searching chapter 18 copyright ©2012 by pearson education, inc. all rights reserved

Searching

Chapter 18

Copyright ©2012 by Pearson Education, Inc. All rights reserved

Contents

• The Problem

• Searching an Unsorted Array An Iterative Sequential Search of an Unsorted

Array A Recursive Sequential Search of an

Unsorted Array The Efficiency of a Sequential Search of an

Array


Contents

• Searching a Sorted Array A Sequential Search of a Sorted Array A Binary Search of a Sorted Array Java Class Library: The Method binarySearch

The Efficiency of a Binary Search of an Array


Contents

• Searching an Unsorted Chain An Iterative Sequential Search of an Unsorted

Chain A Recursive Sequential Search of an

Unsorted Chain The Efficiency of a Sequential Search of a

Chain


Contents

• Searching a Sorted Chain A Sequential Search of a Sorted Chain A Binary Search of a Sorted Chain

• Choosing a Search Method


Objectives

• Search an array by using a sequential search

• Search an array by using a binary search

• Search a chain of linked nodes sequentially

• Describe time efficiency of a search


The Problem


Figure 18-1 Searching is an everyday occurrence

Searching an Unsorted Array

• Iterative search, unsorted array


Figure 18-2 An iterative sequential search of an array that (a) finds its target;


Figure 18-2 An iterative sequential search of an array that (b) does not find its target


Recursive Sequential Search of an Unsorted Array


Figure 18-3 A recursive sequential search of an array that (a) finds its target;


Figure 18-3 A recursive sequential search of an array that (b) does not find its target


Recursive Sequential Search of an Unsorted Array

• Efficiency of a sequential search of an array


Sequential Search of a Sorted Array

• Sequential search can be more efficient if the data is sorted.


Figure 18-4 Coins sorted by their mint dates

Binary Search of a Sorted Array


Figure 18-5 Ignoring one half of the data when the data is sorted


• Algorithm for binary search


Figure 18-6 A recursive binary search of a sorted array that (a) finds its target;


Figure 18-6 A recursive binary search of a sorted array that (b) does not find its target



• Implementation of a sorted list

• Method contains that will call binarySearch



• Implementation of binarySearch


Java Class Library: The Method binarySearch

• Class Arrays contains versions of static method Note specification


Efficiency of a Binary Search of an Array

• Given n elements to be searched

• Number of recursive calls is of order log2 n


Iterative Sequential Search of an Unsorted Chain


Figure 18-7 A chain of linked nodes that contain the entries in a list

Iterative Sequential Search of an Unsorted Chain

• Straightforward implementation


Recursive Sequential Search of an Unsorted Chain

• Method search


Recursive Sequential Search of an Unsorted Chain

• Public method contains Calls method search


Efficiency of a Sequential Search of a Chain


Sequential Search of a Sorted Chain

• Similar to sequentially searching a sorted array


Binary Search of a Sorted Chain

• Recall finding middle element in an array is easy: mid = first + (last - first) / 2

• Finding middle element of sorted chain more difficult Must traverse the chain to middle Less efficient than sequential search


Choosing a Search Method

• Sequential search Suitable for smaller array Objects must have appropriate equals

method

• Binary search Suitable for larger collections Objects must have appropriate compareTo

method

• In both cases ask, “Search how often?”


Figure 18-8 The time efficiency of searching, expressed in Big Oh notation


End

Chapter 18


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