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 80
int
Total Number of distinct Non-Negative pairs is 82
Total Number of distinct Non-Negative pairs is 83
Total Number of distinct Non-Negative pairs is 84_______323_______
Total Number of distinct Non-Negative pairs is 86
Total Number of distinct Non-Negative pairs is 84_______1_______8
Total Number of distinct Non-Negative pairs is 89
int
Total Number of distinct Non-Negative pairs is 81
Total Number of distinct Non-Negative pairs is 82
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 89
int
Total Number of distinct Non-Negative pairs is 86
Total Number of distinct Non-Negative pairs is 87
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 84_______317_______0
#include
1#include
2
#include
3
int
#include
5
Total Number of distinct Non-Negative pairs is 83
#include
7#include
8#include
9
Total Number of distinct Non-Negative pairs is 87
using
1#include
7#include
0 using
4
#include
2
Java
using
6
using
7
using
8
using
9
namespace
0 namespace
1
namespace
2 namespace
3
Total Number of distinct Non-Negative pairs is 83
#include
7namespace
6
#include
7namespace
8
#include
7____322_______
#include
7std;
2 int
Total Number of distinct Non-Negative pairs is 80_______323_______
Total Number of distinct Non-Negative pairs is 82
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9_______323_______ // This function counts number of pairs [x, y] that satisfy
1// This function counts number of pairs [x, y] that satisfy
2// This function counts number of pairs [x, y] that satisfy
3
std;
9_______1_______8
Total Number of distinct Non-Negative pairs is 89
int
// This function counts number of pairs [x, y] that satisfy
8// This function counts number of pairs [x, y] that satisfy
2// the inequality x*x + y*y < n.
0// the inequality x*x + y*y < n.
1
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 89
int
// the inequality x*x + y*y < n.
5// This function counts number of pairs [x, y] that satisfy
2// the inequality x*x + y*y < n.
7// the inequality x*x + y*y < n.
8
Total Number of distinct Non-Negative pairs is 88
// the inequality x*x + y*y < n.
8
std;
9_______317_______0 #include
1
#include
7#include
2
#include
7int
7
#include
7int
9 std;
2
Total Number of distinct Non-Negative pairs is 801
Total Number of distinct Non-Negative pairs is 802
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9_______1_______06#include
9
Total Number of distinct Non-Negative pairs is 808
Total Number of distinct Non-Negative pairs is 809
Total Number of distinct Non-Negative pairs is 810
Total Number of distinct Non-Negative pairs is 811
std;
9
#include
7#include
2
#include
2
Total Number of distinct Non-Negative pairs is 816
Python3
Total Number of distinct Non-Negative pairs is 817
Total Number of distinct Non-Negative pairs is 818
Total Number of distinct Non-Negative pairs is 819
Total Number of distinct Non-Negative pairs is 820
Total Number of distinct Non-Negative pairs is 821
Total Number of distinct Non-Negative pairs is 822
#include
7
Total Number of distinct Non-Negative pairs is 824
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2#include
7
Total Number of distinct Non-Negative pairs is 828
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2#include
7
Total Number of distinct Non-Negative pairs is 832
Total Number of distinct Non-Negative pairs is 833
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 835
std;
9_______1_______37
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2std;
9_______1_______32
Total Number of distinct Non-Negative pairs is 833
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 828
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 837
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 848
// the inequality x*x + y*y < n.
1
Total Number of distinct Non-Negative pairs is 824
Total Number of distinct Non-Negative pairs is 825
Total Number of distinct Non-Negative pairs is 824
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 854
// the inequality x*x + y*y < n.
