Sorting

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Chapter 12 Sorting
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Sort Concepts

• Sorting is a process through which data are
  arranged according to their values.
• It is the most common data-processing
  applications.

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Sort Classifications

• Sorting algorithms are classified as either
  internal or external.
• Internal sort holds all data 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 not 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 Stability

• Sort stability is an attribute of a sort,
  including that data with equal keys maintain
  their relative input order in the output.

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Sort Stability
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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.
• Two classic selection sorts
• Straight selection
• Heap sort.

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Straight Selection Sort

• In the straight selection sort, the list at any
  moment is divided into two sublists, sorted and
  unsorted, which are divided by an imaginary wall.
• 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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Straight Selection Sort
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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
FIGURE 12-5 Heap Representations
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Heap Sort Exchange Process
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Heap Sort Process
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Comparison of Selection Sorts
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Straight Insertion Sort

• In a 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
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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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Shell Sort
N 10 Increment (K) 3
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Shell Sort
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Shell Sort
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Shell Sort
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Comparison of Sorts
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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

• In the bubble sort, 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
FIGURE 12-12 Bubble Sort Concept
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Bubble Sort
FIGURE 12-13 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

• Selects an element, known as pivot.
• Divides the list into three groups
• A partition of elements ? the pivots key
• The pivot element that is placed in its
  ultimately correct location in the list.
• A partition of elements ? the pivots key

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Quick Sort

• The sorting then continues by quick sorting the
  left partition followed by quick sorting the
  right partition.

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Quick Sort
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How to Select a Pivot

• 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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Quick Sort 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
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Quick Sort
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Comparison of Sorts
TABLE 12-3 Sort Comparisons
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External Sorting

• In external sorting, portions of the data may be
  stored in secondary memory during the sorting
  process.

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Merging Ordered Files

• A merge is the process that combines two files
  sorted on a given key into one sorted file on the
  same given key.

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Merging Ordered Files
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Merging Unordered Files

• In a merge sort, we usually have a different
  situation.
• Because the files are unsorted, the data runs in
  sequence, and then there is a sequence break
  followed by another series of data in sequence.

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Merging Unordered Files

• The series of consecutively ordered data in a
  file is known as a merge run.
• A stepdown occurs when the sequential ordering of
  the records in a merge file is broken.

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Merging Unordered Files

• The process of copying a consecutive series of
  records to the merge output file after a stepdown
  in the alternate merge input is known as a
  rollout.

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Merging Unordered Files
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Sorting Process

• The first processing of the data into merge runs
  is known as sort phase.
• Each complete reading and merging of the input
  merge files to one or more output merge files is
  considered a separate merge phase.

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Sorting Process
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Natural Merge

• A natural merge sorts a constant number of input
  merge files to one merge output file.
• Between each merge phase, a distribution phase is
  required to redistribute the merge runs to the
  input files for remerging.

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Natural Merge
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Balanced Merge

• A balanced merge uses a constant number of input
  merge files and the same number of output merge
  files.
• The balanced merge eliminates the distribution
  phase by using the same number of input and
  output merge files.

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Balanced Merge
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Polyphase Merge

• In the polyphase merge, a constant number of
  input files are merged to one output file.
• As the data in each input file are completely
  merged, it immediately becomes the output file
  and what was the output file becomes an input
  file.

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Polyphase Merge Sort
FIGURE 12-22 Polyphase Merge Sort
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External Sort Phase (Heap Sort)

• Use a heap of three nodes to sort the data into
  two merge runs.
• Fill the first merge run with non-decreasing
  number until it is full.
• When the first merge run is full, fill the second
  merge run with non-decreasing number.

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Exercises