# Searching

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Searching
Chapter 10
Chapter Contents
   The Problem
   Searching an Unsorted Array
   Iterative Sequential Search
   Recursive Sequential Search
   Efficiency of Sequential Search
   Searching a Sorted Array
   Sequential search
   Binary Search
   Java Class Library: the Method binarySearch
   Searching an Unsorted Chain
   Iterative Sequential Search
   Recursive Sequential Search
   Efficiency of Sequential Search of a Chain
   Searching a Sorted Chain
   Sequential Search
   Binary Search
   Choosing a Search Method

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The Problem

Fig. 1 Searching is an every day occurrence.
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Searching an Unsorted Array
   A method that uses a loop to search an array.

public boolean contains(Object anEntry)
{ boolean found = false;
for (int index = 0; !found && (index < length); index++)
{ if (anEntry.equals(entry[index]))
found = true;
} // end for
return found;
} // end contains
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Searching an Unsorted Array

Fig. 2 An iterative sequential search of an array that
(a) finds its target; (b) does not find its target   5
Searching an Unsorted Array
   Pseudocode for a recursive algorithm to
search an array.
Algorithm to search a[first] through a[last] for desiredItem
if (there are no elements to search)
return false
else if (desiredItem equals a[first])
return true
else
return the result of searching a[first+1] through a[last]

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Searching an Unsorted Array

Fig. 3 A recursive sequential
search of an array that (a) finds its
target; (b) does not find its target.   7
Efficiency of a Sequential Search
   Best case                O(1)
   Locate desired item first
   Worst case               O(n)
   Must look at all the items
   Average case O(n)
   Must look at half the items
   O(n/2) is still O(n)

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Searching a Sorted Array
   A sequential search can be more efficient if
the data is sorted

Fig. 4 Coins sorted by their mint dates.

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Binary Search of Sorted Array

Fig. 5 Ignoring one-half of the data
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when the data is sorted.
Binary Search of Sorted Array
   Algorithm for a binary search
Algorithm binarySearch(a, first, last, desiredItem)
mid = (first + last)/2 // approximate midpoint
if (first > last)
return false
else if (desiredItem equals a[mid])
return true
else if (desiredItem < a[mid])
return binarySearch(a, first, mid-1, desiredItem)
else // desiredItem > a[mid]
return binarySearch(a, mid+1, last, desiredItem)
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Binary Search of Sorted Array

Fig. 6 A recursive binary search of a     12
sorted array that (a) finds its target;
Binary Search of Sorted Array

Fig. 6 A recursive binary search of a sorted
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array that (b) does not find its target.
Java Class Library: The Method
binarySearch

   The class Arrays in java.util defines versions
of a static method with following specification:

/** Task: Searches an entire array for a given item.
* @param array the array to be searched
* @param desiredItem the item to be found in the array
* @return index of the array element that equals desiredItem;
* otherwise returns -belongsAt-1, where belongsAt is
* the index of the array element that should contain
* desiredItem */
public static int binarySearch(type[] array, type desiredItem);

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Efficiency of a Binary Search

   Best case                O(1)
   Locate desired item first
   Worst case               O(log n)
   Must look at all the items
   Average case O(log n)

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Iterative Sequential Search of an
Unsorted Chain

Fig. 7 A chain of linked nodes that contain
the entries in a list.

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Iterative Sequential Search of an
Unsorted Chain
   Implementation of iterative sequential search

public boolean contains(Object anEntry)
{ boolean found = false;
Node currentNode = firstNode;
while (!found && (currentNode != null))
{ if (anEntry.equals(currentNode.getData()))
found = true;
else
currentNode = currentNode.getNextNode();
} // end while
return found;
} // end contains
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Recursive Sequential Search of an
Unsorted Chain
   Recursive search method
/** Task: Recursively searches a chain of nodes for desiredItem,
* beginning with the node that current references. */
private boolean search(Node current, Object desiredItem)
{     boolean found;
if (current = = null)
found = false;
else if (desiredItem.equals(current.getData()))
found = true;
else
found = search(current.getNextNode(), desiredItem);
return found;
} // end search
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Efficiency of a Sequential Search
of a Chain

   Best case                O(1)
   Locate desired item first
   Worst case               O(n)
   Must look at all the items
   Average case O(n)
   Must look at half the items
   O(n/2) is just O(n)
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Searching a Sorted Chain
   Method to search a sorted chain
public boolean contains(Object anEntry)
{ boolean found = false;
Comparable entry = (Comparable)anEntry;
Node currentNode = firstNode;
while ( (currentNode != null) &&
(entry.compareTo(currentNode.getData()) > 0) )
{ currentNode = currentNode.getNextNode();
} // end while
if ( (currentNode != null) &&
entry.equals(currentNode.getData()) )
{ found = true;
} // end if                Note: Binary search of a chain
return found;              of linked nodes is impractical.
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} // end contains
Choosing a Search Method
Best   Average     Worst
Case    Case       Case
Sequential search
O(1)     O(n)       O(n)
(unsorted data)
Sequential search
O(1)     O(n)       O(n)
(sorted data)
Binary Search
O(1)    O(log n)   O(log n)
(sorted array)

   Iterative search saves time, memory over
recursive search
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