1
Total Number of distinct Non-Negative pairs is 837
Total Number of distinct Non-Negative pairs is 825
Total Number of distinct Non-Negative pairs is 837
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 854
std;
9_______1_______28
Total Number of distinct Non-Negative pairs is 825
Total Number of distinct Non-Negative pairs is 828_______1_______45
Total Number of distinct Non-Negative pairs is 854
#include
7____317_______0
Total Number of distinct Non-Negative pairs is 824
Total Number of distinct Non-Negative pairs is 870
Total Number of distinct Non-Negative pairs is 871
Total Number of distinct Non-Negative pairs is 872
Total Number of distinct Non-Negative pairs is 825
Total Number of distinct Non-Negative pairs is 825
Total Number of distinct Non-Negative pairs is 875
Total Number of distinct Non-Negative pairs is 876
#include
7
Total Number of distinct Non-Negative pairs is 878
Total Number of distinct Non-Negative pairs is 89
#include
9Total Number of distinct Non-Negative pairs is 881
Total Number of distinct Non-Negative pairs is 87
Total Number of distinct Non-Negative pairs is 80_______1_______10
Total Number of distinct Non-Negative pairs is 885
Total Number of distinct Non-Negative pairs is 886
Total Number of distinct Non-Negative pairs is 887
C#
Total Number of distinct Non-Negative pairs is 888
using
7
using
8
using
9
using
Total Number of distinct Non-Negative pairs is 893
namespace
2
Total Number of distinct Non-Negative pairs is 895
#include
7
#include
7namespace
6
#include
7namespace
8
#include
7____322_______
#include
7std;
2 int
Total Number of distinct Non-Negative pairs is 80_______323_______
Total Number of distinct Non-Negative pairs is 82
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9______323_______
Total Number of distinct Non-Negative pairs is 86
std;
9
std;
9_______1_______8
Total Number of distinct Non-Negative pairs is 89
int
Total Number of distinct Non-Negative pairs is 81
// the inequality x*x + y*y < n.
1
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 89
int
Total Number of distinct Non-Negative pairs is 86
// the inequality x*x + y*y < n.
8
Total Number of distinct Non-Negative pairs is 88
// the inequality x*x + y*y < n.
8
std;
9_______317_______0 #include
1
#include
7#include
2
#include
7int
7
#include
7int
9 std;
2
Total Number of distinct Non-Negative pairs is 801
Total Number of distinct Non-Negative pairs is 839
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9_______1_______43
Total Number of distinct Non-Negative pairs is 844
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 847
Total Number of distinct Non-Negative pairs is 848
Total Number of distinct Non-Negative pairs is 849
#include
7#include
2
#include
2
Total Number of distinct Non-Negative pairs is 853
PHP
Total Number of distinct Non-Negative pairs is 854
Total Number of distinct Non-Negative pairs is 855
using
7
using
8
Total Number of distinct Non-Negative pairs is 858
Total Number of distinct Non-Negative pairs is 859
Total Number of distinct Non-Negative pairs is 860
// the inequality x*x + y*y < n.
Total Number of distinct Non-Negative pairs is 862
Total Number of distinct Non-Negative pairs is 80_______1_______64
Total Number of distinct Non-Negative pairs is 865
Total Number of distinct Non-Negative pairs is 83
#include
7
Total Number of distinct Non-Negative pairs is 868
Total Number of distinct Non-Negative pairs is 869
#include
7
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 89
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 869
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 878
Total Number of distinct Non-Negative pairs is 864
// This function counts number of pairs [x, y] that satisfy
3Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 882
std;
9_______1_______8
Total Number of distinct Non-Negative pairs is 89
Total Number of distinct Non-Negative pairs is 886
Total Number of distinct Non-Negative pairs is 869
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 886
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 886
Total Number of distinct Non-Negative pairs is 878
Total Number of distinct Non-Negative pairs is 864
// This function counts number of pairs [x, y] that satisfy
3Total Number of distinct Non-Negative pairs is 886_______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 868
// This function counts number of pairs [x, y] that satisfy
3#include
2
#include
08
Total Number of distinct Non-Negative pairs is 83
#include
7#include
11 #include
9// This function counts number of pairs [x, y] that satisfy
3
#include
7#include
11 #include
16
#include
7#include
0 using
4
#include
2
#include
21
#include
22
Javascript
#include
23
namespace
6
namespace
8
// the inequality x*x + y*y < n.
