[JSOI2015]symmetry

链接：https://www.luogu.com.cn/problem/P6083

题目描述：这个题则么这么卡常。

我们可以先想到一个$O(n^3)$的$dp$，令$dp_{i,j,k}$表示以$(i,j)$为左上角边长为$k$的正方形的对称情况，可以$hash$转移。

考虑优化，发现对于每一个中心点，其边长是单调的，所以可以二分边长，二维$hash$判断对称情况。

#include<iostream>
#include<cstdio>
#include<cmath>
#pragma GCC optimize(1)
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
%:pragma GCC optimize("Ofast")
%:pragma GCC optimize("inline")
%:pragma GCC optimize("-fgcse")
%:pragma GCC optimize("-fgcse-lm")
%:pragma GCC optimize("-fipa-sra")
%:pragma GCC optimize("-ftree-pre")
%:pragma GCC optimize("-ftree-vrp")
%:pragma GCC optimize("-fpeephole2")
%:pragma GCC optimize("-ffast-math")
%:pragma GCC optimize("-fsched-spec")
%:pragma GCC optimize("unroll-loops")
%:pragma GCC optimize("-falign-jumps")
%:pragma GCC optimize("-falign-loops")
%:pragma GCC optimize("-falign-labels")
%:pragma GCC optimize("-fdevirtualize")
%:pragma GCC optimize("-fcaller-saves")
%:pragma GCC optimize("-fcrossjumping")
%:pragma GCC optimize("-fthread-jumps")
%:pragma GCC optimize("-funroll-loops")
%:pragma GCC optimize("-fwhole-program")
%:pragma GCC optimize("-freorder-blocks")
%:pragma GCC optimize("-fschedule-insns")
%:pragma GCC optimize("inline-functions")
%:pragma GCC optimize("-ftree-tail-merge")
%:pragma GCC optimize("-fschedule-insns2")
%:pragma GCC optimize("-fstrict-aliasing")
%:pragma GCC optimize("-fstrict-overflow")
%:pragma GCC optimize("-falign-functions")
%:pragma GCC optimize("-fcse-skip-blocks")
%:pragma GCC optimize("-fcse-follow-jumps")
%:pragma GCC optimize("-fsched-interblock")
%:pragma GCC optimize("-fpartial-inlining")
%:pragma GCC optimize("no-stack-protector")
%:pragma GCC optimize("-freorder-functions")
%:pragma GCC optimize("-findirect-inlining")
%:pragma GCC optimize("-fhoist-adjacent-loads")
%:pragma GCC optimize("-frerun-cse-after-loop")
%:pragma GCC optimize("inline-small-functions")
%:pragma GCC optimize("-finline-small-functions")
%:pragma GCC optimize("-ftree-switch-conversion")
%:pragma GCC optimize("-foptimize-sibling-calls")
%:pragma GCC optimize("-fexpensive-optimizations")
%:pragma GCC optimize("-funsafe-loop-optimizations")
%:pragma GCC optimize("inline-functions-called-once")
%:pragma GCC optimize("-fdelete-null-pointer-checks")
#define mod 998244353
#define line1 23
#define line2 131
using namespace std;
char b[501][501];
int r,a[1022][1022],first,last,mid,n,ans[8][1022][1022],res[8];
long long map[8][1022][1022],fast_pow[1022],fast_pow2[1022];
inline long long f_sum(register int k,register int l,register int r,register int x)
{
	if (l<r||k==0||k==2||k==4||k==6)
		return ((map[k][x][r]-map[k][x][l-1]*fast_pow[r-l+1]%mod)%mod+mod)%mod;
	else
		return ((map[k][x][r]-map[k][x][l+1]*fast_pow[l-r+1]%mod)%mod+mod)%mod;
}
inline long long F_sum(register int k,register int l,register int r,register int l2,register int r2)
{
	if (l<r||k==0||k==1||k==4||k==5)
		return ((f_sum(k,l2,r2,r)-f_sum(k,l2,r2,l-1)*fast_pow2[r-l+1]%mod)%mod+mod)%mod;
	else
		return ((f_sum(k,l2,r2,r)-f_sum(k,l2,r2,l+1)*fast_pow2[l-r+1]%mod)%mod+mod)%mod;
}
int main()
{
	scanf("%d",&n);
	for (register int i=1;i<=n;++i)
		for (register int j=1;j<=n;++j)
		{
			while (b[i][j]!='0'&&b[i][j]!='1')
				b[i][j]=getchar();
			a[i][j]=b[i][j]-'0';
		}
	fast_pow[0]=fast_pow2[0]=1;
	for (int i=1;i<=n;++i)
		fast_pow[i]=fast_pow[i-1]*line1%mod;
	 for (int i=1;i<=n;++i)
		fast_pow2[i]=fast_pow2[i-1]*line2%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=1;j<=n;++j)
			map[0][i][j]=(map[0][i][j-1]*line1+a[i][j])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=1;j<=n;++j)
			map[0][i][j]=(map[0][i-1][j]*line2+map[0][i][j])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=n;j>=1;--j)
