2[] is subset of arr1[]
    3
    arr2[] is subset of arr1[]
    313 
    arr2[] is subset of arr1[]
    13211, 3, 7, 1 }, 11 is present in the HashSet = { 1, 3, 7, 11, 13, 21}
  • arr2[] is subset of arr1[]
    2
    arr2[] is subset of arr1[]
    6 
    arr2[] is subset of arr1[]
    3173, 7, 1 }, 3 is present in the HashSet = { 1, 3, 7, 11, 13, 21}
  • arr2[] is subset of arr1[]
    2index7 
    arr2[] is subset of arr1[]
    6 
    arr2[] is subset of arr1[]
    1437, 1 }, 7 is present in the HashSet = { 1, 3, 7, 11, 13, 21}
  • arr2[] is subset of arr1[]
    2index7 
    arr2[] is subset of arr1[]
    6 
    arr2[] is subset of arr1[]
    3331 }, 1 is present in the HashSet = { 1, 3, 7, 11, 13, 21}

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
341
arr2[] is subset of arr1[]
37 
arr2[] is subset of arr1[]
343
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

Algorithm:

arr2[] is subset of arr1[]
6 index0

  • Đầu raHashSet.
  • Độ phức tạp về thời gian: O [MLOG [M] + NLOG [N]] tốt hơn cách tiếp cận 2. Không gian: O [1]HashSet.
  • Cảm ơn Parthsarthi đã đề xuất phương pháp này.HashSet, the code will terminate, arr2[] can never be the subset of arr1[].
  • Tìm xem một mảng có phải là tập hợp con của một mảng khác bằng cách sử dụng băm không

Ý tưởng là chèn tất cả các phần tử của mảng đầu tiên trong một băm, và sau đó lặp lại trên mảng thứ hai và tìm nếu phần tử tồn tại trong băm, nếu hashset không chứa bất kỳ giá trị cụ thể nào thì mảng thứ hai không phải là tập hợp con của mảng đầu tiên.

C++

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1

Cho mảng ARR1 [] = {11, 1, 13, 21, 3, 7} và ARR2 [] = {11, 3, 7, 1}.

Bước 1: Chúng tôi sẽ lưu trữ các phần tử Array ARR1 [] trong Hashset

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
201
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
203

Bước 2: Chúng tôi sẽ tìm kiếm từng phần tử trong ARR2 [] trong ARR1 [] bằng tìm kiếm nhị phân.

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
210

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

ARR2 [] = {11, 3, 7, 1}, 11 có mặt trong Hashset = {1, 3, 7, 11, 13, 21}

ARR2 [] = {11, 3, 7, 1}, 3 có mặt trong Hashset = {1, 3, 7, 11, 13, 21}

ARR2 [] = {11, 3, 7, 1}, 7 có mặt trong Hashset = {1, 3, 7, 11, 13, 21}

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

ARR2 [] = {11, 3, 7, 1}, 1 có mặt trong Hashset = {1, 3, 7, 11, 13, 21}

arr2[] is subset of arr1[]
2

Vì tất cả các yếu tố được tìm thấy, chúng ta có thể kết luận ARR2 [] là tập hợp con của ARR1 [].

arr2[] is subset of arr1[]
2

Thuật toán khá đơn giản. & NBSP;

Lưu trữ mảng đầu tiên ARR1 [] trong một băm.

Tìm kiếm các yếu tố của ARR2 [] trong băm.

Nếu chúng ta gặp phải một giá trị cụ thể có trong ARR2 [] nhưng không phải trong băm, mã sẽ chấm dứt, ARR2 [] không bao giờ có thể là tập hợp con của ARR1 [].

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
257

arr2[] is subset of arr1[]
2index92index4

arr2[] is subset of arr1[]
261
arr2[] is subset of arr1[]
262
arr2[] is subset of arr1[]
263
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index92index99

arr2[] is subset of arr1[]
261
arr2[] is subset of arr1[]
262
arr2[] is subset of arr1[]
263
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

Java

arr2[] is subset of arr1[]
599 
arr2[] is subset of arr1[]
279

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
298
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
300

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
307

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
310

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
312

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
324

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
683

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
56
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
71
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722
arr2[] is subset of arr1[]
723index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
730index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Python3

arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
394

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
396
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
398
arr2[] is subset of arr1[]
399

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____83
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
407

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
409

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____83
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
417

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
420
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
422

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
424

arr2[] is subset of arr1[]
2index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
792

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
796

arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
51
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
438
arr2[] is subset of arr1[]
55

Các

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
73
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
65
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
67__258____259
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
480

