How to implement the Sum of Subsets problem in Java

Question

Does anyone know how to implement the Sum-of-Subsets problem in Java from this pseudo code?

w = an array of positive integers sorted in non-decreasing order.
W = the target sum value
include = an array or arraylist of the solutions who's weight adds up to W. After the print statement, this array can be deleted so that it can store the next solution.
weight = weight of elements in the include array.
total = weight of the remaining elements not in the include array.

public static void sum_of_subsets(index i, int weight, int total)
{
     if(promising(i))
     {
          if(weight == W)
          {
               System.out.print(include[1] through include[i]);
          }
          else
          {
               include[i + 1] = "yes";     //Include w[i + 1]
               sum_of)subsets(i + 1, weight + w[i + 1], total - w[i + 1]);
               include[i + 1] = "no";      //Do not include w[i + 1]
               sum_of_subsets(i + 1, weight, total - w[i + 1]);
          }
     }
}

public static boolean promising(index i);
{
     return (weight + total >= W) && (weight == W || weight + w[i + 1] <= W);
}

this is really baffling me, so if you could add comments that would be great!!!

Answer 1

Algorithms Coded in Java

First the algorithm removes all numbers that are larger than the sum to begin with.

Then for the largest number smaller than the sum, it checks if there are any numbers in the list that it can add to itself to get the sum. Once we have either found a pair, or the sum is greater than the desired sum, we can break since the list is sorted. We then consider the second largest number and see if we can make a pair with that, and so on.

   /**
    * This will find how many pairs of numbers in the given array sum
    * up to the given number.
    *
    * @param array - array of integers
    * @param sum - The sum
    * @return int - number of pairs.
    */
public static int sumOfSubset(int[] array, int sum)
{
        // This has a complexity of O ( n lg n )
        Arrays.sort(array);

        int pairCount = 0;
        int leftIndex = 0;
        int rightIndex = array.length - 1;

        // The portion below has a complextiy of
        //  O ( n ) in the worst case.
        while (array[rightIndex] > sum + array[0])
        {
            rightIndex--;    
        }

        while (leftIndex < rightIndex)
        {
            if (array[leftIndex] + array[rightIndex] == sum)
            {
                pairCount++;
                leftIndex++;
                rightIndex--;
            }
            else if(array[leftIndex] + array[rightIndex]  < sum)
            {
                leftIndex++;
            }
            else
            {
                rightIndex--;   
            }
        }

        return pairCount;
}

The algorithm above does not return the pairs, but that is trivially to add.

Answer 2

This program finds the exact pairs from a set of numbers to form the desired sum, the program also returns the unique pairs in the end. The program also returns a nearest/closest subset to form the desired sum if no exact subset is found. You can run the program as is to see the demo and then do the modification if needed. The logic I have applied here is based on all combinations of numbers in a given set to get the desired sum, you can refer to inline comments for further information

package com.test;

import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;

/**
 * 
 * @author ziya sayed
 * @email : sayedziya@gmail.com
 */
public class SumOfSubsets{

//  private static int[] numbers= {1,1,2,2,3,4};//set of numbers
    private static int[] numbers= {18,17,1};//set of numbers
//  private static final int SUM = 4;//desired sum
    private static final int SUM = 20;//desired sum

    public static void main(String[] args) {

        String binaryCount="";
        int[] nos=new int[numbers.length];
        //input set, and setting binary counter
        System.out.print("Input set numbers are : ");
        for (int no : numbers) {            
            if (no<=SUM) {
                System.out.print(no+" ");                                       
                nos[binaryCount.length()]=no;
                binaryCount+=1; //can we use sring builder or string.format
            }       

        }
        System.out.println();
        Arrays.sort(nos);//sort asc

        int totalNos = binaryCount.length();
        String subset="";   //chosen subset 
        int subsetSum=0;//to temp hold sum of chosen subset every iteration
        String nearestSubset="";//chosen closest subset if no exact subset
        int nearestSubsetSum=0;//to hold sum of chosen closest subset

        Set<String> rs = new HashSet<String>();//to hold result, it will also avoide duplicate pairs
        for (int i = Integer.parseInt(binaryCount, 2) ; i >0;i-- ) {//for all sum combinations
        //  System.out.println(i);
            binaryCount=String.format("%1$#" + totalNos + "s", Integer.toBinaryString(i)).replace(" ","0");//pad 0 to left if number is less than 6 digit binary for proper combinations

            subset="";
            subsetSum=0;

            for (int j=0 ;j<totalNos; j++) {//for active combinations sum

                if (binaryCount.charAt(j)=='1') {                   
                    subset+=nos[j]+" ";
                    subsetSum+=nos[j];
                }
            }
            if (subsetSum == SUM) {
            //  System.out.println(subset);//we can exit here if we need only one set
                rs.add(subset);
            }
            else{//use this for subset of numbers with nearest to desired sum
                if (subsetSum < SUM  && subsetSum > nearestSubsetSum && rs.isEmpty()) {
                    nearestSubsetSum = subsetSum;
                    nearestSubset = subset;

                }
            }

        }

        if (rs.isEmpty()) {
                System.out.println("Nearest Subset of "+SUM);
                System.out.println(nearestSubset);
        }
        else{
            System.out.println("Exact Subset of "+SUM);
            System.out.println(rs);//unique sub sets to remove duplicate pairs
        }

    }


}