Heap

External

• https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/iIzo8/heaps-operations-and-applications

Internal

• Data Structures
• Tree Concepts
• Tree Representation in Memory
• Heap Sort

Overview

This article is about binary heaps. A binary heap data structure is an array where data is placed to form a complete binary tree, plus the index of the last node in the heap. Each element of the array contains a pointer to tree nodes. Each node contains at least a key. The heap works by comparing key and placing the pointer of the associated nodes in the right position in the heap. Duplicate key values are supported.

More details CLRS page 151, page 1177.

Canonical Use of a Heap

The primary reason to use a heap is if you notice that your program does repeated minimum (maximum) computations, usually via exhaustive search.

Supported Operations

INSERT

Insert a node in the tree. The running time is O(log n) where n is the number of nodes.

Also see:

Data Structures | INSERT

REMOVE-MIN

Remove the node from the heap with minimum key value. The running time is O(log n) where n is the number of nodes.

Also see:

Data Structures | DELETE

Min Heap and Max Heap

A heap is constructed in such a way that it maintains a minimum value or a maximum value, but not both. A heap that maintains the minimum value is called a min heap. A heap that maintains the maximum value is called a max heap. If both extracting minimum and maximum are required, use a binary search tree instead.

HEAPIFY

Initialize the heap in linear time O(n). Using INSERT would take O(n log n), but HEAPIFY does it in O(n) when invoked on a batch of n elements.

DELETE

Delete an arbitrary node in the middle of the heap in O(log n) time. This is useful when implementing Dijkstra's Algorithm

Also see:

Data Structures | DELETE