前缀和：

上述图片是求范围内的总和的图和公式

 

上述图片是初始化前缀和数组的图和公式

 差分：

上图是差分公式

#include<iostream>
#include<climits>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<queue>
#include<string>
#include<vector>
#include<tuple>
#include<set>
using namespace std;
using ll = long long;
const int N = 1e3 + 9, mod = 1e8, INF = 0x3f3f3f3f, M = 1;
#define x first
#define y second
typedef pair<ll, ll> PII;
int T, n, m, k, len, a[N][N], res, e[M], ne[M], h[N], w[M], idx, dist[N], f[N][2], 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()
{ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);cin >> n >> m >> k;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) {insert(i, j, i, j, a[i][j]);}}while (k--){int x1, y1, x2, y2, c;cin >> 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) {a[i][j] = a[i - 1][j] + a[i][j - 1] - a[i - 1][j - 1] + b[i][j];}}for (int i = 1; i <= n; ++i) {for (int j = 1; j <= m; ++j) {cout << a[i][j] << ' ';}cout << '\n';}return 0;
}