Objectives

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Chapter 12
Sorting(1)
Objectives

• Upon completion you will be able to
• Understand the basic concepts of internal and
  external sorts
• Discuss the relative efficiency of different
  sorts
• Recognize and discuss selection, insertion and
  exchange sorts
• Discuss the design and operation of external
  sorts
• Recognize natural, balanced, and polyphase merge
  sorts

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12-1 Sort Concepts

• Sorts arrange data according to their value. In
  this chapter, we discuss both internal and
  external sorts. We divide internal sorts into
  three categories-insertion, selection, and
  exchange-and discuss two different sorts in each
  classification. At the end of the chapter we
  discuss natural, balanced, and polyphase external
  sorts. We begin with a discussion of several sort
  concepts in Section 12.1.
• Sort Order
• Sort Stability
• Sort Efficiency
• Passes
• Sorts and ADTs

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Sort concepts

• Sort
• The process through which data are arranged
  according to their values.
• Sorting is one of the most common data-processing
  applications.

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Sort classifications

• Sorting algorithms are classified as either
  internal or external.
• Internal sort
• All data are hold in primary memory during the
  sorting process.
• External sort
• Uses primary memory for the data currently being
  sorted and secondary storage for any data that
  does fit in primary memory.

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Sort classifications
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Sort order

• The sort order identifies the sequence of sorted
  data, ascending or descending.

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Sort Staility

• The sort order identifies the sequence of sorted
  data, ascending or descending.

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Sort efficiency

• Sort efficiency is a measure of the relative
  efficiency of a sort.
• Quick sort (best)
• O(n logn)

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Passes

• During the sorting process, the data traversed
  many times.
• Each traversal of the data is referred as a sort
  pass.

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12-2 Selection Sorts

• In each pass of the selection sort, the smallest
  element is selected from the unsorted sublist and
  exchanged with the element at the beginning of
  the unsorted list. We discuss two classic
  selection sorts, straight selection and heap
  sort.
• Straight Selection Sort
• Heap Sort
• Selection Sort Efficiency
• Selection Sort Implementation

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Selection sorts

• Selection sorts are among the most intuitive of
  all sorts.
• Straight Selection Sort
• Heap sort
• In each pass of the selection sort, the smallest
  element is selected from the unsorted sublist and
  exchanged with the element at the beginning of
  the unsorted list.

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Straight selection sort
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Selection sort
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Selection sort algorithm
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9-1 Basic Concepts

• A heap is a binary tree whose left and right
  subtrees have values less than their parents. We
  begin with a discussion of the basic heap
  structure and its two primary operations, reheap
  up and reheap down.
• Definition
• Maintenance Operations

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Definition

• A heap is a binary tree structure with the
  following properties
• The tree is complete or nearly complete.
• The key value of each node is greater than or
  equal to the key value in each of its descendents.

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Heap trees
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Invalid heaps
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Maintenance operations

• Reheap up
• Reorders a broken heap by floating the last
  element up the tree until it is in its correct
  location in the heap.
• Reheap down
• Reorders a broken heap by pushing the last
  element up the tree until it is in its correct
  location in the heap.

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Reheap up operation
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Reheap up example
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Reheap down operation
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Reheap down example
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9-2 Heap Implementation

• Heaps are usually implemented in an array
  structure. In this section we discuss and develop
  five heap algorithms.
• Reheap Up
• Reheap Down
• Build a Heap
• Insert a Node into a Heap
• Delete a Node from a Heap

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Heap in arrays
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Building a heap
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Insert node
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Insert node
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Delete node
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Delete node
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Heap sort

• The heap sort is an improved version of the
  selection sort in which the largest element (the
  root) is selected and exchanged with the last
  element in the unsorted list.

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Heap representations
23, 78, 45, 8, 32, 56.
78
32
56
8
23
45
0
1
2
3
4
5
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Heap sort exchange process
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Heap sort process
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Selection sort efficiency

• The straight selection sort efficiency is O(n2).
• The heap sort efficiency is O(n log n)

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Selection sort implementation
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Heap sort implementation
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12-3 Insertion Sorts

• In each pass of an insertion sort, one or more
  pieces of data are inserted into their correct
  location in an ordered list.
• In this section we study two insertion sorts the
  straight insertion sort and the shell sort.
• Straight Insertion Sort
• Shell Sort
• Insertion Sort Efficiency
• Insertion Sort Implementation

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Straight insertion sort

• The list at any moment is divided into sorted and
  unsorted sublists.
• In each pass the first element of the unsorted
  sublist is inserted into the sorted sublist.

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Straight insertion sort
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Straight insertion sort example
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Shell sort

• The shell sort is an improved version of the
  straight insertion sort in which diminishing
  partitions are used to sorted the data.

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Segmented array

• N 10
• Increment (K) 3

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Diminishing increments in shell sort
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Diminishing increments in shell sort
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Diminishing increments in shell sort
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Diminishing increments in shell sort
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incre current hold walker hold key walker key
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Ordered segment in a Shell sort
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Straight insertion sort efficiency

• O(N2)

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Shell sort efficiency

• O(N1.25)

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Comparison of insertion and selection sorts
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12-4 Exchange Sorts

• Bubble Sort
• Quick Sort
• Exchange Sort Efficiency
• Sort Summary
• Exchange Sort Implementation

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Exchanged sort

• In exchange sorts we exchange elements that are
  out of order until the entire list is sorted.
• Bubble sort
• Quick sort

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Bubble sort concept

• The list in any moment is divided into two
  sublists sorted and unsorted.
• The smallest element is bubbled from the unsorted
  sublist and moved to the sorted sublist.

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Bubble sort example
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Quick sort

• Quick sort is an exchange sort in which a pivot
  key is placed in its correct position in the
  array while rearranging other elements widely
  dispersed across the list.

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Quick sort

• Each iteration of the quick sort
• selects an element, known as pivot, and
• Divides the list into three groups
• 1. A partition of elements lt the pivots key
• 2. The pivot element that is placed in its
  ultimately correct location in the list
• 3. A partition of elements ? the pivots key
• The sorting then continues by quick sorting the
  left partition followed by quick sorting the
  right partition.

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Quick sort partitions
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How to select a prvot

• C. A. R. Hoare (1962)
• the first element in the list
• R. C. Singleton (1969)
• the median value of left, right and middle
  elements in the list

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Note

• Knuth suggests that when the sort partition
  becomes small a straight insertion sort be used
  to complete the sorting of the partition.
• The authors of our textbook recommend 16.

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Quick sort algorithm

• Quick sort algorithm
• Straight insertion module (supporting)
• Determine median of three (supporting)

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Quick sort pivot
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Quick sort operation
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Exchange sort efficiency

• The bubble sort efficiency is O(n2).
• The quick sort efficiency is O(n log n).

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Sort comparisons
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