Cho hai số nguyên không âm n1 và n2 Python

Cho một số dương n, hãy đếm tất cả các cặp Số nguyên Không âm riêng biệt (x, y) thỏa mãn bất đẳng thức x*x + y*y < n.  

ví dụ

Input:  n = 5
Output: 6
The pairs are (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (0, 2)

Input: n = 6
Output: 8
The pairs are (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (0, 2),
              (1, 2), (2, 1)

Một giải pháp đơn giản là chạy hai vòng. Vòng lặp bên ngoài đi đến tất cả các giá trị có thể có của x (từ 0 đến √n). Các vòng lặp bên trong chọn tất cả các giá trị có thể có của y cho giá trị hiện tại của x (được chọn bởi vòng lặp bên ngoài).  

Sau đây là việc thực hiện một giải pháp đơn giản.  
 

C++




#include

using namespace std;

 

// This function counts number of pairs (x, y) that satisfy

// the inequality x*x + y*y < n.

int

Total Number of distinct Non-Negative pairs is 8
0int
Total Number of distinct Non-Negative pairs is 8
2

Total Number of distinct Non-Negative pairs is 8
3

Total Number of distinct Non-Negative pairs is 8
4_______323_______
Total Number of distinct Non-Negative pairs is 8
6

Total Number of distinct Non-Negative pairs is 8
4_______1_______8
Total Number of distinct Non-Negative pairs is 8
9int
Total Number of distinct Non-Negative pairs is 8
1

Total Number of distinct Non-Negative pairs is 8
2
Total Number of distinct Non-Negative pairs is 8
8
Total Number of distinct Non-Negative pairs is 8
9int
Total Number of distinct Non-Negative pairs is 8
6

Total Number of distinct Non-Negative pairs is 8
7
Total Number of distinct Non-Negative pairs is 8
8

Total Number of distinct Non-Negative pairs is 8
4_______317_______0 #include 1

#include 2

 

#include 3

int #include 5

Total Number of distinct Non-Negative pairs is 8
3

#include 7#include 8#include 9

Total Number of distinct Non-Negative pairs is 8
7using1

#include 7#include 0 using4

#include 2

Java




using6

using7

using8

using9

namespace0 namespace1

 

namespace2 namespace3

Total Number of distinct Non-Negative pairs is 8
3

#include 7namespace6

#include 7namespace8

#include 7____322_______

#include 7std;2 int

Total Number of distinct Non-Negative pairs is 8
0_______323_______
Total Number of distinct Non-Negative pairs is 8
2

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9_______323_______ // This function counts number of pairs (x, y) that satisfy1// This function counts number of pairs (x, y) that satisfy2// This function counts number of pairs (x, y) that satisfy3

std;9_______1_______8

Total Number of distinct Non-Negative pairs is 8
9int // This function counts number of pairs (x, y) that satisfy8// This function counts number of pairs (x, y) that satisfy2// the inequality x*x + y*y < n.0

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
8
Total Number of distinct Non-Negative pairs is 8
9int // the inequality x*x + y*y < n.5// This function counts number of pairs (x, y) that satisfy2// the inequality x*x + y*y < n.7

// the inequality x*x + y*y < n.8

Total Number of distinct Non-Negative pairs is 8
8

// the inequality x*x + y*y < n.8

std;9_______317_______0 #include 1

#include 7#include 2

 

#include 7int7

#include 7int9 std;2

Total Number of distinct Non-Negative pairs is 8
01
Total Number of distinct Non-Negative pairs is 8
02

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9_______1_______06#include 9

Total Number of distinct Non-Negative pairs is 8
08
Total Number of distinct Non-Negative pairs is 8
09
Total Number of distinct Non-Negative pairs is 8
10
Total Number of distinct Non-Negative pairs is 8
11

std;9

#include 7#include 2

#include 2

 

Total Number of distinct Non-Negative pairs is 8
16

Python3




Total Number of distinct Non-Negative pairs is 8
17

 

