HARD NC#34 Binary Search
4. Median of Two Sorted Arrays
📖 Problem
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)).
🧠 Visual Learning Aid
1 Model the input into the right structure
2 Choose the core technique and invariant
3 Execute step-by-step with a sample
4 Validate complexity and edge cases
JS/TS Refreshers
- •Array methods (`push`, `pop`, `shift`, `slice`)
- •Object/Map/Set usage patterns
- •Function parameter and return typing
- •In-place array updates
- •Sorted array traversal
- •Boundary condition checks
Logical Thinking Concepts
- •Define invariants before coding
- •Check edge cases first (`[]`, single element, duplicates)
- •Estimate time/space before implementation
- •Apply Two Pointers reasoning pattern
- •Apply Binary Search reasoning pattern
💡 Approach
- → Use binary search to partition both arrays into left and right halves
- → Ensure all elements in left half are less than or equal to elements in right half
- → If total length is odd, median is min of right halves; if even, average of max left and min right
- → Always binary search on the smaller array for efficiency
- → Time: O(log(min(m,n))), Space: O(1)
🧭 Prerequisites
🛠️ Hints & Pitfalls
Hints
- •Use binary search to partition both arrays into left and right halves
- •Ensure all elements in left half are less than or equal to elements in right half
- •If total length is odd, median is min of right halves; if even, average of max left and min right
Common Pitfalls
- •Always binary search on the smaller array for efficiency
- •Time: O(log(min(m,n))), Space: O(1)
🧪 Test Cases
Hidden tests on submit: 4
Test Case 1
Not run Input:
findMedianSortedArrays([1,3], [2]); Expected:
2 Test Case 2
Not run Input:
findMedianSortedArrays([1,2], [3,4]); Expected:
2.5 Test Case 3
Not run Input:
findMedianSortedArrays([0,0], [0,0]); Expected:
0 📝 Code Editor
📤 Output