前缀和与差分

一维前缀和 

#include <iostream>

using namespace std;

const int N = 1e5 + 10;
int a[N], b[N];

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

    return 0;
}    

 

二维前缀和

#include <iostream>

using namespace std;
int a[1010][1010], b[1010][1010];

int main()
{
    int n, m, q;
    scanf("%d%d%d", &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] + b[i][j - 1] + b[i - 1][j] - b[i - 1][j - 1];
        }
    }
    while (q -- ) {
        int x1, y1, x2, y2;
        scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
        printf("%d\n", b[x2][y2] - b[x1 - 1][y2] - b[x2][y1 - 1] + b[x1 - 1][y1 - 1]);
    }

    return 0;
}

 

 

一维差分

#include <iostream>

using namespace std;

const int N = 1e5 + 10;
int a[N], b[N];

void insert(int l, int r, int c) //重点就是这个insert，当b[i]加上c后
{                                      //实际上a[i]之后的所有数都加上了c
    b[l] += c;
    b[r + 1] -= c;                //这里是让r+1后的数不要加c
}

int main()
{
    int n, m;
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i ++ ) {
        cin >> a[i];
    }
    for (int i = 1; i <= n; i ++ ) {
        insert(i, i, a[i]);                //构造差分数组，a[1] = b[1], a2 = 
    }                                         //b[2] - b[1], a3 = b[3] - b[2]...
    while (m -- ) {
        int l, r, c;
        cin >> l >> r >> c;
        insert(l, r, c);
    }
    for (int i = 1; i <= n; i ++ ) {
        b[i] += b[i - 1];
    }
    for (int i = 1; i <= n; i ++ ) {
        cout << b[i] << ' ';
    }

    return 0;
}

 

二维差分

#include <iostream>

using namespace std;

const int N = 1010;
int a[N][N], b[N][N];

void insert(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;
}

int main()
{
    int n, m, q;
    scanf("%d%d%d", &n, &m, &q);
    
    for (int i = 1; i <= n; i ++ ) {
        for (int j = 1; j <= m; j ++ ) {
            scanf("%d", &a[i][j]);
        }
    }
    
    for (int i = 1; i <= n; i ++ ) {
        for (int j = 1; j <= m; j ++ ) {
            insert(i, j, i, j, a[i][j]);
        }
    }
    
    while (q -- ) {
        int x1, y1, x2, y2, c;
        scanf("%d%d%d%d%d", &x1, &y1, &x2, &y2, &c);
        insert(x1, y1, x2, y2, c);
    }
    
    for (int i = 1; i <= n; i ++ ) {
        for (int j = 1; j <= m; j ++ ) {
            b[i][j] += b[i][j - 1] + b[i - 1][j] - b[i - 1][j - 1]; 
        }
    }
    
    for (int i = 1; i <= n; i ++ ) {
        for (int j = 1; j <= m; j ++ ) {
            printf("%d ", b[i][j]);
        }
        puts("");
    }
    
    return 0;
}