Total Number of distinct Non-Negative pairs is 862
#include
28Total Number of distinct Non-Negative pairs is 84_______317_______30
Total Number of distinct Non-Negative pairs is 84_______1_______8
#include
33Total Number of distinct Non-Negative pairs is 82
Total Number of distinct Non-Negative pairs is 88
#include
36Total Number of distinct Non-Negative pairs is 87
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 82
#include
2Total Number of distinct Non-Negative pairs is 84_______317_______2
Total Number of distinct Non-Negative pairs is 84_______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 80
int
Total Number of distinct Non-Negative pairs is 82
Total Number of distinct Non-Negative pairs is 83
Total Number of distinct Non-Negative pairs is 84_______323_______
#include
67
Total Number of distinct Non-Negative pairs is 84_______317_______69
Total Number of distinct Non-Negative pairs is 84_______1_______8
#include
72
Total Number of distinct Non-Negative pairs is 84_______317_______74
Total Number of distinct Non-Negative pairs is 84_______317_______76
Total Number of distinct Non-Negative pairs is 84_______317_______78
Total Number of distinct Non-Negative pairs is 84_______1_______32
#include
81Total Number of distinct Non-Negative pairs is 84_______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 832
using
00Total Number of distinct Non-Negative pairs is 87
using
02Total Number of distinct Non-Negative pairs is 84_______317_______2
Total Number of distinct Non-Negative pairs is 84_______317_______0
#include
1#include
2
#include
3
int
#include
5
Total Number of distinct Non-Negative pairs is 83
#include
7#include
8#include
9
Total Number of distinct Non-Negative pairs is 87
using
1#include
7#include
0 using
4
#include
2
Java
using
22
using
23
using
24
namespace
0 namespace
1
namespace
2 namespace
3
Total Number of distinct Non-Negative pairs is 83
#include
7namespace
6
#include
7using
33
#include
7____322_______
#include
7std;
2 int
Total Number of distinct Non-Negative pairs is 80_______323_______
Total Number of distinct Non-Negative pairs is 82
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9int
// This function counts number of pairs [x, y] that satisfy
8// This function counts number of pairs [x, y] that satisfy
2using
48// This function counts number of pairs [x, y] that satisfy
2// This function counts number of pairs [x, y] that satisfy
3
std;
9
std;
9____318_______53
std;
9____318_______55
std;
9_______1_______8 using
58// This function counts number of pairs [x, y] that satisfy
2using
60
std;
9
std;
9____318_______63
std;
9using
65
std;
9____318_______67
std;
9____317_______78
std;
9_______1_______32 using
72// This function counts number of pairs [x, y] that satisfy
2
Total Number of distinct Non-Negative pairs is 865
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 832
using
72// This function counts number of pairs [x, y] that satisfy
2 using
97Total Number of distinct Non-Negative pairs is 854
Total Number of distinct Non-Negative pairs is 865
namespace
00_______319_______01
Total Number of distinct Non-Negative pairs is 854
namespace
03// 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
7int
7
#include
7int
9 std;
2
Total Number of distinct Non-Negative pairs is 801
Total Number of distinct Non-Negative pairs is 802
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9_______1_______06#include
9
namespace
28
Total Number of distinct Non-Negative pairs is 809
Total Number of distinct Non-Negative pairs is 810
namespace
31std;
9
#include
7#include
2
#include
2
Total Number of distinct Non-Negative pairs is 816
Python3
namespace
37
namespace
38
namespace
39
namespace
40
namespace
41
namespace
42
Total Number of distinct Non-Negative pairs is 821
Total Number of distinct Non-Negative pairs is 822
#include
7
#include
7
Total Number of distinct Non-Negative pairs is 828
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2#include
7
Total Number of distinct Non-Negative pairs is 824
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2#include
7namespace
55
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2
#include
7namespace
59
#include
7namespace
61
#include
7
Total Number of distinct Non-Negative pairs is 832
namespace
64Total Number of distinct Non-Negative pairs is 834
namespace
66std;
9_______319_______55_______1_______25 namespace
55
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 854
std;
9
#include
7namespace
75
#include
7namespace
77
#include
7namespace
79
#include
7namespace
81
#include
7namespace
83
#include
7
Total Number of distinct Non-Negative pairs is 832
namespace
86Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2namespace
89std;
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 825
Total Number of distinct Non-Negative pairs is 824_______1_______45
namespace
55
std;
9____320_______05
std;
9_______1_______28
