What is the optimal time complexity of solving Median of Two Sorted Arrays?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Median of Two Sorted Arrays?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Median of Two Sorted Arrays?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Median of Two Sorted Arrays?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Median of Two Sorted Arrays

Learn how to solve the 'Median of Two Sorted Arrays' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

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)).

Write a function findMedianSortedArrays(nums1: List[int], nums2: List[int]) -> float.

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

Examples

Example 1

Input

nums1 = [1, 3], nums2 = [2]

Output

2.0

Explanation

Merged array = [1, 2, 3]. The median is 2.0.

Example 2

Input

nums1 = [1, 2], nums2 = [3, 4]

Output

2.5

Explanation

Merged array = [1, 2, 3, 4]. The median is (2 + 3) / 2 = 2.5.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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