题目请戳这里

题目大意:给一个H行W列的01矩阵,求最少用多少个正方形框住所有的1.

题目分析:又是一个红果果的重复覆盖模型.DLX搞之!

枚举矩阵所有的子正方形,全1的话建图.判断全1的时候,用了一个递推,dp[i][j][w][h]表示左上角(i,j)的位置开始长h宽w的矩形中1的个数,这样后面可以迅速判断某个正方形是否全1.

不过此题直接搜一直TLE,然后改成迭代加深就比较愉快啦

详情请见代码:

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;const int N = 11;
const int M = 50005;
int dp[N][N][N][N];
int n,m,num,ans;
int mp[N][N];
bool vis[105];
int s[M],h[M],col[M],u[M],d[M],l[M],r[M];void init()
{memset(h,0,sizeof(h));memset(s,0,sizeof(s));int i,c;c = m * n;for(i = 0;i <= c;i ++){u[i] = d[i] = i;l[i] = (i + c)%(c + 1);r[i] = (i + 1)%(c + 1);}num = c + 1;
}void ins(int i,int j)
{if(h[i]){r[num] = h[i];l[num] = l[h[i]];r[l[num]] = l[r[num]] = num;}elseh[i] = l[num] = r[num] = num;s[j] ++;u[num] = u[j];d[num] = j;d[u[num]] = num;u[j] = num;col[num] = j;num ++;
}
void del(int c)
{for(int i = u[c];i != c;i = u[i])l[r[i]] = l[i],r[l[i]] = r[i];
}
void resume(int c)
{for(int i = d[c];i != c;i = d[i])l[r[i]] = r[l[i]] = i;
}int A()
{int i,j,k,ret;ret = 0;memset(vis,false,sizeof(vis));for(i = r[0];i;i = r[i]){if(vis[i] == false){ret ++;vis[i] = true;for(j = d[i];j != i;j = d[j])for(k = r[j];k != j;k = r[k])vis[col[k]] = true;}}return ret;
}bool dfs(int k,int lim)
{if(k + A() > lim)return false;if(!r[0]){
//        ans = min(ans,k);return true;}int i,j,c,mn = M;for(i = r[0];i;i = r[i]){if(s[i] < mn){mn = s[i];c = i;}}for(i = d[c];i != c;i = d[i]){del(i);for(j = l[i];j != i;j = l[j])del(j);if(dfs(k + 1,lim)) return true;for(j = r[i];j != i;j = r[j])resume(j);resume(i);}return false;
}bool canfuck(int x,int y,int z)
{return dp[x][y][z][z] == z * z;int i,j;for(i = x;i <= x + z - 1;i ++)for(j = y;j <= y + z - 1;j ++)if(mp[i][j] == 0)return false;return true;
}void fuckba(int x,int y,int z,int id)
{int i,j;for(i = x;i <= x + z - 1;i ++)for(j = y;j <= y + z - 1;j ++)ins(id,(i - 1) * m + j);
}
void build()
{int i,j,k;memset(dp,0,sizeof(dp));for(i = 1;i <= n;i ++)for(j = 1;j <= m;j ++)scanf("%d",&mp[i][j]),dp[i][j][1][1] = mp[i][j];for(int ii = 1;ii <= n;ii ++)for(int jj = 1;jj <= m;jj ++){for(i = 1;i + ii <= n + 1;i ++){for(j = 1;j + jj <= 1 + m;j ++){dp[i][j][ii][jj] = dp[i][j][ii - 1][jj - 1] + dp[i + ii - 1][j][1][jj - 1] + dp[i][j + jj - 1][ii - 1][1] + dp[i + ii - 1][j + jj - 1][1][1];}}}init();int rownum = 1;for(k = 1;k <= min(n,m);k ++)//枚举边长{for(i = 1;i <= n - k + 1;i ++){for(j = 1;j <= m - k + 1;j ++){if(canfuck(i,j,k))fuckba(i,j,k,rownum);rownum ++;}}}for(i = 1;i <= n * m;i ++)if(s[i] == 0)l[r[i]] = l[i],r[l[i]] = r[i];
}
void fuck()
{
//    ans = M;TLE....
//    dfs(0);
//    printf("%d\n",ans);ans = 0;while(!dfs(0,ans ++));printf("%d\n",ans - 1);
}
int main()
{while(scanf("%d%d",&m,&n),(m + n)){build();fuck();}return 0;
}