一维前缀和

#include <bits/stdc++.h>

using namespace std;

const int N = 1e5+10;

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

int main()
{
    cin >> n >> m ;
    for (int i = 1 ; i <= n ; i ++) cin >> a[i];
    for (int i = 1 ; i <= n ; i ++) s[i] = s[i - 1] + a[i];

    while (m --)
    {
        int l , r ;
        cin >> l >> r ;
        int x = s[r] - s[l - 1];
        cout << x << endl ;
    }

    return 0;
}

二维前缀和

#include <bits/stdc++.h>

using namespace std;

const int N = 1010;

int n , m , q ;
int a[N][N] , s[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 ++)
            s[i][j] = s[i - 1][j] + s[i][j - 1] -s[i - 1][j - 1] + a[i][j];

    while (q --)
    {
        int x1 , y1 , x2 , y2 ;
        cin >> x1 >> y1 >> x2 >> y2;
        int x = s[x2][y2] - s[x1 - 1][y2] - s[x2][y1 - 1] + s[x1 -1][y1 - 1];
        cout << x << endl ;
    }

    return 0;
}

一维差分

#include <bits/stdc++.h>

using namespace std;

const int N = 1e5+10;

int n , m ;
int a[N] , s[N] , b[N];//

void fix(int l , int r , int c)//
{
    b[l] += c ;
    b[r + 1] -= c ;
    return ;
}

int main()
{
    cin >> n >> m ;
    for (int i = 1 ; i <= n ; i ++) 
    {
        cin >> a[i];
        fix(i , i , a[i]);
    }

    while (m --)
    {
        int l , r , c ;
        cin >> l >> r >> c ;
        fix(l , r , c) ;
    }

    for (int i = 1 ; i <= n ; i ++)
    {
        s[i] = s[i - 1] +  b[i];
        cout << s[i] << ' ';
    }
    return 0;
}

二维差分

# include <bits/stdc++.h>

using namespace std;

const int N = 1010 ;

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

void fix(int x1 , int y1 , int x2 , int y2 , int c)//
{
    b[x1][y1] += c ;
    b[x1][y2 + 1] -= c ;
    b[x2 + 1][y1] -= c ;
    b[x2 + 1][y2 + 1] += c ;
    return ;
}

int main()
{
    cin >> n >> m >> q ;
    for (int i = 1 ; i <= n ; i ++)
        for (int j = 1 ; j <= m ; j ++)
        {
            cin >> a[i][j];
            fix(i , j , i , j , a[i][j]);
        }

    while (q --)
    {
        int x1 , y1 , x2 , y2 , c ;
        cin >> x1 >> y1 >> x2 >> y2 >> c ;
        fix(x1 , y1 , x2 , y2 , c);
    }

    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] + b[i][j];//
            cout << s[i][j] << ' ' ;
        }
        cout << endl ;
    }    
    return 0;
}