14.差分矩阵

 

 二维差分

原数组a[i][j]

差分数组b[i][j]

使得a数组是b数组的前缀和

同样开始时假定a[i][j]和b[i][j]都等于0

然后对于a数组中的每一个数再插一遍就好了

一维差分是对一段加上一个值

二维差分是对一个子矩阵加上一个值

b[x1][y1]加上c就是x1，y1右下角的所有点加上c

#include <bits/stdc++.h>
using namespace std;
const int N = 1010;
int a[N][N], b[N][N];
//a是原矩阵
//b是差分矩阵 
void insert(int x1, int y1, int x2, int y2, int c) {
    b[x1][y1] += c;
    b[x2 + 1][y1] -= c;
    b[x1][y2 + 1] -= c;
    b[x2 + 1][y2 + 1] += c;
}
int main() {
    int n, m, q;
    cin >> n >> m >> q;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            cin >> a[i][j];
            insert(i, j, i, j, a[i][j]);
        }
    }
    while (q--) {
        int x1, y1, x2, y2, c;
        cin >> x1 >> y1 >> x2 >> y2 >> c;
        insert(x1, y1, x2, y2, c);
    }
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            b[i][j] += b[i - 1][j] + b[i][j - 1] - b[i - 1][j - 1];
            cout << b[i][j] << " ";
        }
        cout << endl;
    }
    return 0;
}