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Median of Two Sorted Arrays

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 12
I'll reformat these additional problems to match the sample format:

Write a C++ program to find the median of two sorted arrays. 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: 
      

    • Step 1: Design a binary search approach to find the correct partition point.
      • 

    • Step 2: Partition both arrays such that elements to the left form the first half of the merged array.
      • 

    • Step 3: Find the median using the maximum of left elements and minimum of right elements.
      • 

    • Step 4: For this example, the merged array would be [1,2,3] and the median is 2.
      • 

    •
Example 2
    

  • Input: nums1 = [1,2], nums2 = [3,4]
    • 

  • Output: 2.50000
    • 

  • Explanation: 
      

    • Step 1: Design a binary search approach to find the correct partition point.
      • 

    • Step 2: Partition both arrays such that elements to the left form the first half of the merged array.
      • 

    • Step 3: Find the median using the maximum of left elements and minimum of right elements.
      • 

    • Step 4: For this example, the merged array would be [1,2,3,4] and the median is (2 + 3) / 2 = 2.5.
      • 

    •
Constraints
    

  • nums1.length == m
    • 

  • nums2.length == n
    • 

  • 0 ≤ m ≤ 1000
    • 

  • 0 ≤ n ≤ 1000
    • 

  • 1 ≤ m + n ≤ 2000
    • 

  • -10^6 ≤ nums1[i], nums2[i] ≤ 10^6
    • 

  • Time Complexity: O(log(min(m,n)))
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Binary search can be applied to the smaller array
    • 
  
  • The problem can be reframed as finding the correct partition point
    • 
  
  • Think about how medians divide arrays into equal halves
    • 
  
  • Consider both even and odd total lengths
    • 
  
  • Use the property that elements on the left side are all smaller than elements on the right side
    •

Steps to solve by this approach:

 Step 1: Ensure we binary search on the smaller array (nums1) for efficiency.
 Step 2: For each partition in nums1 (partitionX), calculate the corresponding partition in nums2 (partitionY).
 Step 3: Find the maximum elements on the left side and minimum elements on the right side of both partitions.
 Step 4: Check if we've found the correct partition (maxX ≤ minY and maxY ≤ minX).
 Step 5: If correct partition is found, calculate median based on whether total length is odd or even.
 Step 6: Adjust the binary search range based on comparison of maxX and minY if needed.
 Step 7: Continue the binary search until the correct partition is found.

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