Total Number of distinct Non-Negative pairs is 8
18

Total Number of distinct Non-Negative pairs is 8
19

Total Number of distinct Non-Negative pairs is 8
20

Total Number of distinct Non-Negative pairs is 8
21
Total Number of distinct Non-Negative pairs is 8
22

 

#include 7

Total Number of distinct Non-Negative pairs is 8
24
Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2

#include 7

Total Number of distinct Non-Negative pairs is 8
28
Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2

#include 7

Total Number of distinct Non-Negative pairs is 8
32
Total Number of distinct Non-Negative pairs is 8
33
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
35

std;9_______1_______37

Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2

std;9_______1_______32

Total Number of distinct Non-Negative pairs is 8
33
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
28
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
37
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
48

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
24
Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
24
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
54

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
37
Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
37
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
54

std;9_______1_______28

Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
28_______1_______45
Total Number of distinct Non-Negative pairs is 8
54

 

#include 7____317_______0

Total Number of distinct Non-Negative pairs is 8
24

 

Total Number of distinct Non-Negative pairs is 8
70

Total Number of distinct Non-Negative pairs is 8
71
Total Number of distinct Non-Negative pairs is 8
72
Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
75
Total Number of distinct Non-Negative pairs is 8
76

#include 7

Total Number of distinct Non-Negative pairs is 8
78
Total Number of distinct Non-Negative pairs is 8
9#include 9
Total Number of distinct Non-Negative pairs is 8
81

Total Number of distinct Non-Negative pairs is 8
7
Total Number of distinct Non-Negative pairs is 8
0_______1_______10
Total Number of distinct Non-Negative pairs is 8
85

 

Total Number of distinct Non-Negative pairs is 8
86

Total Number of distinct Non-Negative pairs is 8
87

C#




Total Number of distinct Non-Negative pairs is 8
88

using7

using8

using9

using

Total Number of distinct Non-Negative pairs is 8
93

 

namespace2

Total Number of distinct Non-Negative pairs is 8
95

#include 7

#include 7namespace6

#include 7namespace8

#include 7____322_______

#include 7std;2 int

Total Number of distinct Non-Negative pairs is 8
0_______323_______
Total Number of distinct Non-Negative pairs is 8
2

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9______323_______

Total Number of distinct Non-Negative pairs is 8
6

std;9

std;9_______1_______8

Total Number of distinct Non-Negative pairs is 8
9int
Total Number of distinct Non-Negative pairs is 8
1

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
8
Total Number of distinct Non-Negative pairs is 8
9int
Total Number of distinct Non-Negative pairs is 8
6

// the inequality x*x + y*y < n.8

Total Number of distinct Non-Negative pairs is 8
8

// the inequality x*x + y*y < n.8

std;9_______317_______0 #include 1

#include 7#include 2

 

#include 7int7

#include 7int9 std;2

Total Number of distinct Non-Negative pairs is 8
01
Total Number of distinct Non-Negative pairs is 8
39

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9_______1_______43

Total Number of distinct Non-Negative pairs is 8
44

Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
47

Total Number of distinct Non-Negative pairs is 8
48
Total Number of distinct Non-Negative pairs is 8
49

#include 7#include 2

#include 2

 

Total Number of distinct Non-Negative pairs is 8
53

PHP




Total Number of distinct Non-Negative pairs is 8
54

Total Number of distinct Non-Negative pairs is 8
55

using7

using8

Total Number of distinct Non-Negative pairs is 8
58

 

Total Number of distinct Non-Negative pairs is 8
59

Total Number of distinct Non-Negative pairs is 8
60

// the inequality x*x + y*y < n.