			map[1][i][j]=(map[1][i][j+1]*line1+a[i][j])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=n;j>=1;--j)
			map[1][i][j]=(map[1][i-1][j]*line2+map[1][i][j])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=1;j<=n;++j)
			map[2][i][j]=(map[2][i][j-1]*line1+a[i][j])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=1;j<=n;++j)
			map[2][i][j]=(map[2][i+1][j]*line2+map[2][i][j])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=n;j>=1;--j)
			map[3][i][j]=(map[3][i][j+1]*line1+a[i][j])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=n;j>=1;--j)
			map[3][i][j]=(map[3][i+1][j]*line2+map[3][i][j])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=1;j<=n;++j)
			map[4][i][j]=(map[4][i][j-1]*line1+a[j][i])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=1;j<=n;++j)
			map[4][i][j]=(map[4][i-1][j]*line2+map[4][i][j])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=n;j>=1;--j)
			map[5][i][j]=(map[5][i][j+1]*line1+a[j][i])%mod;
	for (register int i=1;i<=n;++i)
		for (register int j=n;j>=1;--j)
			map[5][i][j]=(map[5][i-1][j]*line2+map[5][i][j])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=1;j<=n;++j)
			map[6][i][j]=(map[6][i][j-1]*line1+a[j][i])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=1;j<=n;++j)
			map[6][i][j]=(map[6][i+1][j]*line2+map[6][i][j])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=n;j>=1;--j)
			map[7][i][j]=(map[7][i][j+1]*line1+a[j][i])%mod;
	for (register int i=n;i>=1;--i)
		for (register int j=n;j>=1;--j)
			map[7][i][j]=(map[7][i+1][j]*line2+map[7][i][j])%mod;
	for (register double i=1;i<=n;i+=0.5)
		for (register double j=1+0.5*(floor(i)!=i);j<=n;++j)
		{
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(1,floor(i-mid),ceil(i+mid),ceil(j+mid),floor(j-mid)))
				{
					first=mid+1;
					ans[1][(int)(i)][(int)(j)]=max(ans[1][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(2,ceil(i+mid),floor(i-mid),floor(j-mid),ceil(j+mid)))
				{
					first=mid+1;
					ans[2][(int)(i)][(int)(j)]=max(ans[2][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(3,ceil(i+mid),floor(i-mid),ceil(j+mid),floor(j-mid)))
				{
					first=mid+1;
					ans[3][(int)(i)][(int)(j)]=max(ans[3][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(4,floor(j-mid),ceil(j+mid),floor(i-mid),ceil(i+mid)))
				{
					first=mid+1;
					ans[4][(int)(i)][(int)(j)]=max(ans[4][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(5,floor(j-mid),ceil(j+mid),ceil(i+mid),floor(i-mid)))
				{
					first=mid+1;
					ans[5][(int)(i)][(int)(j)]=max(ans[5][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(6,ceil(j+mid),floor(j-mid),floor(i-mid),ceil(i+mid)))
				{
					first=mid+1;
					ans[6][(int)(i)][(int)(j)]=max(ans[6][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
			first=0;
			last=min(n+1-max(i,j),min(i,j))-1;
			while (first<=last)
			{
				mid=(first+last)/2;
				if (F_sum(0,floor(i-mid),ceil(i+mid),floor(j-mid),ceil(j+mid))==F_sum(7,ceil(j+mid),floor(j-mid),ceil(i+mid),floor(i-mid)))
				{
					first=mid+1;
					ans[7][(int)(i)][(int)(j)]=max(ans[7][(int)(i)][(int)(j)],mid*2+(floor(i)!=i));
				}
				else
					last=mid-1;
			}
		}
	for (register int i=1;i<=n;++i)
		for (register int j=1;j<=n;++j)
		{
			res[0]=max(res[0],min(min(min(ans[1][i][j],ans[2][i][j]),ans[4][i][j]),ans[7][i][j]));
			res[1]=max(res[1],min(min(ans[5][i][j],ans[6][i][j]),ans[3][i][j]));
			res[2]=max(res[2],min(ans[1][i][j],ans[2][i][j]));
			res[2]=max(res[2],min(ans[4][i][j],ans[7][i][j]));
			res[3]=max(res[3],ans[3][i][j]);
			res[4]=max(res[4],ans[1][i][j]);
			res[4]=max(res[4],ans[2][i][j]);
			res[4]=max(res[4],ans[4][i][j]);
			res[4]=max(res[4],ans[7][i][j]);
		}
	printf("%d %d %d %d %d\n",res[0]+1,res[1]+1,res[2]+1,res[3]+1,res[4]+1);
	return 0;
}