Flip Game

Flip Game 原题：

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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.

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我的理解：

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Flip游戏规则：16个硬币，每个有两种颜色（白w和黑b），翻转任何一个硬币，其周围相邻的其它硬币也要翻转。

要求：最少的翻转次数，使得16个硬币变为同一种颜色。

输入：4X4的矩阵，b代表黑色，w代表白色。

        bwwb
        bbwb
        bwwb
        bwww

输出：最少的翻转次数。

       4

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AC代码：

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  // Flip Game ：枚举 +　位运算 + DFS #include #include using std::cout; using std::cin; using std::endl; using std::bitset; // 翻转第i个棋子，所影响的位，即当前棋盘 ^ round[i]; long round[16] = {0xC800, 0xE400, 0x7200, 0x3100, 0x8C80, 0x4E40, 0x2720, 0x1310, 0x08C8, 0x04E4, 0x0272, 0x0131, 0x008C, 0x004E, 0x0027, 0x0013}; const long ALL_WHITE = 0x0; const long ALL_BLACK = 0xFFFF; int step = 16; // 输入并转换 long Input() { bitset<16> current; for (int i = 0; i < 16;) { char c = cin.get(); if (c == '/n') continue; current.set(i, (c == 'w' ? 0 : 1)); ++i; } return current.to_ulong(); } void Flip(long current, int flip, int deep) { if (deep >= 16) { if (current == ALL_WHITE || current == ALL_BLACK) if (flip < step) step = flip; return; } Flip(current ^ round[deep], flip + 1, deep + 1); Flip(current, flip, deep + 1); } int main() { Flip(Input(), 0, 0); if (step == 16) cout << "Impossible" << endl; else cout << step << endl; }

 

 

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