矩阵前缀和&矩阵的差分

前缀和

#include<iostream>
using namespace std;

const int N = 1010;

int a[N][N];
int n, m, q;

int main(){
    cin >> n >> m >> q;
    
    for(int i = 1; i <= n; i ++)
        for(int j = 1; j <= m; j ++){
            cin >> a[i][j];
            a[i][j] += a[i - 1][j] + a[i][j - 1] - a[i - 1][j - 1];
        }
        
    while(q --){
        int x1, y1, x2, y2;
        
        cin >> x1 >> y1 >> x2 >> y2;
        cout << a[x2][y2] - a[x2][y1 - 1] - a[x1 - 1][y2] + a[x1 - 1][y1 - 1] << endl;
    }
    
    return 0;
}

差分

#include<iostream>
using namespace std;

const int N = 1010;

int n, m, q;
int a[N][N], b[N][N];

int main(){
    cin >> n >> m >> q;
    
    for(int i = 1; i <= n; i ++)
        for(int j = 1; j <= m; j ++)
            cin >> a[i][j];
            
    for(int i = 1; i <= n; i ++)
        for(int j = 1; j <= m; j ++){
            b[i][j] = a[i][j] - a[i - 1][j] - a[i][j - 1] + a[i - 1][j - 1];
        }
        
    while(q --){
        int x1, y1, x2, y2, c;
        
        cin >> x1 >> y1 >> x2 >> y2 >> c;
        b[x1][y1] += c;
        b[x2 + 1][y1] -= c;
        b[x1][y2 + 1] -= c;
        b[x2 + 1][y2 + 1] += 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];
            
    for(int i = 1; i <= n; i ++){
        for(int j = 1; j <= m; j ++)
            cout << b[i][j] << ' ';
        cout << endl;
    }
    
    return 0;       
}