Given two non-empty arrays of integers, find the pair of values (one value from each array) with the smallest (non-negative) difference.

Example

Input: [1, 3, 15, 11, 2], [23, 127, 235, 19, 8]

Output: [11, 8]; this pair has the smallest difference.

Solution 1. Brute Force approach: Use two for loops

Time complexity: O(n^2)

import java.util.Arrays;

class SmallestDifference {

  public static int[] findSmallestDifferencePair_Naive(int[] a1, int[] a2) {
    double smallestDiff = Double.MAX_VALUE;
    int[] smallestDiffPair = new int[2];

    for(int i = 0; i < a1.length; i++) {
      for(int j = 0; j < a2.length; j++) {
        int currentDiff = Math.abs(a1[i] - a2[j]);
        if(currentDiff < smallestDiff) {
          smallestDiff = currentDiff;
          smallestDiffPair[0] = a1[i];
          smallestDiffPair[1] = a2[j];  
        }
      }
    }
    return smallestDiffPair;
  }

  public static void main(String[] args) {
    int[] a1 = new int[] {-1, 5, 10, 20, 28, 3};
    int[] a2 = new int[] {26, 134, 135, 15, 17};

    int[] pair = findSmallestDifferencePair_Naive(a1, a2);
    System.out.println(pair[0] + " " + pair[1]);
  }
}

Solution 2. Use Sorting

Time complexity: O(mlog(m) + nlog(n))

import java.util.Arrays;

class SmallestDifference {
  public static int[] findSmallestDifferencePair(int[] a1, int[] a2) {
    Arrays.sort(a1);
    Arrays.sort(a2);

    double smallestDiff = Double.MAX_VALUE;
    int[] smallestDiffPair = new int[2];
    int i = 0, j = 0;

    while(i < a1.length && j < a2.length) {
      double currentDiff = Math.abs(a1[i] - a2[j]);
      if(currentDiff < smallestDiff) {
        smallestDiff = currentDiff;
        smallestDiffPair[0] = a1[i];
        smallestDiffPair[1] = a2[j];
      }
      if(a1[i] < a2[j]) {
        i++;
      } else {
        j++;
      }
    }
    return smallestDiffPair;
  }

  public static void main(String[] args) {
    int[] a1 = new int[] {-1, 5, 10, 20, 28, 3};
    int[] a2 = new int[] {26, 134, 135, 15, 17};

    int[] pair = findSmallestDifferencePair(a1, a2);
    System.out.println(pair[0] + " " + pair[1]);
  }
}