Aizu - ALDS1_13_A 8 Queens Problem (八皇后问题入门 DFS)

The goal of 8 Queens Problem is to put eight queens on a chess-board such that none of them threatens any of others. A queen threatens the squares in the same row, in the same column, or on the same diagonals as shown in the following figure.

For a given chess board where kk queens are already placed, find the solution of the 8 queens problem.

Input

In the first line, an integer kk is given. In the following kk lines, each square where a queen is already placed is given by two integers rr and cc. rr and ccrespectively denotes the row number and the column number. The row/column numbers start with 0.

Output

Print a 8×88×8 chess board by strings where a square with a queen is represented by 'Q' and an empty square is represented by '.'.

Constraints

• There is exactly one solution

Sample Input 1

2
2 2
5 3

Sample Output 1

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...

题意:八皇后问题即是在8*8的格子里放置8个皇后，要求任意两个皇后之间不能在同一行、同一列、或是同一对角线上，也即是八个方向。（题中给出了图帮助理解）

解题思路：

可以有规律的搜索，康托展开也可以写

弱智的我只能无脑的DFS。。

AC代码：

#include
#include

int mp[10][10],book[10][10],n,flag,a[10];

int check(int x,int y)
{
	for(int i=0;i<8;i++)//左右 
	{
		if(book[x][i]==1) return 0;
	}
	for(int i=0;i<8;i++)//上下 
	{
		if(book[i][y]==1) return 0;
	}
	for(int i=x,j=y;i>=0&&j>=0;i--,j--)//左上 
	{
		if(book[i][j]==1) return 0;
	}
	for(int i=x,j=y;i<8&&j<8;i++,j++)//右下 
	{
		if(book[i][j]==1) return 0;
	}
	for(int i=x,j=y;i<8&&j>=0;i++,j--)//左下 
	{
		if(book[i][j]==1) return 0;
	}
	for(int i=x,j=y;i>=0&&j<8;i--,j++)//右上 
	{
		if(book[i][j]==1) return 0;
	}
	return 1;
}

void dfs(int x,int cnt)
{
	if(cnt>=8-n)
	{
		flag=1;
		return;
	}
	if(x>8) return;
	for(int i=0;i<8;i++)
	{
		if(a[x]==1)
		{
			dfs(x+1,cnt);
			if(flag) return;
		}

		if(book[x][i]==0&&check(x,i)==1)
		{
			book[x][i]=1;
			mp[x][i]=1;
			dfs(x+1,cnt+1);
			if(flag) return;
			book[x][i]=0;
			mp[x][i]=0;
		}
	}
	
}

int main()
{
	while(~scanf("%d",&n))
	{
		memset(mp,0,sizeof(mp));
		memset(book,0,sizeof(book));
		memset(a,0,sizeof(a));
		flag=0;
		int x,y;
		for(int i=0;i