---
title: "heap"
tags: 
- cosc201 
- datastructure
---

A tree where:

1. every elements should be greater than ites children
2. the structure should be filled from top to bottom and left to right


To remove an element

- remove from the top, replace with the last element
- to fix the first condition swap the top element with the highest of its children until fixed


To Add an element

- add to the next position
- If its larger than its parent then swap them


How deep is the tree?

- each layer is twice as deep and the preceding one
- layer k can hold $2^k$ elements
- to store n elements we use k layers where $k = lg n$
- so we need ϴ(lg n) layers
- So any algorithm that 'walk along a branch' in while or in part will have Ο(n) complexity (assuming constant time work at each node)