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CS 3343 Analysis of Algorithms Heapsort – 1 Heapsort Binary Heaps The Heap Property Building a Heap Heapsort Priority Queues

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Page 1: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

CS 3343 Analysis of Algorithms Heapsort – 1

Heapsort

Binary Heaps

The Heap Property

Building a Heap

Heapsort

Priority Queues

Page 2: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Illustration of a Max-heap

⊲ Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 2

Page 3: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Parent Left Right

Illustration

⊲Parent Left

Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 3

Page 4: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heap Property

Illustration

Parent Left Right

⊲ Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 4

Page 5: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Max-Heapify

Illustration

Parent Left Right

Heap Property

⊲ Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 5

Page 6: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Max-Heapify Illustration

Illustration

Parent Left Right

Heap Property

Max-Heapify

⊲ Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 6

Page 7: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Build-Max-Heap

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

⊲ Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 7

Page 8: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Build-Max-Heap Illustration, Part 1

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

⊲Build-Max-Heap

1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 8

Page 9: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Build-Max-Heap Illustration, Part 2

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

⊲Build-Max-Heap

2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 9

Page 10: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heapsort Algorithm

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

⊲ Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 10

Page 11: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heapsort Illustration, Part 1

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

⊲ Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 11

Page 12: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heapsort Illustration, Part 2

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

⊲ Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 12

Page 13: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Priority Queue Operations

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

⊲ Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 13

Page 14: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heap-Extract-Max

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

⊲Heap-Extract-

Max

Heap-Increase-Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 14

Page 15: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heap-Increase-Key

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

⊲Heap-Increase-

Key

Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 15

Page 16: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Max-Heap-Insert

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

⊲ Max-Heap-Insert

Heap-Increase-Key 2

CS 3343 Analysis of Algorithms Heapsort – 16

Page 17: Heapsortbylander/cs3343/notes/heapsort.pdfMax-Heapify Max-Heapify2 Build-Max-Heap Build-Max-Heap1 Build-Max-Heap2 Heapsort Heapsort1 Heapsort2 PriorityQueue Heap-Extract-Max Heap-Increase-Key

Heap-Increase-Key Illustration

Illustration

Parent Left Right

Heap Property

Max-Heapify

Max-Heapify 2

Build-Max-Heap

Build-Max-Heap 1

Build-Max-Heap 2

Heapsort

Heapsort 1

Heapsort 2

Priority Queue

Heap-Extract-Max

Heap-Increase-Key

Max-Heap-Insert

⊲

Heap-Increase-

Key

2

CS 3343 Analysis of Algorithms Heapsort – 17


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