(C语言)分支界限法求解旅行商(TSP)问题

1.代码：

#include <stdio.h>
#include <malloc.h>

#define NoEdge           1000

struct MinHeapNode
{
	int lcost; //子树费用的下界
	int cc; //当前费用
	int rcost; //x[s:n-1]中顶点最小出边费用和
	int s; //根节点到当前节点的路径为x[0:s]
	int *x; //需要进一步搜索的顶点是//x[s+1:n-1]
	struct MinHeapNode *next;
};

int n; //图G的顶点数
int **a; //图G的邻接矩阵
//int   NoEdge;   //图G的无边标记
int cc; //当前费用
int bestc; //当前最小费用
MinHeapNode* head = 0; /*堆头*/
MinHeapNode* lq = 0; /*堆第一个元素*/
MinHeapNode* fq = 0; /*堆最后一个元素*/

int DeleteMin(MinHeapNode*&E)
{
	MinHeapNode* tmp = NULL;
	tmp = fq;
	// w = fq->weight ;
	E = fq;
	if(E == NULL)
		return 0;
	head->next = fq->next; /*一定不能丢了链表头*/
	fq = fq->next;
	// free(tmp) ;
	return 0;
}

int Insert(MinHeapNode* hn)
{
	if(head->next == NULL)
	{
		head->next = hn; //将元素放入链表中
		fq = lq = head->next; //一定要使元素放到链中
	}else
	{
		MinHeapNode *tmp = NULL;
		tmp = fq;
		if(tmp->cc > hn->cc)
		{
			hn->next = tmp;
			head->next = hn;
			fq = head->next; /*链表只有一个元素的情况*/
		}else
		{
			for(; tmp != NULL;)
			{
				if(tmp->next != NULL && tmp->cc > hn->cc)
				{
					hn->next = tmp->next;
					tmp->next = hn;
					break;
				}
				tmp = tmp->next;
			}
		}
		if(tmp == NULL)
		{
			lq->next = hn;
			lq = lq->next;
		}
	}
	return 0;
}

int BBTSP(int v[])
{//解旅行售货员问题的优先队列式分支限界法

	/*初始化最优队列的头结点*/
	head = (MinHeapNode*)malloc(sizeof(MinHeapNode));
	head->cc = 0;
	head->x = 0;
	head->lcost = 0;
	head->next = NULL;
	head->rcost = 0;
	head->s = 0;
	int *MinOut = new int[n + 1]; /*定义定点i的最小出边费用*/
	//计算MinOut[i]=顶点i的最小出边费用
	int MinSum = 0;//最小出边费用总合
	for(int i = 1; i <= n; i++)
	{
		int Min = NoEdge; /*定义当前最小值*/
		for(int j = 1; j <= n; j++)
			if(a[i][j] != NoEdge && /*当定点i,j之间存在回路时*/
				(a[i][j] < Min || Min == NoEdge)) /*当顶点i,j之间的距离小于Min*/
				Min = a[i][j]; /*更新当前最小值*/
		if(Min == NoEdge)
			return NoEdge;//无回路
		MinOut[i] = Min;
		//printf("%d\n",MinOut[i]);/*顶点i的最小出边费用*/
		MinSum += Min;
		// printf("%d\n",MinSum); /*最小出边费用的总和*/
	}


