一维前缀和
Acwing795.前缀和
#include <iostream>
using namespace std;
const int N = 100010;
int n, m;
int a[N], s[N];
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 ++ ) s[i] = s[i - 1] + a[i]; // 前缀和的初始化
while (m -- )
{
int l, r;
scanf("%d%d", &l, &r);
printf("%d\n", s[r] - s[l - 1]); // 区间和的计算
}
return 0;
}
二维前缀和
Acwing796.子矩阵的和
#include<iostream>
using namespace std;
const int N =1010;
int n,m,q;
int s[N][N];
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",&s[i][j]);
for(int i = 1;i<=n ; i++)
for(int j =1 ;j<=m ;j++)
s[i][j]+= s[i-1][j]+s[i][j-1]-s[i-1][j-1];
while(q--)
{
int x1,y1,x2,y2;
scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
printf("%d\n",s[x2][y2]-s[x1-1][y2]-s[x2][y1-1] + s[x1-1][y1-1]);
}
return 0;
}
差分
Acwing.797
#include<iostream>
#include<algorithm>
using namespace std;
const int N =100010;
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]);
for(int i =1 ;i<=n;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++)b[i] += b[i-1];
for(int i = 1;i<=n ; i++)printf("%d ",b[i]);
return 0;
}
差分矩阵
Acwing.798
#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[x2+1][y1]-=c;
b[x1][y2+1]-=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][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++)
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++)printf("%d ",b[i][j]);
cout<<endl;
}
return 0;
}