given N absolute values of integers find the combination of N/2 negative and N/2 positive values whose sum is closest to 0

Question

Let\'s say that I have an array of 10 numbers whose absolute value range can go from 1 to 10. Values can be repeated. An example of this could be

{2, 4, 2, 6, 9         


        

Answer 1

This is a java implementation of the algorithm described by amin k.

It's less cool than the Haskell implementation, I have no formal proof that it works in every case, but it seems to be working.

import java.util.Arrays;
import java.util.Random;

public class TestPermutations {

int[] values = new int[10];
int[] positives = new int[5];
int[] negatives = new int[5];

public static void main(String... args) {
    new TestPermutations();
}

public TestPermutations() {
    Random ra = new Random();
    System.out.println("generating sequence...");
    for (int i = 0; i < 10; i++) {
        values[i] = (ra.nextInt(10) + 1);
        System.out.print(values[i] + " ");
    }
    Arrays.sort(values);

    int sum = 0;
    int positiveIndex = 0;
    int negativeIndex = 0;
    for (int i = values.length - 1; i >= 0; i--) {
        if (i == values.length - 1) {
            negatives[negativeIndex] = - values[i];
            negativeIndex++;
            sum -= values[i];
        }
        else {
            if (sum <= 0) {
                if (positiveIndex < 5) {
                    positives[positiveIndex] = values[i];
                    positiveIndex++;
                    sum += values[i];
                }
                else {
                    negatives[negativeIndex] = - values[i];
                    negativeIndex++;
                    sum -= values[i];
                }
            }
            else {
                if (negativeIndex < 5) {
                    negatives[negativeIndex] = - values[i];
                    negativeIndex++;
                    sum -= values[i];
                }
                else {
                    positives[positiveIndex] = values[i];
                    positiveIndex++;
                    sum += values[i];
                }
            }
        }
    }

    System.out.print("\npositives ");
    for (int pos : positives) {
        System.out.print(pos + " ");
    }
    System.out.print("\nnegatives ");
    for (int neg : negatives) {
        System.out.print(neg + " ");
    }
    System.out.println("\nsum closest to 0: " + sum);
}
}