Total Number of distinct Non-Negative pairs is 8
62
Total Number of distinct Non-Negative pairs is 8
0_______1_______64
Total Number of distinct Non-Negative pairs is 8
65

Total Number of distinct Non-Negative pairs is 8
3

#include 7

Total Number of distinct Non-Negative pairs is 8
68
Total Number of distinct Non-Negative pairs is 8
69

#include 7

Total Number of distinct Non-Negative pairs is 8
8
Total Number of distinct Non-Negative pairs is 8
9
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
69
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
78
Total Number of distinct Non-Negative pairs is 8
64// This function counts number of pairs (x, y) that satisfy3
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
82

std;9_______1_______8

Total Number of distinct Non-Negative pairs is 8
9
Total Number of distinct Non-Negative pairs is 8
86
Total Number of distinct Non-Negative pairs is 8
69
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
86
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
86
Total Number of distinct Non-Negative pairs is 8
78
Total Number of distinct Non-Negative pairs is 8
64// This function counts number of pairs (x, y) that satisfy3
Total Number of distinct Non-Negative pairs is 8
86_______1_______82

// the inequality x*x + y*y < n.1____1_______68#include 02

#include 7#include 0

Total Number of distinct Non-Negative pairs is 8
68// This function counts number of pairs (x, y) that satisfy3

#include 2

 

#include 08

Total Number of distinct Non-Negative pairs is 8
3

#include 7#include 11 #include 9// This function counts number of pairs (x, y) that satisfy3

#include 7#include 11 #include 16

#include 7#include 0 using4

#include 2

 

#include 21

#include 22

Javascript




#include 23

 

namespace6

namespace8

// the inequality x*x + y*y < n.

 

Total Number of distinct Non-Negative pairs is 8
62 #include 28

Total Number of distinct Non-Negative pairs is 8
4_______317_______30

Total Number of distinct Non-Negative pairs is 8
4_______1_______8 #include 33

Total Number of distinct Non-Negative pairs is 8
2
Total Number of distinct Non-Negative pairs is 8
8 #include 36

Total Number of distinct Non-Negative pairs is 8
7
Total Number of distinct Non-Negative pairs is 8
8

Total Number of distinct Non-Negative pairs is 8
2#include 2

Total Number of distinct Non-Negative pairs is 8
4_______317_______2

Total Number of distinct Non-Negative pairs is 8
4_______317_______0 #include 1

#include 2

 

#include 3

#include 48____317_______9#include 50

 

#include 51

đầu ra.  

Total Number of distinct Non-Negative pairs is 8

Giới hạn trên cho độ phức tạp thời gian của giải pháp trên là O(n). Vòng lặp bên ngoài chạy √n lần. Vòng lặp bên trong chạy tối đa √n lần.  

Không gian phụ trợ. Ô(1)
 

Sử dụng một Giải pháp hiệu quả, chúng ta có thể tìm thấy số đếm trong thời gian O(√n). Ý tưởng là trước tiên tìm số đếm của tất cả các giá trị y tương ứng với giá trị 0 của x. Đặt số giá trị y khác biệt là yCount. Chúng ta có thể tìm thấy yCount bằng cách chạy một vòng lặp và so sánh yCount*yCount với n.  
Sau khi chúng ta có yCount ban đầu, chúng ta có thể lần lượt tăng giá trị của x và tìm giá trị tiếp theo của yCount bằng cách giảm yCount.  
 

C++




#include 52

#include 53

#include

using namespace std;

 

// This function counts number of pairs (x, y) that satisfy

// the inequality x*x + y*y < n.

int

Total Number of distinct Non-Negative pairs is 8
0int
Total Number of distinct Non-Negative pairs is 8
2

Total Number of distinct Non-Negative pairs is 8
3

Total Number of distinct Non-Negative pairs is 8
4_______323_______ #include 67

 

Total Number of distinct Non-Negative pairs is 8
4_______317_______69

Total Number of distinct Non-Negative pairs is 8
4_______1_______8 #include 72

 

