一维前缀和

#include <iostream>
using namespace std;
#include <vector>
int main() {
    int n,q;
    cin >> n >> q;
    
    vector<long long> arr(n+1);
    for(int i =1;i<=n;i++)
    {
        cin >> arr[i];
    }

    //创造前缀和数组
    vector<long long> dp(n+1);
    dp[0] = 0;
    for(int i=1;i<=n;i++)
    {
        dp[i] = dp[i-1] + arr[i];
    }
       
       //使用前缀和
       while(q--)
       {
        int a,b;
        cin >> a >> b;
        cout << dp[b] - dp[a-1] <<endl;
       }

}

二维前缀和

#include <iostream>
using namespace std;
#include <vector>
int main() {
    int n , m , q;
    cin >> n >> m >> q;
    //创建dp表
    vector<vector<int>> arr(n+1,vector<int>(m+1));
    vector<vector<long long>> dp(n+1,vector<long long>(m+1));
    for(int i=1;i<=n;i++)
    {
        for(int j =1;j<=m;j++)
        {
            cin >> arr[i][j];
        }
    }
    //初始化＋填表
   for(int i=1;i<=n;i++)
    {
        for(int j =1;j<=m;j++)
        {
            dp[i][j] = dp[i-1][j]+dp[i][j-1]+arr[i][j] - dp[i-1][j-1];
        }
    }
    while(q--)
    {
        int x1,y1,x2,y2;
        cin >> x1 >> y1 >> x2 >>y2;
        //用表
        cout << dp[x2][y2]-dp[x1-1][y2] -dp[x2][y1-1] + dp[x1-1][y1-1] <<endl;

    }

    return 0;  
}