八皇后问题一种求解思路

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#iostream #vc++

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//这个程序是用来求八皇后问题的所有解
//基本思路是当(i,j)位置被皇后占了的时候，i行，j列,和i+j,i-j相等的斜行也不能够被其他皇后占有

#include"stdio.h"
#include"stdlib.h"
#define SIZE  8
#define TOTALNUM 100

int row[ SIZE ] ;//记录行的数组
int col[ SIZE ] ;//记录列的数组
int titlr[2*SIZE-3];//记录斜行的数组
int titll[2*SIZE-3];//记录斜行左的数组
int totalway[8];//记录所有的解
int totalwayLen = 0 ;

void PrintWay()  //打印每一组解
{
    printf("The Number %2d of Way : ",totalwayLen ) ;
for ( int i = 0 ; i < SIZE ; i ++ )
  printf("%-2d",totalway[i]+1);
printf(" ");
}

void ReturnLast( int i )  //返回时将上一组还原
{

int temp = totalway[i-1];
row[i-1] = 0 ;
    col[temp] = 0 ;
    titlr[i-1-temp+6] = 0 ;
titll[i-1+temp-1] = 0 ;

}

void SeacherWay( int i ) //从何行开始搜索
{
     for ( int j = 0 ; j < SIZE ; j ++ )
  {
   if ( row[i] == 0 && col[j] == 0 && titlr[i-j+6] == 0 && titll[i+j-1] == 0 ) //当这个位置还是空闲的时候
   {
    totalway[i] = j ; //记录列的位置
    if ( i == SIZE - 1 )  //最后一组分配位置成功
    {
     totalwayLen ++ ;
     PrintWay();
                 ReturnLast(i);
                 return ;
    }
    row [i] = 1; //将占的位置恢复
    col [j] = 1;
    titlr[i-j+6] = 1;
    titll[i+j-1] = 1;
             SeacherWay(i+1);

   }

  }
  if ( j == SIZE )
  {
     ReturnLast(i);
  return ;
  }
}

int main()
{
      SeacherWay(0) ;
   printf("%d " ,totalwayLen ) ;
   return 0 ;
}

最近写的:

#include<iostream>
#include<cmath>
using namespace std;
#define SIZE 8

int queen[SIZE][SIZE],count = 0 ;

bool isCan(int nowrow ,int col)
{
    for ( int row = 0 ; row < nowrow ; row ++)
    {
        if ( queen[row][col] == 1)
        {
            return false;
        }
        for ( int i = 0 ; i < SIZE ; i ++)
        {
            bool flag = ((row + i == nowrow +col) || ( row - i == nowrow - col));
            if ( flag && queen[row][i] == 1)
            {
                return false;
            }
        }
    }
    return true ;
}

void eightQueen(int n)
{
    if ( n == 0)
    {
        for ( int i = 0 ; i < SIZE ; i ++ )
        {
            for ( int j = 0 ; j < SIZE ; j++ )
            {
                if ( queen[i][j] == 1)
                    cout<<j;
            }

        }
        cout<<endl;
        count ++ ;
        return ;
    }
    else
    {
        int row = SIZE - n ;
        for ( int col = 0 ; col < SIZE ; col ++ )
        {
            if(isCan(row,col))
            {
                queen[row][col] = 1 ;
                eightQueen(n-1);
                queen[row][col] = 0 ;
            }
        }
    }
}

int main()
{
    eightQueen(8);
    cout<<"count:"<<count<<endl;
    return 0 ;
}

在vc++中运行结果为(共有92组解):

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