装箱问题

问题

假设有编号分别为0、1、……、n-1的n种物品，体积分别为V0、V1、……、Vn-1。将这n种物品装到容量都为V(V=100)的箱子里。约定这n种物品的体积均不超过V，即对于0<=i

思路

用贪心算法解决此问题的思路很简单。就是你要确保每一个箱子里面装的物品是当前最大的量就行，于是你需要对待装入物品按照体积从大到小排个序。然后把当前最大的物品装入箱子里面，然后在剩余的物品中挑选一个能装入箱子剩余空间的最大的物品，以此类推，直到无法再装入任何剩余物品为止。再开始下一个箱子。直到所有物品都被装入箱子，那么算法结束。

使用

package com.company;

public class Main {

    public static void main(String[] args) {
    // write your code here
        int[] goodsArray = {35,60,45,20,20,20};
        int boxSpace = 100;
        Solution.fillBoxes(goodsArray,boxSpace);
    }
}

输出

箱子实装:95
箱子实装:85
箱子实装:20

Process finished with exit code 0

实现

package com.company;

public class Solution {
    /**
     * 用贪心算法来找到装箱问题的最优解
     * @param goodsArray
     * @param boxSpace
     */
    static public void fillBoxes(int[] goodsArray,int boxSpace) {
        //先排序
        Good headerPointer = Solution.sortGoods(goodsArray);
        Box boxHeader = null;
        Box currentBoxPointer = null;
        while (headerPointer.nextPointer != null) {
            Box currentBox = new Box(boxSpace);
            if (boxHeader == null) {
                boxHeader = currentBox;
                currentBoxPointer = boxHeader;
            }
            else {
                currentBoxPointer.nextPointer = currentBox;
                currentBoxPointer = currentBox;
            }
            Good currentGood = headerPointer;
            while (currentGood.nextPointer != null) {
                if (currentGood.nextPointer.getVolume() <= currentBox.getRemainSpace()) {
                    Good tempGood = currentGood.nextPointer;
                    currentGood.nextPointer = currentGood.nextPointer.nextPointer;
                    tempGood.nextPointer = null;
                    currentBox.addGood(tempGood);
                } else currentGood = currentGood.nextPointer;
            }
        }
        while (boxHeader != null) {
            System.out.println("箱子实装:" + (boxSpace - boxHeader.getRemainSpace()));
            boxHeader = boxHeader.nextPointer;
        }
    }

    /**
     * 给待装箱物品排序
     * @param goodsArray
     * @return
     */
    static private Good sortGoods(int[] goodsArray) {
        Good header = new Good(-1);
        Good currentPointer = null;
        for (int counter = 0;counter < goodsArray.length;counter++) {
            currentPointer = header;
            while (currentPointer.nextPointer != null && currentPointer.nextPointer.getVolume() > goodsArray[counter])
                currentPointer = currentPointer.nextPointer;
            Good tempGood = new Good(goodsArray[counter]);
            tempGood.nextPointer = currentPointer.nextPointer;
            currentPointer.nextPointer = tempGood;
        }
        return header;
    }
}

package com.company;

public class Good {
    public Good nextPointer = null;
    private int volume = 0;

    public Good(int volume) {
        this.volume = volume;
    }

    public int getVolume() {
        return volume;
    }
}

package com.company;

public class Box {
    public Box nextPointer = null;
    private int remainSpace = 0;
    private int origialSpace = 0;
    public Good goodPointer = null;

    public Box(int origialSpace) {
        this.origialSpace = origialSpace;
        this.remainSpace = this.origialSpace;
    }

    public int getRemainSpace() {
        return remainSpace;
    }

    /**
     * 添加商品
     * @param good
     */
    public void addGood(Good good) {
        if (good == null)return;
        if (goodPointer == null)goodPointer = good;
        else {
            goodPointer.nextPointer = good;
            goodPointer = goodPointer.nextPointer;
        }
        remainSpace = remainSpace - goodPointer.getVolume();
    }
}