算法: 找子集合并按权值和排序 (货郎有关问题辅助算法)

算法: 找子集合并按权值和排序 (货郎问题辅助算法)

假设给出的 1-8 个数, 选4个

1) 最小的权值的几个 ( 1, 2, 3, 4)

2) 假设当前(a, b, c, d), 如果我们能确定权值和刚好大过它的组合, 不难找到所有组合按权值和排序

数据结构

需要两个结构 selects和 remains, selects 是已经选择的子集合, remains 是要考虑的数

他们是列表并需要排序, 先开始元素放置如下

算法

1) 用 remains 中最小的元素到 selects 中找到刚好它能大过的元素

2) 如果找到, 交换这两个元素

3) 如果不能找到, 从 remains 中删除此元素, 取下一个元素继续找 ( 就是到 1) )

------------ 能找到的情况

selects

remains

selects

remains

------------ 不能找到的情况

selects

remains

selects

remains

( 1 不用在考虑了, 放入 selects 必然会造成权值减少 )

================= 具体程序如下 ==================

package com.pnp.findnextnumber;

import java.util.ArrayList;
import java.util.Collections;

public class NextWeighSum {

    ArrayList<Integer> remains = new ArrayList<Integer>();
    ArrayList<Integer> selects = new ArrayList<Integer>();
    int TOTAL_COUNT = 10;
    int SELECT_COUNT = 4;

    void init() {
        for( int i=0; i<TOTAL_COUNT; i++)
            remains.add(i+1);
        Collections.sort(remains);
        for (int i=0; i<SELECT_COUNT; i++)
            selects.add( remains.remove(0));
    }
    
    /*
     * selects give the subset, need to return the next subset which the weight sum is just larger than current subset  
     */
    boolean selectNext() {
        while( remains.size() > 0) {
            int cur = remains.get(0);
            int pos = Collections.binarySearch(selects, cur);
            if (pos < 0) // binarySearch (-(insertion point) - 1)
                pos = (-pos) -1;
            else {
                System.err.print("Not allow equal elements");
                System.exit(-1); // Not allow equal elements
            }
            
            if ( pos == 0 )  {// that means current element is less that any in selects, we won't need to consider this elem
                remains.remove(0);
                continue;
            }
            else {
                int insert_pos = pos-1;
                remains.set(0,selects.get(insert_pos));
                selects.set(insert_pos, cur);
                System.out.print(" an select ---");
                print(selects);
                return true;
            }
        }
        return false;
    }
    
    void selectAll() {
        while (selectNext())
            ;
    }


    static void print(ArrayList<Integer> list ) {
        int sum = 0;
        for (int i=0; i< list.size(); i++) {
            sum += list.get(i);
            System.out.print( " " + list.get(i));
        }
        System.out.println("   sum:"+sum  );
    }

    public static void main(String[] args) {
        NextWeighSum m = new NextWeighSum();
        m.init();
        m.selectAll();
    }

}

这个算法打算在 "货郎问题" 中使用, 货郎问题是选择权值和最小的边集合,试探是否其构成路径. 构成则问题解决,否则试探下一个.

算法: 找子集合并按权值和排序 (货郎有关问题辅助算法)

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