前缀和算法总结

前缀和思维导图：

一维前缀和算法模版：

 1 #include <iostream>
 2 
 3 using namespace std;
 4 
 5 const int N = 100010;
 6 
 7 int n, m;
 8 int s[N];
 9 
10 int main()
11 {
12     scanf("%d%d", &n, &m);
13     for (int i = 1; i <= n; i++)
14     {
15         int x;
16         scanf("%d", &x);
17         s[i] = s[i - 1] + x;  // 前缀和的初始化
18     }
19     
20     while (m--)
21     {
22         int l, r;
23         scanf("%d%d", &l, &r);
24         printf("%d\n", s[r] - s[l - 1]);  // 区间和的计算
25     }
26     
27     return 0;
28 }

二维前缀和算法模版：

 1 #include <iostream>
 2 
 3 using namespace std;
 4 
 5 const int N = 1010;
 6 
 7 int n, m, q, x;
 8 int s[N][N];
 9 
10 int main()
11 {
12     scanf("%d%d%d", &n, &m, &q);
13     for (int i = 1; i <= n; i++)
14         for (int j = 1; j <= m; j++)
15         {
16             scanf("%d", &x);
17             s[i][j] = s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1] + x;
18         }
19     
20     while (q--)
21     {
22         int x1, y1, x2, y2;
23         scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
24         printf("%d\n", s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 - 1][y1 - 1]);
25     }
26     
27     return 0;
28 }