Solution: Sliding Window Median

Explore how to solve the sliding window median problem by applying the heaps data structure pattern. Understand managing two heaps—a max-heap for smaller elements and a min-heap for larger ones—to find medians efficiently as the window slides. Learn balancing heaps and using a hash map to handle element removals with improved time complexity.

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Statement
Solution
- Naive approach
- Optimized approach using heaps

Statement

Given an integer array, nums, and an integer, k, there is a sliding window of size k, which is moving from the very left to the very right of the array. We can only see the k numbers in the window. Each time the sliding window moves right by one position.

Given this scenario, return the median of the each window. Answers within $10^{-5}$ of the actual value will be accepted.

Constraints:

$1 \leq$ k $\leq$ nums.length $\leq 10^3$
$-2^{31} \leq$

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