Total Number of distinct Non-Negative pairs is 825
Total Number of distinct Non-Negative pairs is 828_______1_______45
Total Number of distinct Non-Negative pairs is 854
std;
9_______320_______13
std;
9____320_______15
std;
9____320_______17
std;
9____320_______19
std;
9_______1_______32 namespace
86
Total Number of distinct Non-Negative pairs is 825
// This function counts number of pairs [x, y] that satisfy
2 std;
25 Total Number of distinct Non-Negative pairs is 833
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 828
std;
29_______1_______45 namespace
64std;
32
Total Number of distinct Non-Negative pairs is 854
Total Number of distinct Non-Negative pairs is 865
Total Number of distinct Non-Negative pairs is 834
std;
29_______319_______64_______320_______32
Total Number of distinct Non-Negative pairs is 854
std;
40Total Number of distinct Non-Negative pairs is 825
std;
42// the inequality x*x + y*y < n.
1namespace
55_______1_______25 namespace
55std;
32
Total Number of distinct Non-Negative pairs is 854
std;
9
#include
7____317_______0
Total Number of distinct Non-Negative pairs is 824
std;
53
std;
54
Total Number of distinct Non-Negative pairs is 878
Total Number of distinct Non-Negative pairs is 89_______320_______57
Total Number of distinct Non-Negative pairs is 881
std;
59std;
60
std;
61______320_______62
Total Number of distinct Non-Negative pairs is 810
Total Number of distinct Non-Negative pairs is 885
std;
65
C#
std;
66
using
23
using
24
using
Total Number of distinct Non-Negative pairs is 893
namespace
2
Total Number of distinct Non-Negative pairs is 895
#include
7
#include
7namespace
6
#include
7using
33
#include
7____322_______
#include
7std;
2 int
Total Number of distinct Non-Negative pairs is 80_______323_______
Total Number of distinct Non-Negative pairs is 82
#include
7
Total Number of distinct Non-Negative pairs is 83
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;
9using
65
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 satisfy
19
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
21
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
23
// 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 satisfy
35
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
37
// the inequality x*x + y*y < n.
1
Total Number of distinct Non-Negative pairs is 832
// This function counts number of pairs [x, y] that satisfy
40// This function counts number of pairs [x, y] that satisfy
41______321_______42
// This function counts number of pairs [x, y] that satisfy
43____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
7int
7
#include
7int
9 std;
2
Total Number of distinct Non-Negative pairs is 801
Total Number of distinct Non-Negative pairs is 839
#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9_______1_______43
Total Number of distinct Non-Negative pairs is 844
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 847
// This function counts number of pairs [x, y] that satisfy
71______321_______72
#include
7#include
2
#include
2
Total Number of distinct Non-Negative pairs is 853
PHP
Total Number of distinct Non-Negative pairs is 854
// This function counts number of pairs [x, y] that satisfy
78
// This function counts number of pairs [x, y] that satisfy
79
// This function counts number of pairs [x, y] that satisfy
80
// This function counts number of pairs [x, y] that satisfy
81
// This function counts number of pairs [x, y] that satisfy
82
Total Number of distinct Non-Negative pairs is 862
Total Number of distinct Non-Negative pairs is 80_______1_______64
Total Number of distinct Non-Negative pairs is 865
Total Number of distinct Non-Negative pairs is 83
#include
7
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 869
// This function counts number of pairs [x, y] that satisfy
91// This function counts number of pairs [x, y] that satisfy
3Total Number of distinct Non-Negative pairs is 868
Total Number of distinct Non-Negative pairs is 869
#include
7
#include
7// This function counts number of pairs [x, y] that satisfy
97
#include
7// This function counts number of pairs [x, y] that satisfy
99
#include
7
Total Number of distinct Non-Negative pairs is 88
Total Number of distinct Non-Negative pairs is 89
// This function counts number of pairs [x, y] that satisfy
91 Total Number of distinct Non-Negative pairs is 869
// This function counts number of pairs [x, y] that satisfy
91Total Number of distinct Non-Negative pairs is 834
// This function counts number of pairs [x, y] that satisfy
91 Total Number of distinct Non-Negative pairs is 878
Total Number of distinct Non-Negative pairs is 864
// This function counts number of pairs [x, y] that satisfy
3// 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 832
Total Number of distinct Non-Negative pairs is 89
// This function counts number of pairs [x, y] that satisfy
91 // the inequality x*x + y*y < n.
