差分(一维和二维)

一维差分

思路：


代码：

# include<iostream>
# include<cstdio>
# include<cstring>
# include<algorithm>
using namespace std;

const int N = 100010;
int a[N],b[N];
int n,m;

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

int main()
{
    
    
    cin >> n >> m;
    for(int i = 1;i <= n;i++) 
    {
    
    
        cin >> a[i];
        insert(i,i,a[i]);//将初始的插入，不需要构造
    }
    while(m--)
    {
    
    
        int l,r,c;
        cin >> 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;
}

二维差分

思路：

代码：

# include<iostream>
# include<cstdio>
# include<cstring>
# include<algorithm>
using namespace std;

const int N = 1010;
int a[N][N],b[N][N];
int n,m,q;

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++)
        {
    
    
            scanf("%d",&a[i][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];
            printf("%d ",b[i][j]);
        }
        puts("");
    }
     
    return 0;
}