Flip Game dfs

本文介绍了一种在4x4棋盘上进行的名为Flipgame的游戏的解决方案。玩家需要翻转选定及其相邻的棋子,目标是使所有棋子颜色一致。文章提供了详细的算法思路及C++实现代码。

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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
bwwb
bbwb
bwwb
bwww
Sample Output
4


解题报告


不要想太复杂就好,要明确如果有答案,那么答案小于等于8

#include<stdio.h>
#include<string.h>
bool map[6][6];
int ox[]={0,0,0,1,-1};
int oy[]={0,1,-1,0,0};
int best;

bool check(){
    //end check
    for(int j=1;j<=4;j++)
        for(int k=1;k<=4;k++)
            if(map[1][1]!=map[j][k])
                return false;
    return true;
}

void op(int X,int Y){
    for(int i=0;i<5;i++){
        int x=X+ox[i];
        int y=Y+oy[i];
        map[x][y]=!map[x][y];
    }
}

void dfs(int t,int cnt){
    if(check()){
        if(cnt<best) best=cnt;
        return ;
    }
    if(cnt>best||t>16) return ;

    int X=t%4+1;
    int Y=t/4+1;

    //剪枝 加上该条件 78ms立马变0ms
    if(Y>1&&X>1&&map[X-1][Y-1]!=map[1][1]) return ;

    dfs(t+1,cnt);

    op(X,Y);
    dfs(t+1,cnt+1);
    op(X,Y);
}

int main()
{
    char str[5];
    for(int i=1;i<=4;i++){
        scanf("%s",str);
        for(int j=1;j<=4;j++)
            map[i][j]=str[j-1]=='b';
    }
    best=9;
    dfs(0,0);
    if(best<9) printf("%d\n",best);
    else puts("Impossible");
    return 0;
}



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