差分可以看成前缀和的逆运算
构造差分数组b[]
的方法:
作用:可以在\(O(1)\)的时间给区间[l, r]
内的数都加上一个数c
模板题:AcWing 797. 差分
#include <iostream> using namespace std; const int N = 1e5 + 10; 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]); 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 ++ ) { a[i] = a[i - 1] + b[i]; printf("%d ", a[i]); } return 0; }
模板题:AcWing 798. 差分矩阵
#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[x1][y2 + 1] -= c; b[x2 + 1][y1] -= 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][i]); insert(i, j, i, j, a[i][i]); } 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 ++ ) { a[i][j] = a[i - 1][j] + a[i][j - 1] - a[i - 1][j - 1] + b[i][j]; printf("%d ", a[i][j]); } puts(""); } return 0; }