	MinHeapNode *E = 0;
	E = (MinHeapNode*)malloc(sizeof(MinHeapNode));
	E->x = new int[n];
	// E.x=new int[n];
	for(int i = 0; i < n; i++)
		E->x[i] = i + 1;
	E->s = 0;
	E->cc = 0;
	E->rcost = MinSum;
	E->next = 0; //初始化当前扩展节点
	int bestc = NoEdge; /*记录当前最小值*/
	//搜索排列空间树
	while(E->s < n - 1)
	{//非叶结点
		if(E->s == n - 2)
		{//当前扩展结点是叶结点的父结点
			/*
			首先考虑s=n-2的情形，此时当前扩展结点是排列树中某个叶结点的父结点。如果该叶结点相应一条可行回路
			且费用小于当前最小费用，则将该叶结点插入到优先队列中，否则舍去该叶结点
			*/
			if(a[E->x[n - 2]][E->x[n - 1]] != NoEdge && /*当前要扩展和叶节点有边存在*/
				a[E->x[n - 1]][1] != NoEdge && /*当前页节点有回路*/
				(E->cc + a[E->x[n - 2]][E->x[n - 1]] + a[E->x[n - 1]][1] < bestc /*该节点相应费用小于最小费用*/
				|| bestc == NoEdge))
			{
				bestc = E->cc + a[E->x[n - 2]][E->x[n - 1]] + a[E->x[n - 1]][1]; /*更新当前最新费用*/
				E->cc = bestc;
				E->lcost = bestc;
				E->s++;
				E->next = NULL;
				Insert(E); /*将该页节点插入到优先队列中*/
			}else
				free(E->x);//该页节点不满足条件舍弃扩展结点 
		}else
		{/*产生当前扩展结点的儿子结点
		 当s<n-2时，算法依次产生当前扩展结点的所有儿子结点。由于当前扩展结点所相应的路径是x[0:s]，
		 其可行儿子结点是从剩余顶点x[s+1:n-1]中选取的顶点x[i]，且(x[s]，x[i])是所给有向图G中的一条边。
		 对于当前扩展结点的每一个可行儿子结点，计算出其前缀(x[0:s]，x[i])的费用cc和相应的下界lcost。
		 当lcost<bestc时，将这个可行儿子结点插入到活结点优先队列中。*/
			for(int i = E->s + 1; i < n; i++)
				if(a[E->x[E->s]][E->x[i]] != NoEdge)
				{ /*当前扩展节点到其他节点有边存在*/
					//可行儿子结点
					int cc = E->cc + a[E->x[E->s]][E->x[i]]; /*加上节点i后当前节点路径*/
					int rcost = E->rcost - MinOut[E->x[E->s]]; /*剩余节点的和*/
					int b = cc + rcost; //下界
					if(b < bestc || bestc == NoEdge)
					{//子树可能含最优解,结点插入最小堆
						MinHeapNode * N;
						N = (MinHeapNode*)malloc(sizeof(MinHeapNode));
						N->x = new int[n];
						for(int j = 0; j < n; j++)
							N->x[j] = E->x[j];
						N->x[E->s + 1] = E->x[i];
						N->x[i] = E->x[E->s + 1];/*添加当前路径*/
						N->cc = cc; /*更新当前路径距离*/
						N->s = E->s + 1; /*更新当前节点*/
						N->lcost = b; /*更新当前下界*/
						N->rcost = rcost;
						N->next = NULL;
						Insert(N); /*将这个可行儿子结点插入到活结点优先队列中*/
					}
				}
				free(E->x);
		}//完成结点扩展
		DeleteMin(E);//取下一扩展结点
		if(E == NULL)
			break; //堆已空

	}
	if(bestc == NoEdge)
		return NoEdge;//无回路
	for(int i = 0; i < n; i++)
		v[i + 1] = E->x[i];//将最优解复制到v[1:n]
	while(true)
	{//释放最小堆中所有结点
		free(E->x);
		DeleteMin(E);
		if(E == NULL)
			break;
	}
	return bestc;
}

int main()
{
	n = 0;
	int i = 0;
	//FILE *in, *out;
	//in = fopen("input.txt", "r");
	//out = fopen("output.txt", "w");
	//if(in == NULL || out == NULL)
	//{
	//	printf("没有输入输出文件\n");
	//	return 1;
	//}
	//fscanf(in, "%d", &n);
	n=5;
	a = (int**)malloc(sizeof(int*) * (n + 1));
	for(i = 1; i <= n; i++)
	{
		a[i] = (int*)malloc(sizeof(int) * (n + 1));
	}
// 	for(i = 1; i <= n; i++)
// 		for(int j = 1; j <= n; j++)
// 			//fscanf(in, "%d", &a[i][j]);
// 			a[i][j]=1;
	a[1][1]=0;
	a[1][2]=5;
	a[1][3]=8;
	a[1][4]=5;
	a[1][5]=4;

	a[2][1]=5;
	a[2][2]=0;
	a[2][3]=5;
	a[2][4]=6;
	a[2][5]=3;

	a[3][1]=8;
	a[3][2]=5;
	a[3][3]=0;
	a[3][4]=5;
	a[3][5]=4;

	a[4][1]=5;
	a[4][2]=6;
	a[4][3]=6;
	a[4][4]=0;
	a[4][5]=3;

	a[5][1]=4;
	a[5][2]=3;
	a[5][3]=4;
	a[5][4]=3;
	a[5][5]=0;

	// prev = (int*)malloc(sizeof(int)*(n+1)) ;
	int*v = (int*)malloc(sizeof(int) * (n + 1));// MaxLoading(w , c , n) ;
	for(i = 1; i <= n; i++)
		v[i] = 0;
	bestc = BBTSP(v);

	printf("\n");
	for(i = 1; i <= n; i++)
		fprintf(stdout, "%d\t", v[i]);
	fprintf(stdout, "\n");
	fprintf(stdout, "%d\n", bestc);
	return 0;
}

2.输出结果

1->2->5->3->4->1
距离：22