算法基础班–第一章–12.二维差分模板
算法模板
b[x1][ y1 ] +=c ; 让整个a数组中蓝色矩形面积的元素都加上了c。
b[x1,][y2+1]-=c ; 让整个a数组中绿色矩形面积的元素再减去c,使其内元素不发生改变。
b[x2+1][y1]- =c ; 让整个a数组中紫色矩形面积的元素再减去c,使其内元素不发生改变。
b[x2+1][y2+1]+=c; 让整个a数组中红色矩形面积的元素再加上c,红色内的相当于被减了两次,再加上一次c,才能使其恢复。
#include <iostream>
#include <cstdio>
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() {
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++ )
insert(i, j, i, j, a[i][j]);
while (q--) {
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++ ) //求前缀和
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] << " ";
puts("");
}
return 0;
}