Data structures in typescript 13 binary heaps

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data structures in typescript: binary heaps (detailed tutorial)

this tutorial delves deep into binary heaps, a fundamental data structure with various applications, including priority queues, heap sort, and graph algorithms like dijkstra's algorithm. we'll cover the theory, implementation in typescript, and examples.

*1. what are binary heaps?*

a binary heap is a complete binary tree (meaning all levels are filled except possibly the last, which is filled from left to right) that satisfies the *heap property*. there are two main types:

*min heap:* the value of each node is less than or equal to the value of its children. the root node holds the smallest element in the heap.
*max heap:* the value of each node is greater than or equal to the value of its children. the root node holds the largest element in the heap.

*key concepts:*

*complete binary tree:* essential for space efficiency. since it's almost a fully balanced tree, it can be efficiently represented using an array (more on this later).
*heap property:* this is the defining characteristic that ensures the root node (in a min heap) is always the minimum element, allowing for o(1) retrieval. similarly, in a max heap, the root node is the maximum.

*2. why use binary heaps?*

binary heaps provide efficient performance for specific operations:

*finding the minimum/maximum:* o(1) - the root node always contains the smallest (min heap) or largest (max heap) element.
*insertion:* o(log n) - adding a new element.
*deletion of minimum/maximum:* o(log n) - removing the root node and re-heapifying the structure.
*priority queue implementation:* ideal for implementing priority queues due to their efficient extraction of the minimum/maximum element.
*heap sort:* can be used as the basis for an efficient sorting algorithm.

*3. array representation of a binary heap*

a key advantage of a complete binary tree is its efficient array representation ...

#DataStructures #TypeScript #windows
data structures
typescript
binary heaps
heap operations
priority queue
min heap
max heap
heapify
insert element
remove element
time complexity
array representation
tree structure
efficient algorithms
data manipulation