CS2420: Lecture 21

1
CS2420 Lecture 21

• Vladimir Kulyukin
• Computer Science Department
• Utah State University

2
Outline

• HeapSort (Chapter 7)
• Binary Heaps as Priority Queues (Chapter 6)

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Notational Convention

• If A is an array that represents a binary heap,
  let mHeapSize be a variable that represents the
  current size of the heap, i.e., the number of
  elements in the array.
• If we wanted to implement a class called
  CBinaryHeap, we may have that class contain 2
  member variables mHeapSize and mArray, the
  second being an array of templatized elements.

4
Building a Heap
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Building a Heap Asymptotic Analysis
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BuildHeap Asymptotic Analysis
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BuildHeap Asymptotic Analysis
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HeapSort
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HeapSort Asymptotic Analysis

• BuildHeap O(N).
• The For-Loop executes N times where N is the
  length of the array A.
• Swap O(1).
• Decrementing HeapSize O(1).
• RestoreHeap O(logN).
• Conclusion HeapSort O(NlogN).