1.代码
package com.test;
import java.util.*;
public class Main {
static double c;
static int n;
static double w[];
static double p[];
static double cw;
static double cp;
static int bestX[];
static MaxHeap heap;
//上界函数bound计算结点所相应价值的上界
private static 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
private static void addLiveNode(double up,double pp,double ww,int lev,BBnode par,boolean 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 =new HeapNode(b,up,pp,ww,lev);
heap.put(node);
}
private static 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=null;
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 =(HeapNode)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;
}
public static double knapsack(double pp[],double ww[],double cc,int xx[]){
//返回最大值，bestX返回最优解
c=cc;
n=pp.length-1;
//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]=new 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;
}
public static void main(String [] args){
double w[]=new double[4];
w[1]=16;w[2]=15;w[3]=15;
double v[]=new double[4];
v[1]=45;v[2]=25;v[3]=25;
double c=30;
int x[] = new int[4];
double m = knapsack(v,w,c,x);
// System.out.println("请输入物器数：");
// Scanner sc=new Scanner(System.in);
// n=sc.nextInt();
// System.out.println("请输入包容容量：");
// c=sc.nextDouble();
// System.out.println("请输入物品数组：3个int");
// w[0]=sc.nextDouble();
// w[1]=sc.nextDouble();
// w[2]=sc.nextDouble();
// System.out.println("请输入价值数组3个int：");
// v[0]=sc.nextDouble();
// v[1]=sc.nextDouble();
// v[2]=sc.nextDouble();
System.out.println("*****分支限界法*****");
System.out.println("*****物品个数：n="+n);
System.out.println("*****背包容量：c="+c);
System.out.println("*****物品重量数组：w= {"+w[0]+" "+w[1]+" "+w[2]+"}");
System.out.println("*****物品价值数组：v= {"+v[0]+" "+v[1]+" "+v[2]+"}");
System.out.println("*****最优值：="+m);
System.out.println("*****选中的物品是:");
for(int i=1;i<=3;i++)
System.out.print(x[i]+" ");
}
}
//子空间中节点类型
class BBnode{
BBnode parent;//父节点
boolean leftChild;//左儿子节点标志
BBnode(BBnode par,boolean ch){
parent=par;
leftChild=ch;
}
}
class HeapNode implements Comparable{
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
public HeapNode(BBnode node, double up, double pp , double ww,int lev){
liveNode = node;
upperProfit = up;
profit = pp;
weight = ww;
level = lev;
}
public int compareTo(Object o) {
double xup = ((HeapNode)o).upperProfit;
if(upperProfit < xup)
return -1;
if(upperProfit == xup)
return 0;
else
return 1;
}
}
class Element implements Comparable{
int id;
double d;
public Element(int idd,double dd){
id=idd;
d=dd;
}
public int compareTo(Object x){
double xd=((Element)x).d;
if(d<xd)return -1;
if(d==xd)return 0;
return 1;
}
public boolean equals(Object x){
return d==((Element)x).d;
}
}
class MaxHeap{
static HeapNode [] nodes;
static int nextPlace;
static int maxNumber;
public MaxHeap(int n){
maxNumber = (int)Math.pow((double)2,(double)n);
nextPlace = 1;//下一个存放位置
nodes = new HeapNode[maxNumber];
}
public static void put(HeapNode node){
nodes[nextPlace] = node;
nextPlace++;
heapSort(nodes);
}
public static HeapNode removeMax(){
HeapNode tempNode = nodes[1];
nextPlace--;
nodes[1] = nodes[nextPlace];
heapSort(nodes);
return tempNode;
}
private static 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;
}
private static void heapSort(HeapNode [] nodes){
for(int i=(nextPlace-1)/2;i>0;--i){
heapAdjust(nodes,i,nextPlace-1);
}
}
}
2.结果：
*****分支限界法*****
*****物品个数：n=3
*****背包容量：c=30.0
*****物品重量数组：w= {15.0 16.0 15.0}
*****物品价值数组：v= {25.0 45.0 25.0}
*****最优值：=50.0
*****选中的物品是:
0 1 1