裝載問題-回溯法

有兩艘貨船，載重分別爲w1、w2，物品總重量不超過載重總量w1+w2，問物品是否都可以裝下。如，w1=w2=10，物品g1=g2=9，g3=2，則無法裝下；w1=w2=5，w3=10，則可以裝下。

    這是個典型的裝載問題，多箱多物可否容納。思路是儘可能將前邊的箱子裝滿，判斷剩餘物品是否可以裝入最後一個箱子。

package test;

import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

/**

• Created by zuohao on 2018/11/30.
  */
  public class BinPackingProblem {

  private List<Node> nodeList=new ArrayList<>();

  public static void main(String[] arg) {
  // new BinPackingProblem().greedy();
  new BinPackingProblem().backtracking();
  }

  /**

  • 回溯算法
  • 建立左右子結點是爲了形成物理上的樹結構，實際對應這個算法可以不建立左右子結點，因爲構建樹和計算結果同步進行，獲得結果後就停止了，不會再次使用構建好的樹
    */
    public void backtracking(){
    int rucksackWeight1=10;
    int rucksackWeight2=10;
    List<Goods> goodsList=new ArrayList<>();
    goodsList.add(new Goods("書",1));
    goodsList.add(new Goods("足球",3));
    goodsList.add(new Goods("大箱子",7));
    goodsList.add(new Goods("macbook",3));
    goodsList.add(new Goods("iphone",1));
    goodsList.add(new Goods("禮盒",5));
    // //裝不下的情況
    // goodsList.add(new Goods("書",2));
    // goodsList.add(new Goods("足球",9));
    // goodsList.add(new Goods("大箱子",9));
    int allWeight=0;
    for (Goods goods:goodsList){
    allWeight=allWeight+goods.getWeight();
    }
    if (allWeight>rucksackWeight1+rucksackWeight2){
    System.out.println("物品總重量已超出兩貨船總承載");
    return;
    }
    //【1】裝第一艘貨船，儘可能多的裝
    Node parentNode=new Node();
    parentNode.setSurplusWeight(rucksackWeight1);
    again(goodsList, parentNode,0);
    Collections.sort(nodeList, new Comparator<Node>() {br/>@Override
    public int compare(Node o1, Node o2) {
    int surplus=o1.getSurplusWeight()-o2.getSurplusWeight();
    if (surplus<0)
    return -1;
    else if (surplus>0)
    return 1;
    return 0;
    }
    });
    Node first=nodeList.get(0);
    if (allWeight-(rucksackWeight1-first.getSurplusWeight())<=rucksackWeight2){
    System.out.println("兩貨船可以裝下所有物品");
    System.out.println("第一艘貨船需裝如下物品，其餘物品裝第二艘貨船");
    List<Goods> goodsList1=first.getGoodsList();
    for (Goods goods:goodsList1){
    System.out.print(goods.getName()+",");
    }
    System.out.println();
    }
    else {
    System.out.println("兩貨船無法裝下所有物品");
    }

  }

  private void again(List<Goods> goodsList, Node parentNode,int i) {
  if (i>=goodsList.size()){
  nodeList.add(parentNode);
  return;
  }
  Goods goods=goodsList.get(i);
  int surplus=parentNode.getSurplusWeight()-goods.getWeight();
  if (surplus>=0){
  Node leftNode=new Node();
  leftNode.setSurplusWeight(surplus);
  parentNode.setLeftNode(leftNode);
  leftNode.getGoodsList().addAll(parentNode.getGoodsList());
  leftNode.getGoodsList().add(goods);
  again(goodsList,leftNode,i+1);
  }
  Node rightNode=new Node();
  rightNode.setSurplusWeight(parentNode.getSurplusWeight());
  parentNode.setRightNode(rightNode);
  rightNode.getGoodsList().addAll(parentNode.getGoodsList());
  again(goodsList,rightNode,i+1);
  }

  class Goods{
  private String name;
  private int weight;

  public Goods(String name, int weight) {
      this.name = name;
      this.weight = weight;
  }
  
  public String getName() {
      return name;
  }
  
  public void setName(String name) {
      this.name = name;
  }
  
  public int getWeight() {
      return weight;
  }
  
  public void setWeight(int weight) {
      this.weight = weight;
  }

  }

  class Node{
  private int surplusWeight;
  private Node leftNode;
  private Node rightNode;
  private List<Goods> goodsList=new ArrayList<>();

  public int getSurplusWeight() {
      return surplusWeight;
  }
  
  public void setSurplusWeight(int surplusWeight) {
      this.surplusWeight = surplusWeight;
  }
  
  public Node getLeftNode() {
      return leftNode;
  }
  
  public void setLeftNode(Node leftNode) {
      this.leftNode = leftNode;
  }
  
  public Node getRightNode() {
      return rightNode;
  }
  
  public void setRightNode(Node rightNode) {
      this.rightNode = rightNode;
  }
  
  public List<Goods> getGoodsList() {
      return goodsList;
  }
  
  public void setGoodsList(List<Goods> goodsList) {
      this.goodsList = goodsList;
  }

  }
  }