27#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9// This function counts number of pairs [x, y] that satisfy
19
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 satisfy
91// This function counts number of pairs [x, y] that satisfy
3
#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 89
// This function counts number of pairs [x, y] that satisfy
91 // the inequality x*x + y*y < n.
58std;
25 Total Number of distinct Non-Negative pairs is 89
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 834
Total Number of distinct Non-Negative pairs is 873
Total Number of distinct Non-Negative pairs is 845
std;
59
Total Number of distinct Non-Negative pairs is 89
// This function counts number of pairs [x, y] that satisfy
91_______322_______68// This function counts number of pairs [x, y] that satisfy
91// the inequality x*x + y*y < n.
70Total Number of distinct Non-Negative pairs is 864
Total Number of distinct Non-Negative pairs is 885
// 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 868
// This function counts number of pairs [x, y] that satisfy
3#include
2
#include
3
#include
11 // the inequality x*x + y*y < n.
86
Total Number of distinct Non-Negative pairs is 881
std;
9_______322_______89____322_______90// the inequality x*x + y*y < n.
91// This function counts number of pairs [x, y] that satisfy
3
// the inequality x*x + y*y < n.
93
#include
22
Javascript
#include
23
#include
7// the inequality x*x + y*y < n.
97
#include
7using
23
#include
7using
24
#include
7
#include
7namespace
6
#include
7using
33
#include
7____322_______
#include
7
Total Number of distinct Non-Negative pairs is 862
int
11#include
7
Total Number of distinct Non-Negative pairs is 83
std;
9____323_______15
Total Number of distinct Non-Negative pairs is 87
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 87
std;
9____318_______63
std;
9using
65
std;
9____321_______07
std;
9____321_______09
std;
9____321_______11
std;
9_______1_______32 #include
81
std;
9____1_______3
int
42
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
19
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
21
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
23
// the inequality x*x + y*y < n.
1____318_______82
int
42
// the inequality x*x + y*y < n.
1____317_______91
// the inequality x*x + y*y < n.
1____317_______93
int
42
// 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 satisfy
35
// the inequality x*x + y*y < n.
1// This function counts number of pairs [x, y] that satisfy
37
// the inequality x*x + y*y < n.
1
Total Number of distinct Non-Negative pairs is 832
// This function counts number of pairs [x, y] that satisfy
40// This function counts number of pairs [x, y] that satisfy
41______321_______42
// This function counts number of pairs [x, y] that satisfy
43____321_______44
// the inequality x*x + y*y < n.
1____318_______02
std;
9#include
2
Total Number of distinct Non-Negative pairs is 87
std;
9_______317_______0 #include
1
#include
7#include
2
#include
7
#include
7____317_______48
Total Number of distinct Non-Negative pairs is 844
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 845
Total Number of distinct Non-Negative pairs is 847
// This function counts number of pairs [x, y] that satisfy
71______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.