The question ： There are four ways to flip , Ask if you can make all the pieces into 0, Find the minimum number of steps .

Answer key ： Construct enumeration in turn to get the minimum value .

#include <iostream>

#include <cstdio>

#include <cmath>

#include <cstring>

#include <algorithm>

#include <queue>

#include <vector>

#include <map>

#include <ctime>

using namespace std;

const int inf=0x3f3f3f;

const int maxn=;

// Yes equ An equation ,var Variables . The number of rows of the augmented matrix is equ, The number of columns is var+1, Respectively 0 To var

int equ,var;

int a[maxn][maxn]; // Augmented matrix

int x[maxn]; // Solution set

int free_x[maxn];// To store free variables （ Multi solution enumeration of free variables can be used ）

int free_num;// The number of free variables

// The return value is -1 There is no solution , by 0 It's the only solution , Otherwise, the number of free variables is returned

int gauss()

{

int max_r,col,k;

free_num=;

for(k=,col=; k<equ&&col<var; k++,col++)

{

max_r=k;

for(int i=k+; i<equ; i++)

if(abs(a[i][col])>abs(a[max_r][col]))

max_r=i;

if(!a[max_r][col])

{

k--;

free_x[free_num++]=col;

continue;

}

if(max_r!=k)

for(int j=col; j<var+; j++)

swap(a[k][j],a[max_r][j]);

for(int i=k+; i<equ; i++)

{

if(a[i][col])

{

for(int j=col; j<var+; j++)

a[i][j]^=a[k][j];

}

}

}

for(int i=k; i<equ; i++)

if(a[i][col])

return -;

if(k<var) return var-k;

for(int i=var-; i>=; i--)

{

x[i]=a[i][var];

for(int j=i+; j<var; j++)

x[i]^=(a[i][j]&&x[j]);

}

return ;

}

int n,m;

// Be sure to distinguish the bottom left from the top right ！！！

void init1()

{

memset(a,,sizeof(a));

memset(x,,sizeof(x));

equ=n*m;

var=n*m;

for(int i=; i<n; i++)

for(int j=; j<m; j++)

{

int t=i*m+j;

a[t][t]=;

if(i>) a[(i-)*m+j][t]=; // On

if(i<(n-)) a[(i+)*m+j][t]=; // Next

if(j>) a[i*m+j-][t]=; // Left

if(j<(m-)) a[i*m+j+][t]=; // Right

}

}

void init2()

{

memset(a,,sizeof(a));

memset(x,,sizeof(x));

equ=n*m;

var=n*m;

for(int i=; i<n; i++)

for(int j=; j<m; j++)

{

int t=i*m+j;

a[t][t]=;

if(i>) a[(i-)*m+j][t]=; // On

//if(i<n-1) a[(i+1)*m+j][t]=1; // Next

if(j>) a[i*m+j-][t]=; // Left

if(j<(m-)) a[i*m+j+][t]=; // Right

if(i>&&j>) a[(i-)*m+j-][t]=; // Top left

//if(i>0&&j<(m-1)) a[(i-1)*m+j+1][t]=1; // The upper right

if(i<n-&&j>) a[(i+)*m+j-][t]=; // The lower left

//if(i<n-1&&j<m-1) a[(i+1)*m+j+1][t]=1; // The lower right

}

}

void init3()

{

memset(a,,sizeof(a));

memset(x,,sizeof(x));

equ=n*m;

var=n*m;

for(int i=; i<n; i++)

for(int j=; j<m; j++)

{

int t=i*m+j;

a[t][t]=;

if(i>) a[(i-)*m+j][t]=; // On

if(i<(n-)) a[(i+)*m+j][t]=; // Next

if(j>) a[i*m+j-][t]=; // Left

if(j<(m-)) a[i*m+j+][t]=; // Right

//if(i>0&&j>0) a[(i-1)*m+j-1][t]=1; // Top left

if(i>&&j<m-) a[(i-)*m+j+][t]=; // The upper right

//if(i<(n-1)&&j>0) a[(i+1)*m+j-1][t]=1; // The lower left

//if(i<n-1&&j<m-1) a[(i+1)*m+j+1][t]=1; // The lower right

}

}

void init4()

{

memset(a,,sizeof(a));

memset(x,,sizeof(x));

equ=n*m;

var=n*m;

for(int i=; i<n; i++)

for(int j=; j<m; j++)

{

int t=i*m+j;

a[t][t]=;

if(i>) a[(i-)*m+j][t]=; // On

if(i<(n-)) a[(i+)*m+j][t]=; // Next

if(j>) a[i*m+j-][t]=; // Left

//if(j<m-1) a[i*m+j+1][t]=1; // Right

//if(i>0&&j>0) a[(i-1)*m+j-1][t]=1; // Top left

if(i>&&j<m-) a[(i-)*m+j+][t]=; // The upper right

//if(i<(n-1)&&j>0) a[(i+1)*m+j-1][t]=1; // The lower left

if(i<(n-)&&j<(m-)) a[(i+)*m+j+][t]=; // The lower right

}

}

int solve()

{

int t=gauss();

if(t==-)

{

return inf;

}

else if(t==)

{

int ans=;

for(int i=; i<n*m; i++)

ans+=x[i];

return ans;

}

else

{

// Enumerate free variables

int ans=0x3f3f3f3f;

int tot=(<<t);

for(int i=; i<tot; i++)

{

int cnt=;

for(int j=; j<t; j++)

{

if(i&(<<j)) // Notice that it's not &&

{

x[free_x[j]]=;

cnt++;

}

else x[free_x[j]]=;

}

for(int j=var-t-; j>=; j--)

{

int idx;

for(idx=j; idx<var; idx++)

if(a[j][idx])

break;

x[idx]=a[j][var];

for(int l=idx+; l<var; l++)

if(a[j][l])

x[idx]^=x[l];

cnt+=x[idx];

}

ans=min(ans,cnt);

}

return ans;

}

}

char data[][];

int main()

{

while(scanf("%d%d",&n,&m)&&n&&m)

{

//getchar();

for(int i=; i<n; i++)

cin>>data[i]; init1();

for(int i=; i<n; i++)

for(int j=; j<m; j++)

if(data[i][j]=='') a[i*m+j][n*m]=;

int ans1=solve(); init2();

for(int i=; i<n; i++)

for(int j=; j<m; j++)

if(data[i][j]=='') a[i*m+j][n*m]=;

int ans2=solve(); init3();

for(int i=; i<n; i++)

for(int j=; j<m; j++)

if(data[i][j]=='') a[i*m+j][n*m]=;

int ans3=solve(); init4();

for(int i=; i<n; i++)

for(int j=; j<m; j++)

if(data[i][j]=='') a[i*m+j][n*m]=;

int ans4=solve(); int ans=min(min(ans1,ans2),min(ans3,ans4));

if(ans==inf) puts("Impossible");

else

{

if(ans==ans1) printf("1 %d\n",ans);

else if(ans==ans2) printf("2 %d\n",ans);

else if(ans==ans3) printf("3 %d\n",ans);

else if(ans==ans4) printf("4 %d\n",ans);

}

}

return ;

}

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