Sorting Chapter 12 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 Data Structures: A Pseudocode Approach with C, Second Edition

12-1 Sort Concepts Sort Order Sort Stability Sort Efficiency Passes 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 Data Structures: A Pseudocode Approach with C, Second Edition

Sort concepts Sort The process through which data are arranged according to their values. Sorting is one of the most common data-processing applications. Data Structures: A Pseudocode Approach with C, Second Edition

Sort classifications Data Structures: A Pseudocode Approach with C, Second Edition

Sort order The sort order identifies the sequence of sorted data, ascending or descending. Data Structures: A Pseudocode Approach with C, Second Edition

Sort order Data Structures: A Pseudocode Approach with C, Second Edition

Sort stability Sort stability is an attribute of a sort, indicating that data with equal keys maintain their relative input order in the output. Data Structures: A Pseudocode Approach with C, Second Edition

Sort efficiency Sort efficiency is a measure of the relative efficiency of a sort. Quick sort (best) Data Structures: A Pseudocode Approach with C, Second Edition

Passes During the sorting process, the data traversed many times. Each traversal of the data is referred as a sort pass. Data Structures: A Pseudocode Approach with C, Second Edition

12-2 Selection 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. We discuss two classic selection sorts, straight selection and heap sort. Straight Selection Sort Heap Sort Selection Sort Efficiency Selection Sort Implementation Data Structures: A Pseudocode Approach with C, Second Edition

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. Data Structures: A Pseudocode Approach with C, Second Edition

Straight selection sort Data Structures: A Pseudocode Approach with C, Second Edition

Selection sort Data Structures: A Pseudocode Approach with C, Second Edition

Selection sort algorithm Data Structures: A Pseudocode Approach with C, Second Edition

Selection sort algorithm Data Structures: A Pseudocode Approach with C, Second Edition

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. Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Heap sort exchange process Data Structures: A Pseudocode Approach with C, Second Edition

Heap sort process Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Selection sort efficiency The straight selection sort efficiency is O(n2). The heap sort efficiency is O(n log n) Data Structures: A Pseudocode Approach with C, Second Edition

Selection sort implementation Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Heap sort implementation Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

12-3 Insertion Sorts Straight Insertion Sort Shell Sort 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 Data Structures: A Pseudocode Approach with C, Second Edition

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. Data Structures: A Pseudocode Approach with C, Second Edition

Straight insertion sort Data Structures: A Pseudocode Approach with C, Second Edition

Straight insertion sort example Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Shell sort The shell sort is an improved version of the straight insertion sort in which diminishing partitions are used to sorted the data. Data Structures: A Pseudocode Approach with C, Second Edition

Segmented array N = 10 Increment (K) = 3 Data Structures: A Pseudocode Approach with C, Second Edition

Diminishing increments in shell sort Data Structures: A Pseudocode Approach with C, Second Edition

Diminishing increments in shell sort Data Structures: A Pseudocode Approach with C, Second Edition

Diminishing increments in shell sort Data Structures: A Pseudocode Approach with C, Second Edition

Diminishing increments in shell sort Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Straight insertion sort efficiency Data Structures: A Pseudocode Approach with C, Second Edition

Shell sort efficiency O(N1.25) Data Structures: A Pseudocode Approach with C, Second Edition

Comparison of insertion and selection sorts Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

12-4 Exchange Sorts Bubble Sort Quick Sort Exchange Sort Efficiency Sort Summary Exchange Sort Implementation Data Structures: A Pseudocode Approach with C, Second Edition

Exchanged sort In exchange sorts we exchange elements that are out of order until the entire list is sorted. Data Structures: A Pseudocode Approach with C, Second Edition

Bubble sort Data Structures: A Pseudocode Approach with C, Second Edition

Bubble sort concept Data Structures: A Pseudocode Approach with C, Second Edition

Bubble sort example Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

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. Data Structures: A Pseudocode Approach with C, Second Edition

Quick sort Each iteration of the quick sort selects an element, known as pivot, and Divides the list into three groups A partition of elements < the pivot’s key The pivot element that is placed in its ultimately correct location in the list A partition of elements ≧ the pivot’s key The sorting then continues by quick sorting the left partition followed by quick sorting the right partition. Data Structures: A Pseudocode Approach with C, Second Edition

Quick sort partitions Data Structures: A Pseudocode Approach with C, Second Edition

Quick sort algorithm Straight insertion module Determine median of three Quick sort algorithm Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Quick sort pivot Data Structures: A Pseudocode Approach with C, Second Edition

Quick sort operation Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Exchange sort efficiency The bubble sort efficiency is O(n2). The quick sort efficiency is O(n log n). Data Structures: A Pseudocode Approach with C, Second Edition

Sort comparisons Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

12-5 External Sorts Merging Ordered Files Merging Unordered Files In external sorting portions of the data may be stored in secondary memory during the sorting process. Included in this section is a discussion of file merging and three external sort approaches-natural, balanced, and polyphase. Merging Ordered Files Merging Unordered Files The Sorting Process Sort Phase Revisited Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

12-6 Quick Sort Efficiency We revisit the general approach to analyzing algorithm efficiency with an in-depth discussion of the quick sort's efficiency. Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition

Data Structures: A Pseudocode Approach with C, Second Edition