12：二维差分_二维差分公式

原数组p[N][N]

前缀和数组s[N][N]

二维前缀和公式：

s[i][j] = p[i][j] + s[i][j - 1] + s[i - 1][j] - s[i - 1][j - 1]

差分数组：q[N][N]

二维差分公式：

将（x1, y1) (x2,y2) 围成的矩阵内的所有数加上 x

q[x1][x2] += x; q[x2 + 1][y2 + 1] += x;

q[x2 + 1][y1] -= x; q[x1][y2 + 1] -= x;

例题链接

//例题代码
 
#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 1e3 + 5;
 
int n, m, q;
int s[N][N], p[N][N];
 
void insert(int x1, int y1, int x2, int y2, int num)
{
    p[x1][y1] += num; p[x2 + 1][y2 + 1] += num;
    p[x2 + 1][y1] -= num; p[x1][y2 + 1] -= num;
}
 
int main()
{
    scanf("%d %d %d", &n, &m, &q);
    
    for(int i = 1; i <= n; i ++)
    {
        for(int j = 1; j <= m; j ++)
        {
            int num;
            scanf("%d", &num);
            insert(i, j, i , j, num);
        }
    }
    
    while(q --)
    {
        int x1, y1, x2, y2, num;
        scanf("%d %d %d %d %d", &x1, &y1, &x2, &y2, &num);
        insert(x1, y1, x2, y2, num);
    }
    
    for(int i = 1; i <= n; i ++)
    {
        for(int j = 1; j <= m; j ++)
        {
            s[i][j] = p[i][j] + s[i -1][j] + s[i][j - 1] - s[i - 1][j - 1];
            printf("%d ", s[i][j]);
        }
        printf("\n");
    }
return 0;}