Total Number of distinct Non-Negative pairs is 8
4_______317_______74

Total Number of distinct Non-Negative pairs is 8
4_______317_______76

Total Number of distinct Non-Negative pairs is 8
4_______317_______78

Total Number of distinct Non-Negative pairs is 8
4_______1_______32 #include 81

Total Number of distinct Non-Negative pairs is 8
4_______1_______3

#include 84____317_______85

#include 84#include 87

#include 84____317_______89

 

#include 84____317_______91

#include 84#include 93

 

#include 84#include 95

#include 84____317_______97

#include 84

Total Number of distinct Non-Negative pairs is 8
32 using00

Total Number of distinct Non-Negative pairs is 8
7using02

Total Number of distinct Non-Negative pairs is 8
4_______317_______2

 

Total Number of distinct Non-Negative pairs is 8
4_______317_______0 #include 1

#include 2

 

#include 3

int #include 5

Total Number of distinct Non-Negative pairs is 8
3

#include 7#include 8#include 9

Total Number of distinct Non-Negative pairs is 8
7using1

#include 7#include 0 using4

#include 2

Java




using22

using23

using24

namespace0 namespace1

 

namespace2 namespace3

Total Number of distinct Non-Negative pairs is 8
3

#include 7namespace6

#include 7using33

#include 7____322_______

#include 7std;2 int

Total Number of distinct Non-Negative pairs is 8
0_______323_______
Total Number of distinct Non-Negative pairs is 8
2

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9int // This function counts number of pairs (x, y) that satisfy8// This function counts number of pairs (x, y) that satisfy2using48// This function counts number of pairs (x, y) that satisfy2// This function counts number of pairs (x, y) that satisfy3

std;9

std;9____318_______53

std;9____318_______55

std;9_______1_______8 using58// This function counts number of pairs (x, y) that satisfy2using60

std;9

std;9____318_______63

std;9using65

std;9____318_______67

std;9____317_______78

std;9_______1_______32 using72// This function counts number of pairs (x, y) that satisfy2

Total Number of distinct Non-Negative pairs is 8
65

std;9____1_______3

// the inequality x*x + y*y < n.1____318_______78

// the inequality x*x + y*y < n.1____318_______80

// the inequality x*x + y*y < n.1____318_______82

// the inequality x*x + y*y < n.1

// the inequality x*x + y*y < n.1____317_______91

// the inequality x*x + y*y < n.1____317_______93

// the inequality x*x + y*y < n.1

// the inequality x*x + y*y < n.1____318_______90

// the inequality x*x + y*y < n.1____318_______92

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
32 using72// This function counts number of pairs (x, y) that satisfy2 using97
Total Number of distinct Non-Negative pairs is 8
54
Total Number of distinct Non-Negative pairs is 8
65

namespace00_______319_______01

Total Number of distinct Non-Negative pairs is 8
54namespace03

// the inequality x*x + y*y < n.1____318_______02

// the inequality x*x + y*y < n.1

std;9#include 2

std;9_______317_______0 #include 1

std;9

#include 7#include 2

#include 7

#include 7int7

#include 7int9 std;2

Total Number of distinct Non-Negative pairs is 8
01
Total Number of distinct Non-Negative pairs is 8
02

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9_______1_______06#include 9

namespace28

Total Number of distinct Non-Negative pairs is 8
09
Total Number of distinct Non-Negative pairs is 8
10namespace31

std;9

#include 7#include 2

#include 2

 

Total Number of distinct Non-Negative pairs is 8
16

Python3




namespace37

namespace38

namespace39

 

namespace40

namespace41

namespace42

Total Number of distinct Non-Negative pairs is 8
21
Total Number of distinct Non-Negative pairs is 8
22

#include 7

#include 7

Total Number of distinct Non-Negative pairs is 8
28
Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2

#include 7

Total Number of distinct Non-Negative pairs is 8
24
Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2

#include 7namespace55

Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2

 

