[题解] luogu P1985 [USACO07OPEN]翻转棋

题面
今天学搜索，正好水一发以前做的这道毒瘤题

话说这道题做了我一天，别人都是各种优化，不超100行

天真的我硬核刚了220行，全程0优化水过

但其实不用这么长，我有的函数写的有点重复了（

思路：

显然是dfs，一行一行的来

搜到[i, j]时(i > 1)，看[i - 1, j]是否为黑，是的话就翻转[i, j],

也就是说搜完当前行就要保证上一行的棋全都翻成了白色

当搜到最后一行时，

既要保证上一行翻成白色，还要保证自己也都翻成白色，

最后还要特判一下最后两个的翻转.

当时年少轻狂，我想着层次一定要清晰，
于是就SB地分别打了四个函数：

1. 特判第一行,firstLineS
2. 当只有一列的时候,dfs1
3. 当搜到最后一行时或本来只有一行时，dfsn
4. 正常搜索,dfs

这个题有个坑，92分卡了一下午: 搜到的第一个解不能直接输出，它是最优解，但不一定是字典序最小的，所以继续搜完

[collapse title="Code" status="false"]

#include <bits/stdc++.h>

using namespace std;

int n, m, a, minans = 99999;
int Chess[25][25], ans[25][25], minan[25][25];

void c(int i, int j) 
{
	if(Chess[i][j]%2 == 0) Chess[i][j] = 1;
	else Chess[i][j] = 0;
}
void print() 
{
	a = 0;
	for (int i = 1; i <= m; i++)
		for (int j = 1; j <= n; j++)
			if (Chess[i][j] % 2 == 1) return ;
	for (int i = 1; i <= m; i++)
		for (int j = 1; j <= n; j++)
			a += ans[i][j] % 2;
	if(minans > a) 
    {
	    minans = a;
	    for (int i = 1; i <= m; i++)
			for (int j = 1; j <= n; j++)
				minan[i][j] = ans[i][j] % 2;
	}
}
int back1(int p) 
{
	if ( Chess[m][p] == 1 && p == n)
		return 1;
	else if (p != n)
		return 1;
	return 0;
}
int back2(int p) 
{
	if ( Chess[m][p] == 0 && p == n)
		return 0;
	else if (p != n)
		return 0;
	return 1;
}
void dfsn(int num) {	
    if (num == n + 1) {
		print();
		return ;
    }
    int line = m;
    if (m == 1)
    {
    	if (num == 1)
    	{
			dfsn(num + 1);    
		    c(line, num + 1);
		    c(line, num);
		    ans[line][num]++;
			dfsn(num + 1);
		}
		if (Chess[line][num - 1]==0 && back2(num)==0)
			dfsn(num+1);
		else if (Chess[line][num - 1]==1 && back1(num)==1)
    	{
			c(line, num - 1);
			c(line, num + 1);
			c(line, num);
			ans[line][num]++;
		
			dfsn(num + 1);
		}
	}
	else if (num == 1)
	{
		if (Chess[m - 1][1] == 0)
	    	dfsn(2);	
    
		else 
		{
	    	c(m - 1 , 1);
			c(m, 2);
			c(m, 1);
			ans[m][1]++;
		
			dfsn(2);
		}
	}
	
    else if (Chess[line - 1][num]==1 && Chess[line][num - 1]==1 && back1(num)==1)
	{
	    c(line - 1 , num);
		c(line, num - 1);
		c(line, num + 1);
		c(line, num);
		ans[line][num]++;
		
		dfsn(num + 1);
		/*	
		ans[line][num]--;
		c(line - 1, num);
		c(line, num - 1);
		c(line, num + 1);
		c(line, num);
		*/
	}
    else if (Chess[line - 1][num] == 0 && Chess[line - 1][num] == 0 && back2(num) == 0)
	    dfsn(num + 1);
}
void dfs(int line, int num)
{
	if (num == n + 1 && line == m - 1)
	{
		dfsn(1);
		return ;
	}
	if (num == n + 1)
	{
		dfs(line + 1, 1);
		return ;
	}
	if (Chess[line - 1][num] == 0)
		dfs(line, num + 1);
	else
	{
	    c(line - 1, num);
		c(line + 1, num);
		c(line, num - 1);
		c(line, num + 1);
		c(line, num);
		ans[line][num]++;
		dfs(line, num + 1);
 /*
		ans[line][num]--;		
		c(line - 1, num);
		c(line + 1, num);
		c(line, num - 1);
		c(line, num + 1);
		c(line, num);
*/
	}
}
void firstLineS(int k)
{
	if (k == n + 1) 
	{
		if (m > 2)
	    	dfs(2, 1);
		else if (m == 2)
			dfsn(1);
	    return ;
    } 
	firstLineS(k + 1);
	c(1, k);
	c(1, k - 1);
	c(1, k + 1);
	c(2, k);
    ans[1][k]++;
	firstLineS(k + 1);
	ans[1][k]--;
    c(1, k);
    c(1, k - 1);
	c(1, k + 1);
	c(2, k);
}
void dfs1(int num)
{
    if (num == m + 1) 
    {
    	print();
    	return ;
	}
	if (num == 1)
	{
		dfs1(num + 1);
		ans[num][1]++;
		c(num, 1);
		c(num + 1, 1);
		dfs1(num + 1);
		ans[num][1]--;
		c(num, 1);
		c(num + 1, 1);
	}
	if(Chess[num - 1][1] == 0)
	    dfs1(num + 1);
	else  {
		ans[num][1]++;
		c(num, 1);
		c(num + 1, 1);
		c(num - 1, 1);
		
		dfs1(num + 1); 
		
		ans[num][1]--;
		c(num + 1, 1);
		c(num - 1, 1);
		c(num, 1);
	}
}

int main()   
{
	cin >> m>> n;
    for (int i = 1; i <= m; i++)
    	for (int j = 1; j <= n; j++)
    	    cin >> Chess[i][j];
    if (m == 1) dfsn(1);
    if (n == 1) dfs1(1);
    firstLineS(1);
    if (minans==99999)
    	cout<<"IMPOSSIBLE"<<endl;
    else
        for (int i = 1; i <= m; i++)
		{	
			for (int j = 1; j <= n; j++)
				cout << minan[i][j]%2<<" ";
			cout << endl;
		}
	return 0;
}

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