一维和二维前缀和

• 一维：

#include <iostream>
#include <vector>

using namespace std;

vector<int> arr(1e6+10,0);
vector<long long> sum(1e6+10,0);

int main(){
    int n, m, l, r;
    cin >> n >> m;
    for(int i = 1;i <= n;++i)
        cin >> arr[i];
        
    sum[0] = 0;    
    for(int i = 1;i <= n;++i)
        sum[i] = sum[i-1] + arr[i]; 
    
        
    for(int i = 0;i < m;++i){
        cin >> l >> r;
        cout << sum[r] - sum[l-1] << endl;
    }
    
    
}

• 二维

#include <iostream>

using namespace std;

const int N = 1000+10;
int arr[N][N] = {0}, s[N][N] = {0};
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 >> arr[i][j];
    
    for(int i = 1;i <= n;++i)
        for(int j = 1;j <= m;++j)
            s[i][j] = s[i-1][j] + s[i][j-1] - s[i-1][j-1] + arr[i][j];//公式
            
    int x1,y1, x2,y2;//左上角和右下角下标
    for(int i = 0;i < q;++i){
        cin >> x1 >> y1 >> x2 >> y2;
        cout << s[x2][y2] - s[x1-1][y2] - s[x2][y1-1] + s[x1-1][y1-1] << endl;
    }
        
    return 0;
}