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Heap-like Data Structures

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Max Heap

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Back to Heap Data Structures

Binary Heap

A complete binary tree satisfying the heap property — every parent is greater than or equal to its children. Stored efficiently as an array.

Heap Visualization

Speed

Empty heap — insert a value to begin

Array Representation

[ empty ]

Select an operation to begin. Try inserting a few values first.

Complexity

O(log n)

Insert

O(log n)

Extract Root

O(1)

Peek

O(n)

Space (array storage)

Heap Properties

•Complete binary tree — all levels filled except possibly the last, filled left to right
•Heap property — every parent ≥ both children (max-heap)
•Array layout — left child at 2i+1, right at 2i+2, parent at ⌊(i−1)/2⌋
•Height — always O(log n) due to completeness

Applications

•Priority Queues — OS scheduling, event simulation
•Heap Sort — In-place O(n log n) sorting
•Dijkstra's / Prim's — Graph shortest paths and MST
•Median Finding — Two-heap trick for streaming data
•K-way Merge — Merging k sorted arrays efficiently

Active Recall Quiz

Question 1 of 3

For a node at index i (0-indexed) in a binary heap array, what index holds its left child?