D - Fliptile

POJ - 3279

Farmer John knows that an intellectually satisfied cow is a happy cow who will give more milk. He has arranged a brainy activity for cows in which they manipulate an M × N grid (1 ≤ M ≤ 15; 1 ≤ N ≤ 15) of square tiles, each of which is colored black on one side and white on the other side.

As one would guess, when a single white tile is flipped, it changes to black; when a single black tile is flipped, it changes to white. The cows are rewarded when they flip the tiles so that each tile has the white side face up. However, the cows have rather large hooves and when they try to flip a certain tile, they also flip all the adjacent tiles (tiles that share a full edge with the flipped tile). Since the flips are tiring, the cows want to minimize the number of flips they have to make.

Help the cows determine the minimum number of flips required, and the locations to flip to achieve that minimum. If there are multiple ways to achieve the task with the minimum amount of flips, return the one with the least lexicographical ordering in the output when considered as a string. If the task is impossible, print one line with the word "IMPOSSIBLE".

Input

Line 1: Two space-separated integers: M and N
Lines 2.. M+1: Line i+1 describes the colors (left to right) of row i of the grid with N space-separated integers which are 1 for black and 0 for white

Output

Lines 1.. M: Each line contains N space-separated integers, each specifying how many times to flip that particular location.

Sample Input

4 4
1 0 0 1
0 1 1 0
0 1 1 0
1 0 0 1

AC代码

#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<string>
#include<cstdio>
#include<cstring>
#include<sstream>
#include<cstdlib>
#include<cstring>
#include<sstream>
#include<iostream>
#include<algorithm>

using namespace std;
const int maxn = 20;
const int INF = 0x3f3f3f3f;
const int mod = 7;
typedef long long ll;
#define PI 3.1415927

int ans;
int n, m;
int mp[maxn][maxn];
int opt[maxn][maxn];
int flip[maxn][maxn];
int dir[5][2]={{1,0},{-1,0},{0,0},{0,-1},{0,1}};

bool judge(int x, int y)//判断该点是否为空白
{
    int c = mp[x][y];
    for(int i=0;i<5;++i)
	{
		int x2=x+dir[i][0],y2=y+dir[i][1];
		if(0<=x2&&x2<n&&0<=y2&&y2<m)
			c+=flip[x2][y2];
	}
	return c%2;
}
int calc()//根据确定的第一行向下递推
{
    int res;
    for(int i = 1; i < n; ++i)
    {
        for(int j = 0; j < m; ++j)
        {
            if(judge(i-1, j))
                flip[i][j] = 1;
        }
    }
    for(int i = 0; i < m; ++i)//判断最后一行是否全为空白
    {
        if(judge(n-1, i))
            return -1;
    }
    res = 0;
    for(int i = 0; i < n; ++i)//对该答案进行计数
    {
        for(int j = 0;j < m; ++j)
        {
            res += flip[i][j];
        }
    }
    return res;
}
int main()
{
    scanf("%d%d", &n, &m);
    for(int i = 0; i < n; ++i)
    {
        for(int j = 0; j < m; ++j)
        {
            scanf("%d", &mp[i][j]);
        }
    }
    ans = -1;
    for(int i = 0; i < 1<<m; ++i)//按照字典序遍历第一行后进行搜索
    {
        memset(flip, 0, sizeof(flip));
        for(int j = 0; j < m; ++j)//给临时变量按字典序赋值
            flip[0][m-j-1]=i>>j&1;
        int num=calc();
        if(num>=0&&(ans<0||ans>num))
        {
            ans = num;
            memcpy(opt, flip, sizeof(flip));
        }

    }
    if(ans == -1) printf("IMPOSSIBLE\n");
    else
    {
        for(int i = 0; i < n; ++i)
        {
            for(int j = 0; j < m; ++j)
            {
                if(j==m-1)
                    printf("%d\n",opt[i][j]);
                else
                    printf("%d ",opt[i][j]);
            }
        }
    }
    return 0;
}