【Algorithm】前缀和与差分

一维前缀和

#include <iostream>

using namespace std;

const int N = 100010;

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

int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);

    for (int i = 1; i <= n; i++) sum[i] = sum[i - 1] + a[i]; // 前缀和的初始化

    while (m--)
    {
        int l, r;
        scanf("%d%d", &l, &r);
        printf("%d\n", sum[r] - sum[l - 1]); // 区间和的计算
    }

    return 0;
}

二维前缀和

#include <iostream>

using namespace std;

const int N = 1010;

int n, m, q;
int a[N][N], sum[N][N];

int main()
{
    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++)
            sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] + a[i][j];

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

    return 0;
}

一维差分

#include <iostream>

using namespace std;

const int N = 100010;

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

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

int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);

    for (int i = 1; i <= n; i++) insert(i, i, a[i]);

    while (m--)
    {
        int l, r, c;
        scanf("%d%d%d", &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++) printf("%d ", b[i]);

    return 0;
}

二维差分

#include <iostream>

using namespace std;

const int N = 1010;

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

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

int main()
{
    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 - 1][j] + b[i][j - 1] - 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;
}