Flip Game

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 24957		Accepted: 10755

Description

Flip game is played on a rectangular 4x4 field with two-sided pieces placed on each of its 16 squares. One side of each piece is white and the other one is black and each piece is lying either it's black or white side up. Each round you flip 3 to 5 pieces, thus changing the color of their upper side from black to white and vice versa. The pieces to be flipped are chosen every round according to the following rules:

1. Choose any one of the 16 pieces.
2. Flip the chosen piece and also all adjacent pieces to the left, to the right, to the top, and to the bottom of the chosen piece (if there are any).

Consider the following position as an example:

bwbw

wwww

bbwb

bwwb

Here "b" denotes pieces lying their black side up and "w" denotes pieces lying their white side up. If we choose to flip the 1st piece from the 3rd row (this choice is shown at the picture), then the field will become:

bwbw

bwww

wwwb

wwwb

The goal of the game is to flip either all pieces white side up or all pieces black side up. You are to write a program that will search for the minimum number of rounds needed to achieve this goal.

Input

The input consists of 4 lines with 4 characters "w" or "b" each that denote game field position.

Output

Write to the output file a single integer number - the minimum number of rounds needed to achieve the goal of the game from the given position. If the goal is initially achieved, then write 0. If it's impossible to achieve the goal, then write the word "Impossible" (without quotes).

Sample Input

bwwbbbwbbwwbbwww

Sample Output

4

Source

开始时直接枚举16种状态，用的bfs不过超时了，后来看了一下网上的思路，大多是bfs加位运算，不过表示不怎么懂位运算，

试着用dfs也没搞出来，看了一下别人的代码，表示很神奇的说

 

1 #include
       
         2 char map[4][4]; 3 int vis[4][4]; 4 int step,flag; 5 int judge() 6 { 7      int i,j; 8      for(i=0;i<4;i++) 9        for(j=0;j<4;j++)10          if(vis[i][j]!=vis[0][0])11          return 0;12 13          return 1;14 }15 void turn(int i,int j)16 {17      vis[i][j]=!vis[i][j];18      if(i>0) vis[i-1][j]=!vis[i-1][j];19      if(i<3)  vis[i+1][j]=!vis[i+1][j];20      if(j>0)  vis[i][j-1]=!vis[i][j-1];21      if(j<3)  vis[i][j+1]=!vis[i][j+1];22 }23 void dfs(int i,int j,int step1)24 {25 26      if(step==step1)27      {28           if(judge())29           flag=1;30 31           return ;32      }33      if(flag ||i==4)  return ;34      turn(i,j);35      if(j<3)36      dfs(i,j+1,step1+1);37      else38      dfs(i+1,0,step1+1);39      turn(i,j);40           if(j<3)41      dfs(i,j+1,step1);42      else43      dfs(i+1,0,step1);44      return ;45 }46 int main()47 {48      int i,j;49      for(i=0;i<4;i++)50      scanf("%s",map[i]);51      for(i=0;i<4;i++)52      {53           for(j=0;j<4;j++)54           {55                if(map[i][j]=='b')56           vis[i][j]=1;57           else58           vis[i][j]=0;59 60           }61 62      }63      flag=0;64      for(step=0;step<=16;step++)65      {66           dfs(0,0,0);67           if(flag)68           break;69      }70      if(flag)71      printf("%d\n",step);72      else73      printf("Impossible\n");74      return 0;75 }