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
98index3index4
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
98index3index99
arr2[] is subset of arr1[]
01

C#

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
11

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
497

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
298
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
300

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
307

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
310

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
533

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
324

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
683

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
56
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
71
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
723index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 index0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
730index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
730index5

arr2[] is subset of arr1[]
25

arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
394

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
396
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
398
arr2[] is subset of arr1[]
399

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0
arr2[] is subset of arr1[]
619

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____83
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
407

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____83
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
417

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
312

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0
arr2[] is subset of arr1[]
631

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
420
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
422

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
792

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
796

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
63

arr2[] is subset of arr1[]
65

arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
69

arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
51
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
438
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74
arr2[] is subset of arr1[]
723index5

index7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74
arr2[] is subset of arr1[]
730index5

arr2[] is subset of arr1[]
89

Các 

arr2[] is subset of arr1[] 

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
73
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
65
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
67__258____259
arr2[] is subset of arr1[]
71O[n*logn]
Auxiliary Space: O[n]

Tìm xem một mảng có phải là tập hợp con của một mảng khác bằng cách sử dụng tập hợpSet

Ý tưởng là chèn tất cả các phần tử của mảng thứ nhất và mảng thứ hai trong tập hợp, nếu kích thước của tập hợp bằng kích thước của ARR1 [] thì ARR2 [] là tập hợp con của ARR1 []. Vì không có phần tử mới nào được tìm thấy trong ARR2 [] do đó là tập hợp con.

Illustration:

Cho mảng ARR1 [] = {11, 1, 13, 21, 3, 7} và ARR2 [] = {11, 3, 7, 1}.arr1[] = { 11, 1, 13, 21, 3, 7 } and arr2[] = { 11, 3, 7, 1 }.

Bước 1: Chúng tôi sẽ lưu trữ mảng mảng ARR1 [] và ARR2 [] các phần tử trong tập hợpWe will storethe array arr1[] and arr2[] elements in Set

  • Tập hợp cuối cùng = {1, 3, 7, 11, 13, 21}Set = { 1, 3, 7, 11, 13, 21}

Bước 2: Kích thước của ARR1 [] = 6 và kích thước của tập hợp = 6Size of arr1[] = 6 and size of the Set = 6

  • Do đó, không có phần tử mới nào được tìm thấy trong ARR2 []

Vì tất cả các yếu tố được tìm thấy, chúng ta có thể kết luận ARR2 [] là tập hợp con của ARR1 [].

Algorithm:

Thuật toán khá đơn giản. & NBSP;

  • Lưu trữ mảng đầu tiên ARR1 [] trong một bộ.Set.
  • Lưu trữ mảng đầu tiên ARR1 [] trong cùng một tập hợp. Set.
  • Nếu kích thước của ARR1 [] = kích thước của tập hợp, ARR2 [] là tập hợp con của ARR1 [].
  • Khác ARR2 [] không phải là tập hợp con của ARR1 [].

C++

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
92 
arr2[] is subset of arr1[]
93

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
692
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
694

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
208

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
701

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
706

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
217

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
713

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
718

arr2[] is subset of arr1[]
2index92index4

arr2[] is subset of arr1[]
261
arr2[] is subset of arr1[]
262
arr2[] is subset of arr1[]
263
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index92
arr2[] is subset of arr1[]
733

arr2[] is subset of arr1[]
261
arr2[] is subset of arr1[]
262
arr2[] is subset of arr1[]
263
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

Java

arr2[] is subset of arr1[]
599 
arr2[] is subset of arr1[]
745

arr2[] is subset of arr1[]
599 
arr2[] is subset of arr1[]
747

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
683

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
56
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
71
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58__

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
790
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
792

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
307

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
801

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
706

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
815

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
718

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722index4

arr2[] is subset of arr1[]
204
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
263index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
733

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
263index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Python3

Is

Các

arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93

arr2[] is subset of arr1[]
880
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
398
arr2[] is subset of arr1[]
399

arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222
arr2[] is subset of arr1[]
29

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
890

arr2[] is subset of arr1[]
891
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
894

arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222
arr2[] is subset of arr1[]
23

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
901

arr2[] is subset of arr1[]
6 index3
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
905
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
908

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
98index3index4
arr2[] is subset of arr1[]
01

index7

arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
98index3
arr2[] is subset of arr1[]
733
arr2[] is subset of arr1[]
01

C#

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
11

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
497

arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
48 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
66

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
77

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
80

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
517
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
950
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
517
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
523

