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Sliding Window Median

Explore how to solve the sliding window median problem by applying heaps for dynamic data handling. Understand how to move a fixed-size window across an array and compute medians efficiently using heap operations, helping you master this pattern useful in many coding interviews.

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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 10−510^{-5} of the actual value will be accepted.

Constraints:

  • 1≤1 \leq k ≤\leq nums.length ≤103\leq 10^3
  • −231≤-2^{31} \leq nums[i] ≤231−1\leq 2^{31} - 1

Examples

Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Sliding Window Median

1.

What should be the output if the following array and value of k are given as input?

nums = [1, 1, 1, 1, 1, 1]

k = 3

A.

[1.0, 1.0, 1.0, 1.0]

B.

[1.5, 1.5, 1.5, 1.5]

C.

[1.0, 1.0, 1.0, 1.0, 1.0]

D.

[1.5, 1.5, 1.5, 1.5, 1.5]

1 / 3

Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
1
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7

Try it yourself

Implement your solution in the following coding playground:

Java
usercode > SlidingWindow.java
import java.util.*;
public class SlidingWindow{
   public static double[] medianSlidingWindow(int[] nums, int k) {
      
      // Replace this placeholder return statement with your code
         
      return new double[]{};
   }
}
Sliding Window Median