分支限界法求tsp问题,根据原博文修改后的代码

原文出处:http://blog.csdn.net/JarvisChu/archive/2010/10/29/5974895.aspx

#include <stdio.h> 
#include <iostream>  
using namespace std;  
//———————宏定义—————————————— 
#define MAX_CITY_NUMBER 10          //城市最大数目 
#define MAX_COST 10000000           //两个城市之间费用的最大值  
//———————全局变量—————————————-  
int City_Graph[MAX_CITY_NUMBER][MAX_CITY_NUMBER];  
                            //表示城市间边权重的数组  
int City_Size;              //表示实际输入的城市数目  
int Best_Cost;              //最小费用  
int Best_Cost_Path[MAX_CITY_NUMBER];  
                            //最小费用时的路径    
//————————定义结点—————————————  
typedef struct Node{  
    int lcost;              //优先级  
    int cc;                 //当前费用  
    int rcost;              //剩余所有结点的最小出边费用的和  
    int s;                  //当前结点的深度,也就是它在解数组中的索引位置  
    int x[MAX_CITY_NUMBER]; //当前结点对应的路径  
    struct Node* pNext;     //指向下一个结点  
}Node;  
//———————定义堆和相关对操作——————————–  
typedef struct MiniHeap{  
    Node* pHead;             //堆的头  
}MiniHeap;  
//初始化  
void InitMiniHeap(MiniHeap* pMiniHeap){  
    pMiniHeap->pHead = new Node;  
    pMiniHeap->pHead->pNext = NULL;  
}  
//入堆  
void put(MiniHeap* pMiniHeap,Node node){  
    Node* next;  
    Node* pre;   
 int k;
    Node* pinnode = new Node;         //将传进来的结点信息copy一份保存  
                                      //这样在函数外部对node的修改就不会影响到堆了  
    pinnode->cc = node.cc;  
    pinnode->lcost = node.lcost;  
    pinnode->pNext = node.pNext;  
    pinnode->rcost = node.rcost;  
    pinnode->s = node.s;  
    pinnode->pNext = NULL;  
    for(k=0;k<City_Size;k++){  
        pinnode->x[k] = node.x[k];  
    }  
    pre = pMiniHeap->pHead;  
    next = pMiniHeap->pHead->pNext;  
    if(next == NULL){  
        pMiniHeap->pHead->pNext = pinnode;  
    }  
    else{  
        while(next != NULL){  
            if((next->lcost) > (pinnode->lcost)){ //发现一个优先级大的,则置于其前面  
                pinnode->pNext = pre->pNext;  
                pre->pNext = pinnode;  
                break;                            //跳出  
            }  
            pre = next;  
            next = next->pNext;  
        }  
        pre->pNext = pinnode;                           //放在末尾  
    }     
}  
//出堆  
Node* RemoveMiniHeap(MiniHeap* pMiniHeap){  
    Node* pnode = NULL;  
    if(pMiniHeap->pHead->pNext != NULL){  
        pnode = pMiniHeap->pHead->pNext;  
        pMiniHeap->pHead->pNext = pMiniHeap->pHead->pNext->pNext;  
    }  
    return pnode;  
}  
//———————分支限界法找最优解——————————–  
void Traveler(){  
    int i,j;  
    int temp_x[MAX_CITY_NUMBER];  
    Node* pNode = NULL;  
    int miniSum;                    //所有结点最小出边的费用和  
    int miniOut[MAX_CITY_NUMBER];  
                                    //保存每个结点的最小出边的索引  
    MiniHeap* heap = new MiniHeap;  //分配堆  
    InitMiniHeap(heap);             //初始化堆  
                                      
