Median of Two Sorted Arrays🚚

Question

Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays.

The overall run time complexity should be O(log (m+n)).

Example 1:

Input: nums1 = [1,3], nums2 = [2]
Output: 2.00000
Explanation: merged array = [1,2,3] and median is 2.

Example 2:

Input: nums1 = [1,2], nums2 = [3,4]
Output: 2.50000
Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5.

Constraints:

• nums1.length == m
• nums2.length == n
• 0 <= m <= 1000
• 0 <= n <= 1000
• 1 <= m + n <= 2000
• -106 <= nums1[i], nums2[i] <= 106

Java Solution

Two different solutions with two different time complexities

O(n+n2) where n is the size of array1 and n2 size of array2
In the worst case, the below code will go through all the elements in both the arrays separately so O(n + n2).

Code

O(log min(n,n2))
If array1 has the less numbers of elements, so the below code will apply binary search method on that array, so O(log x) where x is the size of the array which have less number of elements.

Code