Efficiently Computing the Running Median in TypeScript Using Heaps

A Step-by-Step Guide to Calculating the Running Median of a Number Stream with Optimized Algorithms

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Problem

Compute the running median of a sequence of numbers. That is, given a stream of numbers, print out the median of the list so far on each new element.

Recall that the median of an even-numbered list is the average of the two middle numbers.

For example, given the sequence [2, 1, 5, 7, 2, 0, 5], your algorithm should print out:

2
1.5
2
3.5
2
2
2

Problem Breakdown

Median Definition:

For an odd-sized list, the median is the middle element.

For an even-sized list, the median is the average of the two middle elements.

Efficient Calculation:

We need to efficiently insert numbers into the list and then quickly find the median after each insertion.

Maintaining a sorted list would work, but re-sorting the list after each insertion is costly (O(n log n)).