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A binary heap is a complete binary tree that satisfies the heap property: the key in each node is either greater than or equal to (max-heap) or less than or equal to (min-heap) the keys in the node's children. Learn how to insert, extract, decrease-key and merge elements in a binary heap with O (log n) time complexity.
A heap is a tree-based data structure that satisfies the heap property: the key of a parent node is always greater than or equal to the key of its child node in a max heap, or vice versa in a min heap. Learn about the operations, implementation, and variants of heaps, and how they are used in sorting and graph algorithms.
Heapsort is an in-place algorithm that divides its input into a sorted and an unsorted region, and iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. It uses a binary heap data structure to efficiently find the largest element in each step, and has a worst-case runtime of O (n log n).
An associative array, also known as a map, is an abstract data type that stores a collection of (key, value) pairs. Learn about its operations, properties, applications, and implementations using hash tables, search trees, and other methods.
A trie is a type of k-ary search tree that stores keys, usually strings, based on their characters. Tries support efficient operations such as insertion, deletion, and lookup of strings, and can be used for applications such as spell checking and autocompletion.
The user can search for elements in an associative array, and delete elements from the array. The following shows how multi-dimensional associative arrays can be simulated in standard AWK using concatenation and the built-in string-separator variable SUBSEP:
A min-max heap is a binary tree data structure that combines a min-heap and a max-heap, allowing constant time retrieval and logarithmic time removal of both the minimum and maximum elements. Learn how to build, insert, delete, and perform other operations on min-max heaps with examples and algorithms.
An array is a data structure consisting of a collection of elements, each identified by an index or key. Arrays are used for various purposes, such as vectors, matrices, tables, and control flow, and have different indexing methods and implementations.