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
208

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
961

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
966

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
217

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
973

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
978

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85index4

arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
263index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
733

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
263index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

JavaScript

arr2[] is subset of arr1[]
25

arr2[] is subset of arr1[]
005

arr2[] is subset of arr1[]
006

arr2[] is subset of arr1[]
007

arr2[] is subset of arr1[]
008

arr2[] is subset of arr1[]
009
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
616

arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
619

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
801

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
018

arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
631

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
815

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
026

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74index4 
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
032index5

arr2[] is subset of arr1[]
2

index7

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
74
arr2[] is subset of arr1[]
733 
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
032 index5

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
89

Đầu ra

arr2[] is subset of arr1[]

Độ phức tạp về thời gian: O [m+n] vì chúng tôi đang sử dụng unetered_set và chèn vào nó, nếu chúng tôi sẽ sử dụng một bộ chèn đặt theo thứ tự sẽ lấy log n làm tăng tc lên o [mlogm+nLogn], nhưng thứ tự không quan trọng Cách tiếp cận này.AUXILIOR Không gian: O [N+M] O[m+n] because we are using unordered_set and inserting in it, If we would be using an ordered set inserting would have taken log n increasing the TC to O[mlogm+nlogn], but order does not matter in this approach.
Auxiliary Space: O[n+m]

Tìm xem một mảng có phải là tập hợp con của một mảng khác bằng cách sử dụng bảng tần số không

Ý tưởng là lưu trữ tần số của các phần tử có trong mảng đầu tiên, sau đó tìm kiếm các phần tử có trong ARR2 [] trong mảng tần số. Vì không có phần tử mới nào được tìm thấy trong ARR2 [] do đó là tập hợp con.

Illustration:

Cho mảng ARR1 [] = {11, 1, 13, 21, 3, 7} và ARR2 [] = {11, 3, 7, 1}.arr1[] = { 11, 1, 13, 21, 3, 7 } and arr2[] = { 11, 3, 7, 1 }.

Bước 1: Chúng tôi sẽ lưu trữ tần số phần tử Array Array [] trong mảng tần sốWe will storethe array arr1[] elements frequency in the frequency array

  • Mảng tần số trông như thế nàywill look like this

Mảng tần số

Bước 2: Chúng tôi sẽ tìm kiếm các phần tử ARR2 [] trong mảng tần số.We will look for arr2[] elements in the frequency array.

  • ARR2 [] = {11, 3, 7, 1}, 11 có mặt trong mảng tần số11, 3, 7, 1 }, 11 is present in the frequency array
  • ARR2 [] = {11, 3, 7, 1}, 3 có mặt trong mảng tần số3, 7, 1 }, 3 is present in the frequency array
  • ARR2 [] = {11, 3, 7, 1}, 7 có mặt trong mảng tần số7, 1 }, 7 is present in the frequency array
  • ARR2 [] = {11, 3, 7, 1}, 1 có mặt trong mảng tần số1 }, 1 is present in the frequency array

Vì tất cả các yếu tố được tìm thấy, chúng ta có thể kết luận ARR2 [] là tập hợp con của ARR1 [].

Algorithm:

Thuật toán khá đơn giản. & NBSP;

  • Lưu trữ tần số của các phần tử mảng đầu tiên của ARR1 [] trong mảng tần số.
  • Lặp lại trên ARR2 [] và tìm các phần tử của nó trong mảng tần số.
  • Nếu giá trị được tìm thấy trong mảng tần số sẽ giảm giá trị tần số xuống một.
  • Nếu đối với bất kỳ phần tử nào trong tần số ARR2 [] nhỏ hơn 1, chúng tôi sẽ kết thúc ARR2 [] không phải là tập hợp con của ARR1 [],

Dưới đây là việc thực hiện phương pháp trên: & nbsp; & nbsp;

C++14

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
1

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
92 
arr2[] is subset of arr1[]
93

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
5
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
9
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
7

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
061
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
065

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
208

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
072

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
217

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
082

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
084

arr2[] is subset of arr1[]
2index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
6
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7
arr2[] is subset of arr1[]
7

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
257

arr2[] is subset of arr1[]
2index92index4

arr2[] is subset of arr1[]
261
arr2[] is subset of arr1[]
262
arr2[] is subset of arr1[]
263
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2index92index99

arr2[] is subset of arr1[]
261
arr2[] is subset of arr1[]
262
arr2[] is subset of arr1[]
263
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
8

arr2[] is subset of arr1[]
2

Java

arr2[] is subset of arr1[]
599 
arr2[] is subset of arr1[]
745

arr2[] is subset of arr1[]
599 
arr2[] is subset of arr1[]
747

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
93 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3__

arr2[] is subset of arr1[]
01
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
169

