n-皇后问题的实现

最近在学习C语言，随便编写实现了一个8-皇后问题，同时他程序也可以扩展为N-皇后问题.

8-皇后问题描述：八皇后问题是一个古老而著名的问题，是回溯算法的典型例题。该问题是十九世纪著名的数学家高斯1850年提出：在8X8格的国际象棋上摆放八个皇后，使其不能互相攻，即任意两个皇后都不能处于同一行、同一列或同一斜线上，问有多少种摆法。高斯认为有76种方案。1854年在柏林的象棋杂志上不同的作者发表了40种不同的解，后来有人用图论的方法解出92种结果。

源代码：

#include <stdio.h>
#include <math.h>
#define N 8
int X[N];
int NUM=0;
int main()
{
 void print();
 int canPlace(int);
 int i;
 int k = 0;
 X[0] = -1;
 while(k>=0)
 {
  X[k] = X[k]+1;
  while(X[k] < N && !canPlace(k))
   X[k] = X[k]+1;
  if(X[k] < N)//找到位置
  {
   if(k==N-1)//是否为完整的解
    print();
   else
   {
    k++;
    X[k] = -1;
   }
  }
  else
   k--;
 }
 return 0;
}

void print()
{
 int i;
 NUM++;
 printf("the %dth answer is :",NUM);
 for(i=0;i<N;i++)
 {
  printf("%d ",X[i]);
 }
 printf("\n");
}

int canPlace(int k)
{
 int i;
 for(i=0;i<k;i++)
 {
  if(X[k] == X[i] || abs(i-k) == abs(X[k]-X[i]))
   break;
 }
 if(i >= k)
  return 1;
 else
  return 0;
}
结果：

the 1th answer is :0 4 7 5 2 6 1 3
the 2th answer is :0 5 7 2 6 3 1 4
the 3th answer is :0 6 3 5 7 1 4 2
the 4th answer is :0 6 4 7 1 3 5 2
the 5th answer is :1 3 5 7 2 0 6 4
the 6th answer is :1 4 6 0 2 7 5 3
the 7th answer is :1 4 6 3 0 7 5 2
the 8th answer is :1 5 0 6 3 7 2 4
the 9th answer is :1 5 7 2 0 3 6 4
the 10th answer is :1 6 2 5 7 4 0 3
the 11th answer is :1 6 4 7 0 3 5 2
the 12th answer is :1 7 5 0 2 4 6 3
the 13th answer is :2 0 6 4 7 1 3 5
the 14th answer is :2 4 1 7 0 6 3 5
the 15th answer is :2 4 1 7 5 3 6 0
the 16th answer is :2 4 6 0 3 1 7 5
the 17th answer is :2 4 7 3 0 6 1 5
the 18th answer is :2 5 1 4 7 0 6 3
the 19th answer is :2 5 1 6 0 3 7 4
the 20th answer is :2 5 1 6 4 0 7 3
the 21th answer is :2 5 3 0 7 4 6 1
the 22th answer is :2 5 3 1 7 4 6 0
the 23th answer is :2 5 7 0 3 6 4 1
the 24th answer is :2 5 7 0 4 6 1 3
the 25th answer is :2 5 7 1 3 0 6 4
the 26th answer is :2 6 1 7 4 0 3 5
the 27th answer is :2 6 1 7 5 3 0 4
the 28th answer is :2 7 3 6 0 5 1 4
the 29th answer is :3 0 4 7 1 6 2 5
the 30th answer is :3 0 4 7 5 2 6 1
the 31th answer is :3 1 4 7 5 0 2 6
the 32th answer is :3 1 6 2 5 7 0 4
the 33th answer is :3 1 6 2 5 7 4 0
the 34th answer is :3 1 6 4 0 7 5 2
the 35th answer is :3 1 7 4 6 0 2 5
the 36th answer is :3 1 7 5 0 2 4 6
the 37th answer is :3 5 0 4 1 7 2 6
the 38th answer is :3 5 7 1 6 0 2 4
the 39th answer is :3 5 7 2 0 6 4 1
the 40th answer is :3 6 0 7 4 1 5 2
the 41th answer is :3 6 2 7 1 4 0 5
the 42th answer is :3 6 4 1 5 0 2 7
the 43th answer is :3 6 4 2 0 5 7 1
the 44th answer is :3 7 0 2 5 1 6 4
the 45th answer is :3 7 0 4 6 1 5 2
the 46th answer is :3 7 4 2 0 6 1 5
the 47th answer is :4 0 3 5 7 1 6 2
the 48th answer is :4 0 7 3 1 6 2 5
the 49th answer is :4 0 7 5 2 6 1 3
the 50th answer is :4 1 3 5 7 2 0 6
the 51th answer is :4 1 3 6 2 7 5 0
the 52th answer is :4 1 5 0 6 3 7 2
the 53th answer is :4 1 7 0 3 6 2 5
the 54th answer is :4 2 0 5 7 1 3 6
the 55th answer is :4 2 0 6 1 7 5 3
the 56th answer is :4 2 7 3 6 0 5 1
the 57th answer is :4 6 0 2 7 5 3 1
the 58th answer is :4 6 0 3 1 7 5 2
the 59th answer is :4 6 1 3 7 0 2 5
the 60th answer is :4 6 1 5 2 0 3 7
the 61th answer is :4 6 1 5 2 0 7 3
the 62th answer is :4 6 3 0 2 7 5 1
the 63th answer is :4 7 3 0 2 5 1 6
the 64th answer is :4 7 3 0 6 1 5 2
the 65th answer is :5 0 4 1 7 2 6 3
the 66th answer is :5 1 6 0 2 4 7 3
the 67th answer is :5 1 6 0 3 7 4 2
the 68th answer is :5 2 0 6 4 7 1 3
the 69th answer is :5 2 0 7 3 1 6 4
the 70th answer is :5 2 0 7 4 1 3 6
the 71th answer is :5 2 4 6 0 3 1 7
the 72th answer is :5 2 4 7 0 3 1 6
the 73th answer is :5 2 6 1 3 7 0 4
the 74th answer is :5 2 6 1 7 4 0 3
the 75th answer is :5 2 6 3 0 7 1 4
the 76th answer is :5 3 0 4 7 1 6 2
the 77th answer is :5 3 1 7 4 6 0 2
the 78th answer is :5 3 6 0 2 4 1 7
the 79th answer is :5 3 6 0 7 1 4 2
the 80th answer is :5 7 1 3 0 6 4 2
the 81th answer is :6 0 2 7 5 3 1 4
the 82th answer is :6 1 3 0 7 4 2 5
the 83th answer is :6 1 5 2 0 3 7 4
the 84th answer is :6 2 0 5 7 4 1 3
the 85th answer is :6 2 7 1 4 0 5 3
the 86th answer is :6 3 1 4 7 0 2 5
the 87th answer is :6 3 1 7 5 0 2 4
the 88th answer is :6 4 2 0 5 7 1 3
the 89th answer is :7 1 3 0 6 4 2 5
the 90th answer is :7 1 4 2 0 6 3 5
the 91th answer is :7 2 0 5 1 4 6 3
the 92th answer is :7 3 0 2 5 1 6 4