題目連結

題解

題意：給你一個01矩陣，詢問一個矩形區域內最大的全1正方形。

考慮到硬做很麻煩，所以先二分出一個值就可以了。

st表時間複雜度：n^2*log^2 

程式碼：

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
int Q,n,m,ans,x1,y1,x2,y2,log[1001],a[1001][1001],dp[1001][1001],f[1001][1001][10][10];
int query(int x1,int y1,int x2,int y2){
	int n1=log[x2-x1+1],m1=log[y2-y1+1];
	return max(max(f[x1][y1][n1][m1],f[x1][y2-(1<<m1)+1][n1][m1]),
	 max(f[x2-(1<<n1)+1][y1][n1][m1],f[x2-(1<<n1)+1][y2-(1<<m1)+1][n1][m1]));
}
int pd(int x){
	return query(x1+x-1,y1+x-1,x2,y2)>=x;
}
int main(){
	int i,j,ii,jj,l,r,mid;
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;i++)
	 for(j=1;j<=m;j++)scanf("%d",&a[i][j]);
	for(i=1;i<=n;i++)
	 for(j=1;j<=m;j++){
	   if(a[i][j]==1)dp[i][j]=min(dp[i-1][j-1],min(dp[i][j-1],dp[i-1][j]))+1;   
	   f[i][j][0][0]=dp[i][j];
 }
   for(i=2;i<=1000;i++)log[i]=log[i>>1]+1;
   for(ii=1;ii<=log[n];ii++)
    for(i=1;i+(1<<ii)-1<=n;i++)
     for(j=1;j<=m;j++)
      f[i][j][ii][0]=max(f[i][j][ii-1][0],f[i+(1<<(ii-1))][j][ii-1][0]);
    for(ii=0;ii<=log[n];ii++)
	 for(jj=1;jj<=log[m];jj++) 
	  for(i=1;i+(1<<ii)-1<=n;i++)
	   for(j=1;j+(1<<jj)-1<=m;j++)
	    f[i][j][ii][jj]=max(f[i][j][ii][jj-1],f[i][j+(1<<(jj-1))][ii][jj-1]);
	scanf("%d",&Q);
	while(Q--){
		ans=0;
		scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
		l=0;r=min(x2-x1+1,y2-y1+1);
		while(l<=r){
			mid=(l+r)/2;
			if(pd(mid)){
				ans=max(ans,mid);
				l=mid+1;
			}
			 else r=mid-1;
		}
		printf("%d\n",ans);
	}	  
}