Find Median From Data Stream

Problem

Design a data structure that supports adding numbers from a stream one at a time and, at any point, can efficiently return the median of all numbers seen so far.

Examples

Example 1

Input:addNum(1); addNum(2); findMedian()

Output:1.5

Example 2

Input:addNum(3); findMedian()

Output:2

Constraints

-10^5 <= num <= 10^5
Up to 5 * 10^4 calls total.

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How to approach it: the Heap / Priority Queue pattern

A heap keeps the minimum (or maximum) element accessible in O(1), with O(log n) insert and remove. It's the tool whenever you repeatedly need "the smallest/largest remaining item" without needing everything fully sorted.

Look for this pattern when

You need the top-k largest/smallest elements, not a full sort.
You're merging multiple sorted sequences (always take the smallest available head).
You need a running min/max/median as data streams in.

Read the full Heap / Priority Queue guide →

Video walkthroughs

Original problem on LeetCode ↗