01 背包问题的另类解法

百度百科和大部分网站的解释背包问题，
http://baike.baidu.com/view/1731915.htm
感觉时间复杂度O(m*n)；

刚好又别人解看到腾讯问题的文章：
http://baike.baidu.com/view/1731915.htm
感觉背包问题可以只是求最终结果的话，可以用权重来解决；

时间复杂度O(n);

用java编写的如下代码：

import java.util.ArrayList;

import java.util.Collections;

import java.util.List;

public class Backpack {

public static void main(String[] args) {

Backpack test = new Backpack();

List<Rely> relyList = new ArrayList<Rely>();

relyList.add(test.new Rely(1, 1));

relyList.add(test.new Rely(3, 3));

relyList.add(test.new Rely(5, 3));

relyList.add(test.new Rely(10, 3));

relyList.add(test.new Rely(6, 8));

relyList.add(test.new Rely(7, 5));

relyList = test.calcWeight(relyList);

for (Rely rely : relyList) {

System.out.println(rely);

}

System.out.println("Max: "+test.anyazer(6, relyList));

}

public int anyazer(int limit, List<Rely> relyList) {

int max = 0;

int remainder;

int mark = 0;

for (Rely rely : relyList) {

if (limit / rely.engry >= 1) {

max = limit / rely.engry * rely.happiness;

remainder = limit % rely.engry;

mark += max;

if (remainder != 0) {

limit = remainder;

continue;

}

break;

}

}

return mark;

}

public List<Rely> calcWeight(List<Rely> relyList) {

List<Rely> weightList = new ArrayList<Rely>();

for (Rely rely : relyList) {

Double weight = (double) rely.happiness / (double) rely.engry;

rely.setWeight(weight);

weightList.add(rely);

}

Collections.sort(weightList, Collections.reverseOrder());

return weightList;

}

public class Rely implements Comparable<Rely> {

private int happiness;

private int engry;

private double weight;

public Rely() {

}

public Rely(int happiness, int engry) {

this.happiness = happiness;

this.engry = engry;

}

public void setWeight(double weight) {

this.weight = weight;

}

public int getHappiness() {

return this.happiness;

}

public int getEngry() {

return this.engry;

}

@Override

public String toString() {

StringBuilder strBuilder = new StringBuilder();

strBuilder.append(happiness).append("\t").append(engry)

.append("\t").append(weight);

return strBuilder.toString();

}

@Override

public int compareTo(Rely o) {

int flag;

flag = weight > o.weight ? 1 : (weight == o.weight ? 0 : -1);

if (flag == 0) {

flag = engry > o.engry ? 1 : (engry == o.engry ? 0 : -1);

}

return flag;

}

}

}