01背包问题 动态规划

介绍：这个算法自己本有比较深刻的了解，也有很多人从专业的角度去解释了这个算法，而我主要是针对01背包问题而用代码的方式实现了它。

题目场景是这样子的：

假设有一个重量为 totalWeight 的背包

* 现有物品a1,a2,….an,他们的重量为w1,w2,w3….wn 价值为v1,v2,v3….vn.（w1+w2+w3….>totalWeight）

* 请问如何将物品放入背包中才能让物品价值最大化

这个题目拿到的话，反正我是没想到什么方法解决。但是看了分析才焕然大悟。

import java.util.List;

public class ZuiYouJie {

int totalWeight;
int currentWeight;

List<Zone>zoneAllList;
int zuiYouValue [][] = new  int[100][100];

public ZuiYouJie(int totalWeight,List<Zone> zoneAllList){
this.totalWeight = totalWeight;
this.zoneAllList = zoneAllList;
}

public  void getZuiYou(){

int size = zoneAllList.size();
//当i=0的时候
for(int i=0;i<totalWeight;i++){
zuiYouValue[0][i] = 0;
}

for(int i=0;i<size;i++){
zuiYouValue[i][0] = 0;
}

for(int currentWeight=1;currentWeight<=totalWeight;currentWeight++){
for(int i=1;i<=size;i++){
Zone currentZone = zoneAllList.get(i-1);
if(currentWeight<zoneAllList.get(i-1).getWeight()){
zuiYouValue[i][currentWeight]=zuiYouValue[i-1][currentWeight];
}
else{
//如果
if(zuiYouValue[i-1][currentWeight-currentZone.getWeight()]+currentZone.getValue()>zuiYouValue[i-1][currentWeight]){
zuiYouValue[i][currentWeight] =  zuiYouValue[i-1][currentWeight-currentZone.getWeight()]+currentZone.getValue();
}else{
zuiYouValue[i][currentWeight] = zuiYouValue[i-1][currentWeight];
}
}
}
}
int currentWeightForCompare = totalWeight;
for(int k = size;k>0;k--){
if(zuiYouValue[k][currentWeightForCompare]>zuiYouValue[k-1][currentWeightForCompare]){
zoneAllList.get(k-1).setForZuiYou(true);
currentWeightForCompare = currentWeightForCompare-zoneAllList.get(k-1).getWeight();
}
if(currentWeightForCompare==0){
break;
}
}
}

}

public class Zone {
int id;
int value;
int weight;
boolean isForZuiYou = false;

public boolean isForZuiYou() {
return isForZuiYou;
}
public void setForZuiYou(boolean isForZuiYou) {
this.isForZuiYou = isForZuiYou;
}
public int getId() {
return id;
}
public void setId(int id) {
this.id = id;
}
public int getValue() {
return value;
}
public void setValue(int value) {
this.value = value;
}
public int getWeight() {
return weight;
}
public void setWeight(int weight) {
this.weight = weight;
}

}

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

public class DynamicProgramming {
/**
* 动态规划 01背包问题
* 假设有一个重量为 totalWeight 的背包
* 现有物品a1,a2,....an,他们的重量为w1,w2,w3....wn 价值为v1,v2,v3....vn.（w1+w2+w3....>totalWeight）
* 请问如何将物品放入背包中才能让物品价值最大化
* 可以肯定的是要将这n个中的物品选择其中 m个放入背包
* 那么那些要放那些不要放呢？
*
* 可以想象一下场景
* 1.若放的下一个物品大于totalWeight
*  2.1 若是wm>currentWeight那么显然就是
*    当 wm>currentWeight  V(m-1,currentWeight)=V(m,currentWeight)
*
*  2.2 若是currentWeight>wm那么就比较复杂了这里的话可以直接判断出第m个能否成为最优解的一员
*  即V(m,currentWeight)=max{V(m-1,currentWeight) ,V(m-1,currentWeight-wm)+vm }
*/

public static void main(String[] args) {
List<Zone>allList = new ArrayList<Zone>();
for(int i=0;i<10;i++){
Zone zone = new Zone();
zone.setId(i);
zone.setWeight(getRandome(10,5));
zone.setValue(getRandome(20,10));
System.out.println("第"+i+"物品重量为："+zone.getWeight()+"价值为："+zone.getValue());
allList.add(zone);
}
int sumValue = 0;
int sumWeight = 0;
ZuiYouJie zuiYouJie = new ZuiYouJie(50,allList);
zuiYouJie.getZuiYou();
for(int i=0;i<allList.size();i++){
Zone zone = allList.get(i);
if(allList.get(i).isForZuiYou){
System.out.println("最优解 第"+zone.getId()+"物品重量为："+zone.getWeight()+"价值为："+zone.getValue());
sumValue += zone.getValue();
sumWeight += zone.getWeight();
}
}
System.out.println("最优解总价值："+sumValue);
System.out.println("最优解总重量："+sumWeight);
}

public static int getRandome(int max,int min){
Random random = new Random();
int s = random.nextInt(max)%(max-min+1) + min;
return s;
}
}

没怎么做详细的解释，下次理解更加透彻了，再加上。