1.beibao.h文件代码如下：

#ifndef BEIBAO_H
#define  BEIBAO_H

#include <math.h>


//子空间中节点类型
class BBnode{
public: 
	BBnode*  parent;   //父节点
	bool leftChild;   //左儿子节点标志
	BBnode(BBnode* par,bool ch){
		parent=par;
		leftChild=ch;
	}
	BBnode(){

	}
};

class HeapNode {
public:
	BBnode* liveNode; // 活结点
	double  upperProfit; //结点的价值上界
	double  profit; //结点所相应的价值
	double  weight; //结点所相应的重量
	int     level; // 活结点在子集树中所处的层次号

	//构造方法
	 HeapNode(BBnode* node, double up, double pp , double ww,int lev){
		liveNode = node;
		upperProfit = up;
		profit    = pp;
		weight    = ww;
		level    = lev;
	}
	 HeapNode(){

	 }
	 int compareTo(HeapNode o) {
		double xup =o.upperProfit;
		if(upperProfit < xup)
			return -1;
		if(upperProfit == xup)
			return 0;
		else
			return 1;
	}
};

class Element  {
public:
	int id;
	double d;
	Element(){

	}
	Element(int idd,double dd){
		id=idd;
		d=dd;
	}
	int compareTo(Element x){
		double xd=x.d;
		if(d<xd)return -1;
		if(d==xd)return 0;
		return 1;
	}
	 bool equals(Element x){
		return d==x.d;
	}
};

class MaxHeap{
public:
	 HeapNode *nodes;
	 int nextPlace;
	 int maxNumber;
	 MaxHeap(int n){
		maxNumber = pow((double)2,(double)n);
		nextPlace = 1;//下一个存放位置
		nodes = new HeapNode[maxNumber];
	}
	 MaxHeap(){
	 }
    void put(HeapNode node){
		nodes[nextPlace] = node;
		nextPlace++;
		heapSort(nodes);
	}
	HeapNode removeMax(){
		HeapNode tempNode = nodes[1];
		nextPlace--;
		nodes[1] = nodes[nextPlace];
		heapSort(nodes);
		return tempNode;
	}
	 void heapAdjust(HeapNode *  nodes,int s,int m){
		HeapNode rc = nodes[s];
		for(int j=2*s;j<=m;j*=2){
			if(j<m&&nodes[j].upperProfit<nodes[j+1].upperProfit)
				++j;
			if(!(rc.upperProfit<nodes[j].upperProfit))
				break;
			nodes[s] = nodes[j];
			s = j;
		}
		nodes[s] = rc;
	}
    void heapSort(HeapNode * nodes){
		for(int i=(nextPlace-1)/2;i>0;--i){
			heapAdjust(nodes,i,nextPlace-1);
		}
	}
} ;


#endif

2.测试代码

#include <iostream>
using namespace std;



//子空间中节点类型
#include "beibao.h"


double c=30; 
const int n=3;
double *w;
double *p;
double cw;
double cp;
int    *bestX;
MaxHeap * heap;


//上界函数bound计算结点所相应价值的上界
 double bound(int i){
	double cleft=c-cw;
	double b=cp;
	while(i<=n&&w[i]<=cleft){
		cleft=cleft-w[i];
		b=b+p[i];
		i++;
	}
	//装填剩余容量装满背包
	if(i<=n)
		b=b+p[i]/w[i]*cleft;
	return b;
}
//addLiveNode将一个新的活结点插入到子集树和优先队列中
 void addLiveNode(double up,double pp,double ww,int lev,BBnode* par,bool ch){
	//将一个新的活结点插入到子集树和最大堆中
	BBnode *b=new BBnode(par,ch);
	HeapNode  node =HeapNode(b,up,pp,ww,lev);
	heap->put(node);
}
 double MaxKnapsack(){
	//优先队列式分支限界法，返回最大价值，bestx返回最优解
	BBnode * enode=new BBnode();
	int i=1;
	double bestp=0;//当前最优值
	double up=bound(1);//当前上界
	while(i!=n+1){//非叶子结点
		//检查当前扩展结点的左儿子子结点
		double wt=cw+w[i];
		if(wt<=c){
			if(cp+p[i]>bestp)
				bestp=cp+p[i];
			addLiveNode(up,cp+p[i],cw+w[i],i+1,enode,true);
		}
		up=bound(i+1);
		if(up>=bestp)
			addLiveNode(up,cp,cw,i+1,enode,false);
		HeapNode node =heap->removeMax();
		enode=node.liveNode;
		cw=node.weight;
		cp=node.profit;
		up=node.upperProfit;
		i=node.level;
	}
	for(int j=n;j>0;j--){

		bestX[j]=(enode->leftChild)?1:0;
		enode=enode->parent;
	}
	return cp;
}


 double knapsack(double *pp,double *ww,double cc,int *xx){
	//返回最大值，bestX返回最优解
	c=cc;
	//n=sizeof(pp)/sizeof(double);
	//定义以单位重量价值排序的物品数组
	Element *q=new Element[n];
	double ws=0.0;
	double ps=0.0;
	for(int i=0;i<n;i++){
		q[i]=Element(i+1,pp[i+1]/ww[i+1]);
		ps=ps+pp[i+1];
		ws=ws+ww[i+1];
	}
	if(ws<=c){
		return  ps;
	}           
	p=new double[n+1];
	w=new double[n+1];
	for(int i=0;i<n;i++){
		p[i+1]=pp[q[i].id];
		w[i+1]=ww[q[i].id];
	}
	cw=0.0;
	cp=0.0;
	bestX = new int[n+1];
	heap = new MaxHeap(n);
	double bestp = MaxKnapsack();
	for(int j=0;j<n;j++)
		xx[q[j].id]=bestX[j+1];

	return  bestp;

}




void main(){
	
	w=new double[4];
	w[1]=16;w[2]=15;w[3]=15;
	p=new double[4];
	p[1]=45;p[2]=25;p[3]=25;
	int *x = new int[4];
	double m = knapsack(p,w,c,x);


	cout<<"*****分支限界法*****"<<endl;
	cout<<"*****物品个数：n="<<n<<endl;
	cout<<"*****背包容量：c="<<c<<endl;
	cout<<"*****物品重量数组：w= {"<<w[3]<<" "<<w[1]<<" "<<w[2]<<"}"<<endl;
	cout<<"*****物品价值数组：v= {"<<p[3]<<" "<<p[1]<<" "<<p[2]<<"}"<<endl;
	cout<<"*****最优值：="<<m<<endl;
	cout<<"*****选中的物品是:";
	for(int i=1;i<=3;i++)
		cout<<x[i]<<" ";
	cout<<endl;
}

3.测试结果：

*****分支限界法*****
*****物品个数：n=3
*****背包容量：c=30
*****物品重量数组：w= {15 16 15}
*****物品价值数组：v= {25 45 25}
*****最优值：=50
*****选中的物品是:0 1 1