算法设计与分析--N皇后问题实现程…

 

 

#include

#include

#include

#include

#include

 

//定义常量

const int MAXSIZE=100;

 

//第一全局变量

int queen_count=0;                             //记录皇后的个数

int solut_count=0;                               //记录求解个数

int queen_position[MAXSIZE];          //记录皇后在各列上的位置

 

//输出所求解图形

void output()

{

         int row,col,n;

         cout<<"第 "<<++solut_count<<" 种解法:";

         for(row=0; row

                   cout<<" "<<queen_position[row];

         cout<<"\n\n\t\t图示如下: "<<endl;

         for(row=0; row

         {

                   for(col=0; col

                   {

                            n = queen_position[col];

                            if(row==n-1)

                                     cout<<"☆"<<" ";

                            else

                                     cout<<"■"<<" ";

                   }

                   cout<<endl;

         }

         cout<<"\n\t\t请按任意键继续。。。"<<endl;

         getch();

         system("cls");

}

 

//判断当前皇后所放位置正确与否

bool judge_queen(int n)

{

         for(int i=0; i

         {

                   if(queen_position[i]==queen_position[n])                 

                            return false;                                 //同列返回false

                   if(fabs(queen_position[n]-queen_position[i])==fabs(n-i))                            //fabs()

                            return false;                                 //同一对角线上返回false

         }

         return true;

}

 

//递归求解n皇后问题

void queen(int n)                                                                                                   //n表示放置第n个皇后

{

         int row;

 

         if(n==queen_count)

         {

                   output();

                   return;

         }

 

         for(row=1; row<=queen_count;row++)                                                 //核心代码部分

         {

                   queen_position[n]=row;                                                                   //试探第n行皇后的正确位置

                   if(judge_queen(n))

                            queen(n+1);

         }

}

 

////////////////////////////////////////////////////////////////

int main()                                               //主函数入口

{

         cout<<"请输入皇后的个数: ";

         cin>>queen_count;

         queen(0);                                                                                                                                   //从0开始试探

         cout<<queen_count<<"皇后问题解法共有: "<<solut_count<<endl;

         cout<<"\n\n\t\t请按任意键继续。。。"<<endl;

         system("pause");

         return 0;

}