Problem Statement

There are two sorted arrays nums1 and nums2 of size n and m respectively. Find the median of the two sorted arrays. You may assume nums1 and nums2 cannot both be empty.

Examples

Example 1

nums1 = [1, 3] nums2 = [2] The median is 2.0

Example 2

nums1 = [1, 2] nums2 = [3, 4] The median is (2 + 3)/2 = 2.5

Approach 1: Merge Arrays

Since both input arrays are already sorted, a naive solution would be to merge the arrays by iterating through each and inserting the items into a new array. Then calculate the median.

Algorithm

initialize i and j to 0
initialize length of new array to the sum of the length the input arrays
initialize an empty array

while i is less then length of nums1 or j is less than length of nums2
    if all elements from nums1 have been merged
        merge element nums2[j]
        increment j
    else if all elements from nums2 have been merged
        merge element nums1[i]
        increment i
    else
        if element nums1[i] <= element nums2[j]
            merge element nums1[i]
            increment i
        else
            merge element nums2[j]
            increment j
find midpoint (length / 2)
if length is even
    return the average of merged_array[mid] and merged_array[mid - 1]
else
    return merged_array[mid]

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