#include 7namespace59

#include 7namespace61

#include 7

Total Number of distinct Non-Negative pairs is 8
32namespace64
Total Number of distinct Non-Negative pairs is 8
34 namespace66

std;9_______319_______55_______1_______25 namespace55

Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
54

std;9

#include 7namespace75

#include 7namespace77

#include 7namespace79

#include 7namespace81

#include 7namespace83

#include 7

Total Number of distinct Non-Negative pairs is 8
32 namespace86
Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2namespace89

std;9_______319_______91

std;9_______319_______93

std;9_______319_______95

std;9_______319_______97

std;9_______1_______24

Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
24_______1_______45 namespace55

 

std;9____320_______05

std;9_______1_______28

Total Number of distinct Non-Negative pairs is 8
25
Total Number of distinct Non-Negative pairs is 8
28_______1_______45
Total Number of distinct Non-Negative pairs is 8
54

 

std;9_______320_______13

std;9____320_______15

std;9____320_______17

std;9____320_______19

std;9_______1_______32 namespace86

Total Number of distinct Non-Negative pairs is 8
25 // This function counts number of pairs (x, y) that satisfy2 std;25
Total Number of distinct Non-Negative pairs is 8
33
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
28

std;29_______1_______45 namespace64std;32

Total Number of distinct Non-Negative pairs is 8
54
Total Number of distinct Non-Negative pairs is 8
65
Total Number of distinct Non-Negative pairs is 8
34

std;29_______319_______64_______320_______32

Total Number of distinct Non-Negative pairs is 8
54std;40
Total Number of distinct Non-Negative pairs is 8
25 std;42

// the inequality x*x + y*y < n.1namespace55_______1_______25 namespace55std;32

Total Number of distinct Non-Negative pairs is 8
54

std;9

#include 7____317_______0

Total Number of distinct Non-Negative pairs is 8
24

 

std;53

std;54

Total Number of distinct Non-Negative pairs is 8
78
Total Number of distinct Non-Negative pairs is 8
9_______320_______57
Total Number of distinct Non-Negative pairs is 8
81

std;59std;60

std;61______320_______62

Total Number of distinct Non-Negative pairs is 8
10
Total Number of distinct Non-Negative pairs is 8
85

 

std;65

C#




std;66

using23

using24

using

Total Number of distinct Non-Negative pairs is 8
93

 

namespace2

Total Number of distinct Non-Negative pairs is 8
95

#include 7

#include 7namespace6

#include 7using33

#include 7____322_______

#include 7std;2 int

Total Number of distinct Non-Negative pairs is 8
0_______323_______
Total Number of distinct Non-Negative pairs is 8
2

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9____323_______ #include 67

std;9

std;9____318_______53

std;9____318_______55

std;9_______1_______8 std;98

std;99_______321_______00

std;9

std;9____318_______63

std;9using65

std;9____321_______07

std;9____321_______09

std;9____321_______11

std;9_______1_______32 #include 81

std;9____1_______3

// the inequality x*x + y*y < n.1

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy19

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy21

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy23

// the inequality x*x + y*y < n.1____318_______82

// the inequality x*x + y*y < n.1

// the inequality x*x + y*y < n.1____317_______91

// the inequality x*x + y*y < n.1____317_______93

// the inequality x*x + y*y < n.1

// the inequality x*x + y*y < n.1_______321_______33

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy35

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy37

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
32 // This function counts number of pairs (x, y) that satisfy40

// This function counts number of pairs (x, y) that satisfy41______321_______42

// This function counts number of pairs (x, y) that satisfy43____321_______44

// the inequality x*x + y*y < n.1____318_______02

std;9#include 2

std;9

std;9_______317_______0 #include 1

#include 7#include 2

#include 7

#include 7int7

#include 7int9 std;2

Total Number of distinct Non-Negative pairs is 8
01
Total Number of distinct Non-Negative pairs is 8
39

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9_______1_______43

Total Number of distinct Non-Negative pairs is 8
44

Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
47

// This function counts number of pairs (x, y) that satisfy71______321_______72

#include 7#include 2

#include 2

 