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
173

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
307

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
182

arr2[] is subset of arr1[]
183
arr2[] is subset of arr1[]
184
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
59index5

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
08
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
20

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
202
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
204
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
208

arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
210
arr2[] is subset of arr1[]
59index5

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
683

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

Các

Các

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
82

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
257

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722

arr2[] is subset of arr1[]
8index4index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
722

arr2[] is subset of arr1[]
8index99index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

Python3

arr2[] is subset of arr1[]
08 
arr2[] is subset of arr1[]
394

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
290
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
292

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____83
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
407

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
303
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
305

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
307
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
307
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
430 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
2index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
307
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
11
arr2[] is subset of arr1[]
21 
arr2[] is subset of arr1[]
222____83
arr2[] is subset of arr1[]
09
arr2[] is subset of arr1[]
417

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
329______209
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
412

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
333
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
231
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59

arr2[] is subset of arr1[]
2index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
792

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
796

arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
51
arr2[] is subset of arr1[]
12
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
438
arr2[] is subset of arr1[]
55

Các

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
73
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
59
arr2[] is subset of arr1[]
57
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
65
arr2[] is subset of arr1[]
58
arr2[] is subset of arr1[]
67__258____259
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
85
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
88

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
90
arr2[] is subset of arr1[]
12 
arr2[] is subset of arr1[]
87
arr2[] is subset of arr1[]
93

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
480

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
98index3index4
arr2[] is subset of arr1[]
01

arr2[] is subset of arr1[]
3index7
arr2[] is subset of arr1[]
55

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
98index3index99
arr2[] is subset of arr1[]
01

C#

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
11

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
409

arr2[] is subset of arr1[]
10 
arr2[] is subset of arr1[]
497

A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
89 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
90

arr2[] is subset of arr1[]
3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
2 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3__

arr2[] is subset of arr1[]
24
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
1

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
430
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
434

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
81
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
430
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
58
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
523

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
208

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
450

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
452

arr2[] is subset of arr1[]
5index7

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
456

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
0 index3
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
217

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
082

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
468

arr2[] is subset of arr1[]
5index7 
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
8
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
48 
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
92 
arr2[] is subset of arr1[]
50 
arr2[] is subset of arr1[]
66

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
71

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4
arr2[] is subset of arr1[]
74

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
77

arr2[] is subset of arr1[]
2
A = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]
4 
arr2[] is subset of arr1[]
80

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
257

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
8index4index5

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
85

arr2[] is subset of arr1[]
8index99index5

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2

JavaScript

arr2[] is subset of arr1[]
25

arr2[] is subset of arr1[]
04 
arr2[] is subset of arr1[]
525

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
528
arr2[] is subset of arr1[]
299 
arr2[] is subset of arr1[]
530

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
619

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
072

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
0 
arr2[] is subset of arr1[]
631

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
082

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
084

arr2[] is subset of arr1[]
2index7

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
37
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
7 
arr2[] is subset of arr1[]
43
arr2[] is subset of arr1[]
0

arr2[] is subset of arr1[]
2

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
568

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
65

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
67

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
69

arr2[] is subset of arr1[]
3
arr2[] is subset of arr1[]
6 
arr2[] is subset of arr1[]
257

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
74index4

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
263index5

arr2[] is subset of arr1[]
3index7

arr2[] is subset of arr1[]
2
arr2[] is subset of arr1[]
74index99

arr2[] is subset of arr1[]
5
arr2[] is subset of arr1[]
93
arr2[] is subset of arr1[]
263index5

arr2[] is subset of arr1[]
89

Đầu ra

arr2[] is subset of arr1[]

Độ phức tạp về thời gian: O [M+N] tốt hơn các phương pháp không gian 1,2,3AUXILIARY: O [N]O[m+n] which is better than methods 1,2,3
Auxiliary Space: O[n]

Lưu ý rằng Phương pháp 1, Phương pháp 2, Phương pháp 4 và Phương pháp 5 Donith xử lý các trường hợp khi chúng ta có các bản sao trong ARR2 []. Ví dụ: {1, 4, 4, 2} không phải là một tập hợp con của {1, 4, 2}, nhưng các phương thức này sẽ in nó dưới dạng tập hợp con. & nbsp;

Vui lòng viết nhận xét nếu bạn tìm thấy các mã/thuật toán trên không chính xác hoặc tìm các cách khác để giải quyết cùng một vấn đề. & NBSP;

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