Heap
External
- https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/iIzo8/heaps-operations-and-applications
- https://www.coursera.org/learn/algorithms-graphs-data-structures/lecture/KKqlm/heaps-implementation-details-advanced-optional
Internal
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.
Another name used for heaps are priority queues.
More details CLRS page 151, page 1177.
Canonical Uses 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.
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Supported Operations
INSERT
Insert a node in the tree. The running time is O(log n) where n is the number of nodes.
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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.
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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 and supports the REMOVE-MIN operation. A heap that maintains the maximum value is called a max heap and supports the REMOVE-MAX operation. 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
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Representation in Memory
A heap has two conceptual representations: one is a rooted binary tree, as complete as possible, and the other one is an array.