洛谷P1719

P1719 最大加权矩形

容斥原理、二维前缀和、暴力
还有子矩阵求和
入门好题

点击查看代码

#include<bits/stdc++.h>
using namespace std;

vector<vector<int>>a(121, vector<int>(121));
vector<vector<int>>s(121, vector<int>(121));
int qsum(int X1, int Y1, int X2, int Y2) {
    return s[X2][Y2] + s[X1 - 1][Y1 - 1] - s[X2][Y1 - 1] - s[X1 - 1][Y2];
}

int main() {
    int n; cin >> n;
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= n; j++) {
            cin >> a[i][j];
            s[i][j] = s[i][j - 1] + s[i - 1][j] + a[i][j] - s[i - 1][j - 1];
        }
    }
    int ans = INT_MIN;
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <=n; j++) {
            for(int k = i; k <= n; k++) {
                for(int l = j; l <= n; l++){
                    ans = max(ans, qsum(i, j, k, l));
                }
            }
        }
    }
    cout << ans << '\n';
    return 0;    
}