一维和二维差分
例题:数组长度为6,进行三次操作,在区间为(x,y)内的数加上c
6 3
1 2 2 1 2 1
1 3 1
3 5 1
1 6 1
输出:
3 4 5 3 4 2
#include <bits/stdc++.h>
using namespace std;
const int N=100010;
int n,m;
int a[N],b[N];//b数组是差分数组
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++) b[i]=a[i]-a[i-1];//求差分数组
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];//对差分数组求前缀和
for(int i=1;i<=n;i++) printf("%d",a[i]);
return 0;
}
二维差分
#include <iostream>
#include <cstdio>
using namespace std;
const int N = 1010;
int a[N][N],b[N][N];
void insert(int x1, int y1, int x2, int y2, int v){
b[x1][y1] += v;
b[x1][y2 + 1] -= v;
b[x2 + 1][y1] -= v;
b[x2 + 1][y2 + 1] += v;
}
int main(){
int n,m,q; 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]);
insert(i, j, i, j, a[i][j]);
}
}while(q--){
int x1,y1,x2,y2,v; scanf("%d%d%d%d%d", &x1, &y1, &x2, &y2, &v);
insert(x1, y1, x2, y2, v);
}
for(int i = 1; i <= n; i++){
for(int j = 1; j <= m; j++){
a[i][j] = a[i][j - 1] + a[i - 1][j] - a[i - 1][j - 1] + b[i][j];
cout << a[i][j] << " ";
}cout << endl;
}
return 0;
}
/*
3 4 3
1 2 2 1
3 2 2 1
1 1 1 1
1 1 2 2 1
1 3 2 3 2
3 1 3 4 1
*/