Total Number of distinct Non-Negative pairs is 8
53

PHP




Total Number of distinct Non-Negative pairs is 8
54

// This function counts number of pairs (x, y) that satisfy78

// This function counts number of pairs (x, y) that satisfy79

 

// This function counts number of pairs (x, y) that satisfy80

// This function counts number of pairs (x, y) that satisfy81

// This function counts number of pairs (x, y) that satisfy82

Total Number of distinct Non-Negative pairs is 8
62
Total Number of distinct Non-Negative pairs is 8
0_______1_______64
Total Number of distinct Non-Negative pairs is 8
65

Total Number of distinct Non-Negative pairs is 8
3

#include 7

Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
69// This function counts number of pairs (x, y) that satisfy91// This function counts number of pairs (x, y) that satisfy3
Total Number of distinct Non-Negative pairs is 8
68
Total Number of distinct Non-Negative pairs is 8
69

#include 7

#include 7// This function counts number of pairs (x, y) that satisfy97

#include 7// This function counts number of pairs (x, y) that satisfy99

#include 7

Total Number of distinct Non-Negative pairs is 8
8
Total Number of distinct Non-Negative pairs is 8
9// This function counts number of pairs (x, y) that satisfy91
Total Number of distinct Non-Negative pairs is 8
69// This function counts number of pairs (x, y) that satisfy91
Total Number of distinct Non-Negative pairs is 8
34// This function counts number of pairs (x, y) that satisfy91
Total Number of distinct Non-Negative pairs is 8
78
Total Number of distinct Non-Negative pairs is 8
64// This function counts number of pairs (x, y) that satisfy3

// the inequality x*x + y*y < n.11____321_______91// the inequality x*x + y*y < n.13

#include 7

#include 7// the inequality x*x + y*y < n.16

#include 7// the inequality x*x + y*y < n.18

#include 7// the inequality x*x + y*y < n.20

#include 7#include 78

#include 7

Total Number of distinct Non-Negative pairs is 8
32
Total Number of distinct Non-Negative pairs is 8
9// This function counts number of pairs (x, y) that satisfy91 // the inequality x*x + y*y < n.27

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9// This function counts number of pairs (x, y) that satisfy19

std;9____322_______33

std;9____317_______87

std;9_______1_______68 // the inequality x*x + y*y < n.38// This function counts number of pairs (x, y) that satisfy91// This function counts number of pairs (x, y) that satisfy3

#include 7

std;9____317_______91

std;9_______1_______73#include 02

#include 7

std;9____322_______49

std;9____322_______51

std;9____321_______37

std;9_______1_______32

Total Number of distinct Non-Negative pairs is 8
9// This function counts number of pairs (x, y) that satisfy91 // the inequality x*x + y*y < n.58std;25
Total Number of distinct Non-Negative pairs is 8
9
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
34
Total Number of distinct Non-Negative pairs is 8
73
Total Number of distinct Non-Negative pairs is 8
45

std;59

Total Number of distinct Non-Negative pairs is 8
9// This function counts number of pairs (x, y) that satisfy91_______322_______68// This function counts number of pairs (x, y) that satisfy91// the inequality x*x + y*y < n.70
Total Number of distinct Non-Negative pairs is 8
64
Total Number of distinct Non-Negative pairs is 8
85

// the inequality x*x + y*y < n.1____321_______91// the inequality x*x + y*y < n.75

#include 7#include 2

#include 7

#include 7#include 0

Total Number of distinct Non-Negative pairs is 8
68// This function counts number of pairs (x, y) that satisfy3

#include 2

 

#include 3

#include 11 // the inequality x*x + y*y < n.86

Total Number of distinct Non-Negative pairs is 8
81

std;9_______322_______89____322_______90// the inequality x*x + y*y < n.91// This function counts number of pairs (x, y) that satisfy3

 

