quartz/content/notes/heap.md

title	draft
Heap	true

Heap

A tree

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

• 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

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

How deep

• 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)