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CS 332: Algorithms Introduction to heapsort
Review: The Master Theorem ,[object Object],[object Object],[object Object],[object Object]
Review: The Master Theorem ,[object Object]
Sorting Revisited ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],Heaps 16 14 10 8 7 9 3 2 4 1
[object Object],[object Object],Heaps 16 14 10 8 7 9 3 2 4 1 1 1 1 1 1
Heaps ,[object Object],16 14 10 8 7 9 3 2 4 1 A = = 16 14 10 8 7 9 3 2 4 1
Heaps ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],16 14 10 8 7 9 3 2 4 1 A = = 16 14 10 8 7 9 3 2 4 1
Referencing Heap Elements ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Heap Property ,[object Object],[object Object],[object Object],[object Object]
Heap Height ,[object Object],[object Object],[object Object],[object Object],[object Object]
Heap Operations: Heapify() ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Heap Operations: Heapify() ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Heapify() Example 16 4 10 14 7 9 3 2 8 1 16 4 10 14 7 9 3 2 8 1 A =
Heapify() Example 16 4 10 14 7 9 3 2 8 1 16 10 14 7 9 3 2 8 1 A = 4
Heapify() Example 16 4 10 14 7 9 3 2 8 1 16 10 7 9 3 2 8 1 A = 4 14
Heapify() Example 16 14 10 4 7 9 3 2 8 1 16 14 10 4 7 9 3 2 8 1 A =
Heapify() Example 16 14 10 4 7 9 3 2 8 1 16 14 10 7 9 3 2 8 1 A = 4
Heapify() Example 16 14 10 4 7 9 3 2 8 1 16 14 10 7 9 3 2 1 A = 4 8
Heapify() Example 16 14 10 8 7 9 3 2 4 1 16 14 10 8 7 9 3 2 4 1 A =
Heapify() Example 16 14 10 8 7 9 3 2 4 1 16 14 10 8 7 9 3 2 1 A = 4
Heapify() Example 16 14 10 8 7 9 3 2 4 1 16 14 10 8 7 9 3 2 4 1 A =
Analyzing Heapify(): Informal ,[object Object],[object Object],[object Object]
Analyzing Heapify(): Formal ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Analyzing Heapify(): Formal ,[object Object],[object Object],[object Object],[object Object],[object Object]
Heap Operations: BuildHeap() ,[object Object],[object Object],[object Object],[object Object],[object Object]
BuildHeap() ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
BuildHeap() Example ,[object Object],4 1 3 2 16 9 10 14 8 7
Analyzing BuildHeap() ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Analyzing BuildHeap(): Tight ,[object Object],[object Object],[object Object],[object Object],[object Object]
Heapsort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Heapsort ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Analyzing Heapsort ,[object Object],[object Object],[object Object]
Priority Queues ,[object Object],[object Object],[object Object],[object Object],[object Object]
Priority Queue Operations ,[object Object],[object Object],[object Object],[object Object]

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lecture 5