// the inequality x*x + y*y < n.93

#include 22

Javascript




#include 23

#include 7// the inequality x*x + y*y < n.97

#include 7using23

#include 7using24

#include 7

#include 7namespace6

#include 7using33

#include 7____322_______

#include 7

Total Number of distinct Non-Negative pairs is 8
62 int11

#include 7

Total Number of distinct Non-Negative pairs is 8
3

std;9____323_______15

Total Number of distinct Non-Negative pairs is 8
7

std;9____318_______53

std;9____318_______55

std;9_______1_______8 std;98

std;99_______321_______00

Total Number of distinct Non-Negative pairs is 8
7

std;9____318_______63

std;9using65

std;9____321_______07

std;9____321_______09

std;9____321_______11

std;9_______1_______32 #include 81

std;9____1_______3

int42

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy19

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy21

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy23

// the inequality x*x + y*y < n.1____318_______82

int42

// the inequality x*x + y*y < n.1____317_______91

// the inequality x*x + y*y < n.1____317_______93

int42

// the inequality x*x + y*y < n.1_______321_______33

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy35

// the inequality x*x + y*y < n.1// This function counts number of pairs (x, y) that satisfy37

// the inequality x*x + y*y < n.1

Total Number of distinct Non-Negative pairs is 8
32 // This function counts number of pairs (x, y) that satisfy40

// This function counts number of pairs (x, y) that satisfy41______321_______42

// This function counts number of pairs (x, y) that satisfy43____321_______44

// the inequality x*x + y*y < n.1____318_______02

std;9#include 2

Total Number of distinct Non-Negative pairs is 8
7

std;9_______317_______0 #include 1

#include 7#include 2

#include 7

#include 7____317_______48

Total Number of distinct Non-Negative pairs is 8
44

Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
45
Total Number of distinct Non-Negative pairs is 8
47

// This function counts number of pairs (x, y) that satisfy71______321_______72

 

#include 51

đầu ra.  

Total Number of distinct Non-Negative pairs is 8

Độ phức tạp về thời gian của giải pháp trên có vẻ nhiều hơn nhưng nếu chúng ta xem xét kỹ hơn, chúng ta có thể thấy rằng đó là O(√n). Trong mỗi bước bên trong vòng lặp bên trong, giá trị của yCount giảm đi 1. Giá trị yCount có thể giảm tối đa O(√n) lần khi yCount được tính giá trị y cho x = 0. Trong vòng lặp bên ngoài, giá trị của x được tăng lên. Giá trị của x cũng có thể tăng nhiều nhất là O(√n) lần vì x cuối cùng là cho yCount bằng 1.  

Là hai không

Hai số nguyên không âm được gọi là anh em nếu chúng có thể nhận được từ nhau bằng cách sắp xếp lại các chữ số trong biểu diễn thập phân của chúng . Ví dụ: 123 và 213 là anh em. 535 và 355 cũng là anh em. Tập hợp gồm số nguyên không âm N và tất cả các số anh chị em của nó được gọi là họ của N.

kiểu dữ liệu cho không phải là gì

The xs. nonNegativeInteger kiểu dữ liệu đại diện cho một số nguyên lớn hơn hoặc bằng 0. Bắt nguồn từ xs. kiểu dữ liệu số nguyên. Dạng từ vựng của xs. nonNegativeInteger là một dấu hiệu tùy chọn được theo sau bởi một chuỗi các chữ số thập phân có độ dài hữu hạn. Nếu dấu bị bỏ qua, dấu dương (+) được giả định.

không phải là gì

Số không âm là số không hoặc là số dương (lưu ý rằng +0 = 0 và -0 = .

tập hợp không phải là gì

Tập hợp các số thực dương lớn hơn 0 (không) là các số thực không âm. Điều đó có nghĩa là các số thực là dương hoặc bằng không. Tập hợp sẽ bao gồm các số như {0,1, 2, 3, 4, 5,…}.