    miniSum = 0;  
    for (i=0;i<City_Size;i++){  
        miniOut[i] = MAX_COST;      //初始化时每一个结点都不可达  
        for(j=0;j<City_Size;j++){  
            if (City_Graph[i][j]>0 && City_Graph[i][j]<miniOut[i]){  
                                    //从i到j可达,且更小  
                miniOut[i] = City_Graph[i][j];  
            }  
        }  
        if (miniOut[i] == MAX_COST){// i 城市没有出边  
            Best_Cost = -1;  
            return ;  
        }  
        miniSum += miniOut[i];     
    }  
    for(i=0;i<City_Size;i++){       //初始化的最优路径就是把所有结点依次走一遍  
        Best_Cost_Path[i] = i;  
    }  
    Best_Cost = MAX_COST;           //初始化的最优费用是一个很大的数  
    pNode = new Node;               //初始化第一个结点并入堆  
    pNode->lcost = 0;               //当前结点的优先权为0 也就是最优  
    pNode->cc = 0;                  //当前费用为0(还没有开始旅行)  
    pNode->rcost = miniSum;         //剩余所有结点的最小出边费用和就是初始化的miniSum  
    pNode->s = 0;                   //层次为0  
    pNode->pNext = NULL;  
    for(int k=0;k<City_Size;k++){  
        pNode->x[k] = Best_Cost_Path[k];      //第一个结点所保存的路径也就是初始化的路径  
    }  
    put(heap,*pNode);               //入堆  
    while(pNode != NULL && (pNode->s) < City_Size-1){  
                                    //堆不空 不是叶子  
        for(int k=0;k<City_Size;k++){  
            Best_Cost_Path[k] = pNode->x[k] ;      //将最优路径置换为当前结点本身所保存的  
        }  
/* 
* *  pNode 结点保存的路径中的含有这条路径上所有结点的索引 
* *  x路径中保存的这一层结点的编号就是x[City_Size-2] 
* *  下一层结点的编号就是x[City_Size-1] 
*/ 
        if ((pNode->s) == City_Size-2){ //是叶子的父亲  
            int edge1 = City_Graph[pNode->x[City_Size-2]][pNode->x[City_Size-1]];  
            int edge2 = City_Graph[pNode->x[City_Size-1]][pNode->x[0]];  
            if(edge1 >= 0 && edge2 >= 0 &&  (pNode->cc+edge1+edge2) < Best_Cost){  
                                                                             //edge1 -1 表示不可达  
                                                                             //叶子可达起点费用更低  
                   Best_Cost = pNode->cc + edge1+edge2;  
                   pNode->cc = Best_Cost;  
                   pNode->lcost = Best_Cost;                                  //优先权为 Best_Cost  
                   pNode->s++;                                                 //到达叶子层  
            }  
        }  
        else{                                                                 //内部结点  
            for (i=pNode->s;i<City_Size;i++){                                 //从当前层到叶子层  
                if(City_Graph[pNode->x[pNode->s]][pNode->x[i]] >= 0){   //可达  
                                    //pNode的层数就是它在最优路径中的位置  
                    int temp_cc = pNode->cc+City_Graph[pNode->x[pNode->s]][pNode->x[i]];  
                    int temp_rcost = pNode->rcost-miniOut[pNode->x[pNode->s]];  
                                                            //下一个结点的剩余最小出边费用和   
                                                            //等于当前结点的rcost减去当前这个结点的最小出边费用  
                    if (temp_cc+temp_rcost<Best_Cost){      //下一个结点的最小出边费用和小于当前的最优解,说明可能存在更优解  
                        for (j=0;j<City_Size;j++){           //完全copy路径,以便下面修改  
                            temp_x[j]=Best_Cost_Path[j];  
                        }  
                        temp_x[pNode->s+1] = Best_Cost_Path[i];   //和原文不同的地方
                                                            //将当前结点的编号放入路径的深度为s+1的地方  
                        temp_x[i] = Best_Cost_Path[pNode->s+1]; //??????????????  
                                                            //将原路//径中的深度为s+1的结点编号放入当前路径的  
                                                            //相当于将原路径中的的深度为i的结点与深度W为s+1的结点交换  
                        Node* pNextNode = new Node;  
                        pNextNode->cc = temp_cc;  
                        pNextNode->lcost = temp_cc+temp_rcost;  
                        pNextNode->rcost = temp_rcost;  
                        pNextNode->s = pNode->s+1;  
                        pNextNode->pNext = NULL;  
                        for(int k=0;k<City_Size;k++){  
                            pNextNode->x[k] = temp_x[k];  
                        }  
                        put(heap,*pNextNode);  
                        delete pNextNode;  
                    }  
                }  
            }  
        }  
        pNode = RemoveMiniHeap(heap);  
    }  
}  
int main(){  
    int i,j;  
    scanf(“%d”,&City_Size);  
    for(i=0;i<City_Size;i++){  
        for(j=0;j<City_Size;j++){  
   if(i==j)
   {City_Graph[i][j]=-1;
   }
   else
            scanf(“%d”,&City_Graph[i][j]);  
        }  
    }  
    Traveler();  
    printf(“%d\n”,Best_Cost);  
    return 1;  
}  

    原文作者:分支限界法
    原文地址: https://blog.csdn.net/u012806692/article/details/17119687
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
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