回溯发实验

#include<iostream>
#include<cmath>
#include <ctime>
#include<vector>
#include<stack>
#include<iomanip>
using namespace std;
#define INF 0x7fffffff

struct point
{
    int x,y;
}p[40];

int n;             //TSP点数
double d[40][40];  //点的距离
double Min;        //最优解
double cur;        //当前值
int path[40];   //结果路径
int a[40];         //过程路径

//////////////////////////////////////////////////
//随机生成TSP的点并求出之间的距离

void init()
{
    srand(time(NULL));
    memset(d,0,sizeof(d));
    int i,j;
    int x,y;

    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n;j++)
            d[i][j] = INF;
        a[i] = i;
    }

    Min = INF;
    cur = 0.0;

    i = 1;
    while(1)
    {
        if( i == n+1 ) break;
        x = rand()%500;
        y = rand()%500;
        int flag = 0;

        for( j = 1 ; j < i ; j++)
        {
            if( x == p[j].x || y == p[j].y )
            {
                flag = 1;
                break;
            }
        }
        if( flag == 0 )
        {
            p[i].x = x;
            p[i].y = y;
            i++;
        }
    }

    for( i = 1; i <= n;  i++ )
    {
        for(j = 1; j <= n; j++ )
        {
            d[i][j] = sqrt( (p[i].x-p[j].x)*(p[i].x-p[j].x) + (p[i].y-p[j].y)*(p[i].y-p[j].y) );
        }
    }
        
}

////////////////////////////////////////////////////
//回溯法搜索TSP路径和最优值

void dfs(int i)
{
    if( i == n )  //找到最优路径
    {
        if(  d[a[n-1]][a[n]] != INT_MAX && d[a[n]][1] != INT_MAX &&
            ( cur + d[a[n-1]][a[n]] +d[a[n]][1] < Min || Min == INF ) )
        {
            for( int k = 1; k <= n; k++ )  //存储最优路径
                path[k] = a[k];
            Min = cur + d[a[n-1]][a[n]] +d[a[n]][1];
        }
    }

    else
    {
        for( int j = i; j <= n; j++)  //寻求路径子树
        {
            if( d[a[i-1]][a[j]] != INT_MAX && ( cur + d[a[i-1]][a[j]] < Min || Min == INF ) )
            {
                swap(a[i],a[j]);
                cur = cur + d[a[i-1]][a[i]];
                dfs(i+1);
                cur = cur - d[a[i-1]][a[i]];
                swap(a[i],a[j]);
            }
        }
    }
}


int main()
{   
    int i,j;
    int chioce;

    cout<<"            回溯法求解TSP问题            "<<endl;
    while( 1 )
    {
         cout<<"           1.回溯法求解TSP             "<<endl;
         cout<<"           2.退出程序                    "<<endl;
         cin>>chioce;

         if( chioce == 1)
         {
            cout << "请输入TSP的点数 " << endl;
            cin>>n;
            cout<<endl;
            init();

            cout<<"路线矩阵:"<<endl;
            for( i = 1; i <= n;  i++ )
            {
                for(j = 1; j <= n; j++ )
                {
                    printf("%.0lf\t",d[i][j]);
                }
                cout << endl;        
            }

            dfs(2);  //回溯搜索

            path[n+1] = 1;
            printf("长度: %lf\n路径:", Min);
            for( i = 1 ; i <= n+1 ; i++ )
                cout << path[i] << " ";
            cout<<endl;
        }
        else
            break;

    }
    return 0;
}