八皇后问题 回溯法

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Demo
{
    class Program
    {
        static int num = 8;/*可以随意修改，num是多少解的就是几皇后问题*/
        static int[] arr = new int[8];
        static int count = 0;
        static void display()/*一个简单的数组输出函数，顺便统计解的个数*/
        {
            for (int i = 0; i < num; ++i)
            {
                for (int j = 0; j < num; j++)
                {
                    if (arr[i] == j)
                        Console.Write("Q");
                    else
                        Console.Write("*");
                }

                Console.WriteLine(" ");
            }
            count++;
            Console.WriteLine("-------------" + count.ToString() + "--------------------");
        }

        static void queens(int pos = 0)
        {
            /*同在斜线或者直线上*/
            for (int i = 0; i < pos-1; ++i)
             {
                int off = arr[i] - arr[pos - 1];
                if (off == 0 || off == pos - 1 - i || -off == pos - 1 - i)
                    return;
            }

            /*符合条件就输出*/
            if (pos == num)
            { 
                display(); 
                return; 
            }

            /*递归搜索解空间*/
            for (int k = 0; k < num; ++k)
            {
                arr[pos] = k;
                queens(pos + 1);
            }
        }

        static void Main(string[] args)
        {
            queens(0);

            Console.ReadKey();

        }
    }
}