Searching Chapter 10. 2 Chapter Contents The Problem Searching an Unsorted Array Iterative...

Searching

Chapter 10

2

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 forreturn 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

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Searching an Unsorted Array

Pseudocode for a recursive algorithm to search an array.

Algorithm to search a[first] through a[last] for desiredItemif (there are no elements to search)

return falseelse if (desiredItem equals a[first])

return trueelse

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.

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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 when the data is sorted.

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Binary Search of Sorted Array

Algorithm for a binary search

Algorithm binarySearch(a, first, last, desiredItem)mid = (first + last)/2 // approximate midpointif (first > last)

return falseelse if (desiredItem equals a[mid])

return trueelse 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 sorted array that (a) finds its target;

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Binary Search of Sorted Array

Fig. 6 A recursive binary search of a sorted array that (b) does not find its target.

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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 whilereturn 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;

elsefound = 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 chainpublic 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 whileif ( (currentNode != null) &&

entry.equals(currentNode.getData()) ){ found = true;} // end ifreturn found;

} // end contains

Note: Binary search of a chain of linked nodes is impractical.

Note: Binary search of a chain of linked nodes is impractical.

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Choosing a Search Method

Iterative search saves time, memory over recursive search

BestCase

AverageCase

WorstCase

Sequential search(unsorted data) O(1) O(n) O(n)

Sequential search(sorted data) O(1) O(n) O(n)

Binary Search(sorted array) O(1) O(log n) O(log n)