P2601 [ZJOI2009]对称的正方形

题目

题目

思路

通过3次二维hash来判断是否有贡献,二分矩阵半径计算贡献,注意奇偶性问题,可以通过2次二分,也可以通过类似马拉车的方式解决(好学生打死不拉车)
code:

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstdlib>
using namespace std;
int a[1001][1001],b[1001][1001],c[1001][1001];
int n,m;
unsigned long long ha[1001][1001],hb[1001][1001],hc[1001][1001],p[1001],p2[1001],ans;
bool check(int x,int y,int l)
{
    
    
	if (x>n||y>m||x<l||y<l) return 0;
	unsigned long long aa,bb,cc;
	aa=ha[x][y]-ha[x][y-l]*p[l]-ha[x-l][y]*p2[l]+ha[x-l][y-l]*p[l]*p2[l];
	int yy=m-y+l,xx=n-x+l;
	bb=hb[xx][y]-hb[xx][y-l]*p[l]-hb[xx-l][y]*p2[l]+hb[xx-l][y-l]*p[l]*p2[l];
	cc=hc[x][yy]-hc[x][yy-l]*p[l]-hc[x-l][yy]*p2[l]+hc[x-l][yy-l]*p[l]*p2[l];
	return aa==bb&&bb==cc;
}
int main()
{
    
    
	cin>>n>>m;
	for (int i=1;i<=n;i++)
	{
    
    
		for (int j=1;j<=m;j++)
		{
    
    
			cin>>a[i][j];
			c[i][m-j+1]=a[i][j];
			b[n-i+1][j]=a[i][j];
		}
	}
	p2[0]=p[0]=1;
	for (int i=1;i<=1000;i++) p[i]=97*p[i-1],p2[i]=13331*p2[i-1];
	for (int i=1;i<=n;i++)
	{
    
    
		for (int j=1;j<=m;j++)
		{
    
    
			ha[i][j]=ha[i][j-1]*97+a[i][j];
			hb[i][j]=hb[i][j-1]*97+b[i][j];
			hc[i][j]=hc[i][j-1]*97+c[i][j];
		}
	}
	for (int i=2;i<=n;i++)
	{
    
    
		for (int j=1;j<=m;j++)
		{
    
    
			ha[i][j]=ha[i-1][j]*13331+ha[i][j];
			hb[i][j]=hb[i-1][j]*13331+hb[i][j];
			hc[i][j]=hc[i-1][j]*13331+hc[i][j];
		}
	}
	for (int i=1;i<=n;i++)
	{
    
    
		for (int j=1;j<=m;j++)
		{
    
    
			int l=1,r=n+m,mn=0;
			while (l<=r)
			{
    
    
				int mid=(l+r)>>1;
				if (check(i+mid,j+mid,mid*2+1)) l=mid+1,mn=max(mn,mid);
				else r=mid-1;
			}
			ans+=mn;
			l=1,r=n+m,mn=0;
			while (l<=r)
			{
    
    
				int mid=(l+r)>>1;
				if (check(i+mid,j+mid,mid*2)) l=mid+1,mn=max(mn,mid);
				else r=mid-1;
			}
			ans+=mn;
		}
	}
	cout<<ans+n*m;
    return 0;
}

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转载自blog.csdn.net/weixin_49843717/article/details/115186143
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