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Heapsort - Algorithms and Abstract Data Structures - Lecture Slides, Slides of Data Structures and Algorithms

Dhirubhai Ambani Institute of Information and Communication TechnologyData Structures and Algorithms

This course covers topics in algorithms and data structures including algorithm analysis, sorting, heaps, binary search trees, hashing techniques and hash tables, and (as time permits) graphs and graph-based algorithms. Key points in these slides are: Heapsort, Heapsort Exercise, Array-Based Heap Implementation, Sorting Algorithms,

Typology: Slides

2012/2013

Uploaded on 09/09/2013

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10/26/10&
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CPSC 223
Algorithms & Data Abstract Structures
Lecture 16: !
Heapsort!
Today …
• Quiz 7!
• Assignments!
– Assignment 7 due Thursday!!
• Note on passing pointers by-reference!
• Heapsort !!!!!!!!!![Sect. 11.2]!
• Heapsort exercise!
CPSC&223&++&Fall&2010& 2&
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Download Heapsort - Algorithms and Abstract Data Structures - Lecture Slides and more Slides Data Structures and Algorithms in PDF only on Docsity!

CPSC 223

Algorithms & Data Abstract Structures

Lecture 16:

Heapsort

Today …

• Quiz 7

• Assignments

  • Assignment 7 due Thursday!

• Note on passing pointers by-reference

• Heapsort [Sect. 11.2]

• Heapsort exercise

CPSC 223 -­‐-­‐ Fall 2010 2

CPSC 223 -­‐-­‐ Fall 2010 3

Heapsort

Heapsort

  • The basic idea:
    • Build a heap out of the unsorted list
    • Create a temporary array
    • Find max value and delete
    • Put max value in last position of temp array
    • Find next max value and delete
    • Put next max value in the next to last position of temp array
    • Repeat until the heap is empty!
  • What is the cost of doing this?
    • O ( n log n ) for building the heap (repeated insertions)
    • O ( n log n ) for repeatedly deleting elements
    • So, O ( n log n ) CPSC 223 -­‐-­‐ Fall 2010 4

Heapsort

  • Building the Heap more efficiently CPSC 223 -­‐-­‐ Fall 2010 7 6 3 5 9 2 10 6 3 5 9 2 10 0 1 2 3 4 5 array = HeapRebuild (array, 6, 2); a semiheap 6 3 10 9 2 5 6 3 10 9 2 5 0 1 2 3 4 5 array =

Heapsort

  • Building the Heap more efficiently CPSC 223 -­‐-­‐ Fall 2010 8 6 3 10 9 2 5 6 3 10 9 2 5 0 1 2 3 4 5 array = HeapRebuild (array, 6, 1); a semiheap 6 9 10 3 2 5 6 9 10 3 2 5 0 1 2 3 4 5 array =

Heapsort

  • Building the Heap more efficiently CPSC 223 -­‐-­‐ Fall 2010 9 6 9 10 3 2 5 6 9 10 3 2 5 0 1 2 3 4 5 array = a semiheap HeapRebuild (array, 6, 0); 10 9 6 3 2 5 10 9 6 3 2 5 0 1 2 3 4 5 array =

Heapsort

  • Building the Heap more efficiently

// building the heap

for(int i = (size-­‐1)/2; i >= 0; i-­‐-­‐)

HeapRebuild (array, size, i);

CPSC 223 -­‐-­‐ Fall 2010 10

Heapsort

CPSC 223 -­‐-­‐ Fall 2010 13 void heapsort(int theArray[], int size) { for(int i = (size-1)/2; i >= 0; i--) // build heapRebuild(theArray, size, i); int last = size-1; for(int j = 1; j < size; j++) { // delete swap(theArray[0], theArray[last]); heapRebuild(theArray, last, 0); last--; } }

Comparison of Sorting Algorithms

CPSC 223 -­‐-­‐ Fall 2010 14 SelecSon Sort Bubble Sort Best Case Average Case Worst Case O ( n^2 ) O ( n^2 ) O ( n^2 ) O ( n ) O ( n^2 ) O ( n^2 ) InserSon Sort O ( n ) O ( n^2 ) O ( n^2 ) Quicksort O ( n log n ) O ( n log n ) O ( n^2 ) Treesort O ( n log n ) O ( n log n ) O ( n^2 ) Heapsort O ( n log n ) O ( n log n ) O ( n log n ) Mergesort O ( n log n ) O ( n log n ) O ( n log n )