poj1753 Flip Game

本文探讨了使用位运算和暴力搜索算法解决特定位操作谜题的过程,具体展示了如何通过枚举每个位状态并计算翻转次数来找出达到目标状态所需的最少步数。

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#include <iostream>
using namespace std;
int cs[16] = {0x13,0x27,78,140,305,626,1252,2248,4880,8992,20032,35968,12544,29184,58368,51200};
int po[16] = {1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768};
int main()
{
	int t=0;
	char tm;
	for(int i=0;i<16;i++)
	{
		cin>>tm;
		if(tm=='b') t+=po[i];
	}
	int res=17;
	for(int i=0;i<65536;i++)
	{
		int v=t;
		int cnt=0;
		for(int j=0;j<16;j++)
		{
			if(i&(int)po[j])
			{
				cnt++;
				v^=cs[j];
			}
		}
		if(v==0||v==65535)
		{
			if(res>cnt) res=cnt;
		}
	}
	if(res==17)
	{
		cout<<"Impossible";
	}
	else cout<<res;
	return 0;
}

位运算暴搜

Flip Game
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 33269 Accepted: 14547

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

bwwb
bbwb
bwwb
bwww

Sample Output

4

Source


题意是4*4的一个棋盘,每次可以翻转一个子,但是得翻转和他相邻的四个子。问最少的翻转可以使整个棋盘一个颜色是多少。


其中每个点如果翻转2次是没有用的,所以每个点最多就是翻转一次。那么可以枚举每个点是否翻转,而2^16大小的整数就可以代表所有的可能性,再记录一下分别翻转16个子的时候,翻转的子的数记录成一个整数。每次都16一次,如果答案是0或者2^16的话,记录每次最小的数就可以啦





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