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Median of Two Sorted Arrays

Certification: Advanced Level Accuracy: 17.65% Submissions: 17 Points: 12

Write a Java program to find the median of two sorted arrays of different sizes. The median is the middle value of a set of numbers arranged in order. If the set has an even number of elements, the median is the average of the two middle values.

Example 1
    
  
  • Input: nums1 = [1, 3], nums2 = [2]
    • 
  
  • Output: 2.0
    • 
  
  • Explanation: 
    • Merge the two arrays: [1, 2, 3]. 
    • The merged array has odd length (3), so the median is the middle element, which is 2.0.
    •
Example 2
    
  
  • Input: nums1 = [1, 2], nums2 = [3, 4]
    • 
  
  • Output: 2.5
    • 
  
  • Explanation:
    •  Merge the two arrays: [1, 2, 3, 4]. 
    • The merged array has even length (4), so the median is the average of the two middle elements: (2 + 3) / 2 = 2.5.
    •
Constraints
    
  
  • nums1.length + nums2.length >= 1
    • 
  
  • nums1.length, nums2.length <= 1000
    • 
  
  • -10^6 <= nums1[i], nums2[i] <= 10^6
    • 
  
  • Both nums1 and nums2 are sorted in non-decreasing order
    • 
  
  • Time Complexity: O(log(m+n)) where m and n are the sizes of the arrays
    • 
  
  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Do not merge the arrays as it would result in O(m+n) time complexity
    • 
  
  • Instead, use binary search to find the correct partition
    • 
  
  • Partition both arrays such that the left half elements are less than or equal to right half elements
    • 
  
  • Calculate the median using the maximum of left halves and minimum of right halves
    • 
  
  • Handle odd and even total lengths separately
    • 
  
  • Be careful about edge cases when one array is empty or much smaller than the other
    •

Steps to solve by this approach:

 Step 1: Ensure the first array is smaller than the second one for simplification.

 Step 2: Use binary search to find the correct partition in the smaller array.

 Step 3: Calculate the corresponding partition in the larger array.

 Step 4: Check if the partition is correct by comparing the max element of left half with min element of right half.

 Step 5: If partition is correct, calculate the median based on whether the total length is odd or even.

 Step 6: If partition is not correct, adjust the search range and try again.

 Step 7: Handle edge cases where one array might be empty or much smaller than the other.

Submitted Code :