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