Interview Question Median of Two Sorted Arrays

By Fatih KABAKCI

The problem is finding the median value of two sorted arrays. As everyone knows, median value is the middle element of a group of sorted data. If that collection of data has even number of elements, the middle value is the average of two middle values of that collection. For the main solution, we can create a new array to copy of the elements of both previous arrays. After we sort the array, the new median value of the final array is going to be found easily. Solution in Java has been shared below.

Problem #4 - Median of Two Sorted Arrays

Description: Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).

Difficulty: Hard

Solution in Java

package com.fatihkabakci.Hard.MedianTwoSortedArr;

import java.util.Arrays;

/**
 * 
 * @author fkabakci
 * Problem Description: There are two sorted arrays nums1 and nums2 of size m and n respectively.
 * Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).
 * 
 * Examples:
 * 
 * nums1 = [1, 3]
 * nums2 = [2]
 * The median is 2.0
 * 
 * nums1 = [1, 2]
 * nums2 = [3, 4]
 * The median is (2 + 3) / 2 = 2.5
 * 
 * Solution:
 * 
 * 1. Create a new third array.
 * 2. Copy of the all elements of the first array to the third array.
 * 3. Do the second operation for the second array as well.
 * 4. Sort the new array.
 * 5. Find the median value of the new array.
 *
 */
public class MedianOfTwoSortedArrays {
	public double median(int[] nums) {
		int l = nums.length;
		if (l == 0)
			return 0;
		else if(l == 1)
			return nums[0];
		
		int h = l / 2;
		
		if (l % 2 == 0)
			return (nums[h - 1] + nums[h]) / 2.0;
		return nums[h];
	}
	
	public double findMedianSortedArrays(int[] nums1, int[] nums2) {
		int m = nums1.length, n = nums2.length, sum = m + n;
		int[] nums = new int[sum];
		// copy of 1st array
		for(int i = 0; i < m; i++) {
			nums[i] = nums1[i];
		}
		// copy of 2nd array
		for(int i = m; i < sum; i++) {
			nums[i] = nums2[i - m];
		}
		Arrays.sort(nums);
		return median(nums);
    }

	public static void main(String[] args) {
		int[] nums1 = {2};
		int[] nums2 = {};
		MedianOfTwoSortedArrays a = new MedianOfTwoSortedArrays();
		double r = a.findMedianSortedArrays(nums1, nums2);
		System.out.println(r);
	}
}