矩阵的差分

insert函数结合矩阵加对后续元素的影响不难写出。

最后求和的时候，考虑到每次对b[i][j]的影响包含了其本身，只需加等于前面元素带来的影响。

#include <iostream>
using namespace std;

const int maxn = 2e3 + 10;
int a[maxn][maxn], b[maxn][maxn], n, m, q, i, j, k, l, c;

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

int main() {
  cin >> n >> m >> q;
  for (int i = 1; i <= n; i++) 
    for (int j = 1; j <= m; j++)
      cin >> a[i][j], insert(i, j, i, j, a[i][j]);
  while (q--) {
    cin >> i >> j >> k >> l >> c;
    insert(i, j, k, l, 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++) cout << b[i][j] << " ";
    cout << '\n';
  }  
  return 0;
}