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Sliding Window Median

Understand how to calculate the median of each sliding window in an integer array using heap data structures. Learn to efficiently update the median as the window moves right, managing the data dynamically within set constraints.

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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.
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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