Skip to content

Two heaps problems

These are the problems that generally requires two binary heaps i.e. a min heap and a max heap. We can divide the problem in two parts, we'll use a Min Heap to find the smallest element and a Max Heap to find the biggest element and combine the parts together.

Let's see some questions on this.

Find the Median of a Number Stream

Design a class to calculate the median of a number stream. The class should have the following two methods

  • insertNum(int num): stores the number in the class
  • findMedian(): returns the median of all numbers inserted in the class

Just like a normal median function, if the count of numbers inserted in the class is even, the median will be the average of the middle two numbers.


  1. insertNum(3)
  2. insertNum(1)
  3. findMedian() \(\to\) output: 2
  4. insertNum(5)
  5. findMedian() \(\to\) output: 3
  6. insertNum(4)
  7. findMedian() \(\to\) output: 3.5

Sliding Window Median

Given an array of numbers and a number ‘k’, find the median of all the ‘k’ sized sub-arrays (or windows) of the array.


Input: nums=\([1, 2, -1, 3, 5]\), \(k = 2\)

Output: \([1.5, 0.5, 1.0, 4.0]\)

Explanation: Lets consider all windows of size \(2\):

  1. \([1, 2, -1, 3, 5] \to\) median is \(1.5\)
  2. \([1, 2, -1, 3, 5] \to\) median is \(0.5\)
  3. \([1, 2, -1, 3, 5] \to\) median is \(1.0\)
  4. \([1, 2, -1, 3, 5] \to\) median is \(4.0\)


This comments system is powered by GitHub Discussions