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Solution: Sliding Window Median

Explore how to efficiently calculate the median for each sliding window of size k in an integer array using max and min heaps. Understand balancing heaps, lazy removals with hash maps, and improve time complexity compared to naive sorting approaches through this step-by-step solution.

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 10510^{-5} of the actual value will be accepted.

Constraints:

  • 11 \leq k \leq nums.length 103\leq 10^3
  • 231-2^{31} \leq
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