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33 lines
798 B
Markdown
33 lines
798 B
Markdown
---
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title: "heap"
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tags: cosc201 datastructure
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---
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# heap
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A tree where:
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1. every elements should be greater than ites children
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2. the structure should be filled from top to bottom and left to right
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To remove an element
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- remove from the top, replace with the last element
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- to fix the first condition swap the top element with the highest of its children until fixed
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To Add an element
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- add to the next position
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- If its larger than its parent then swap them
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How deep is the tree?
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- each layer is twice as deep and the preceding one
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- layer k can hold $2^k$ elements
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- to store n elements we use k layers where $k = lg n$
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- so we need ϴ(lg n) layers
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- 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)
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