1. Adapted from Pearson Education, Inc.
Searching
Chapter 18
Adapted from Pearson Education, Inc.

2. Contents Searching an Unsorted Array Searching a Sorted Array
An Iterative Sequential Search
A Recursive Sequential Search
The Efficiency of a Sequential Search of an Array
Searching a Sorted Array
A Sequential Search
A Binary Search of a Sorted Array
The Efficiency of a Binary Search of an Array
Searching an Unsorted Chain
An Iterative Sequential Search
A Recursive Sequential Search
The Efficiency of a Sequential Search of a Chain
Searching a Sorted Chain
A Sequential Search
A Binary Search of a Sorted Chain
Choosing a Search Method
Java Class Library: The Method binarySearch
Adapted from Pearson Education, Inc.

3. Contents Searching Unsorted / Sorted Arrays
Searching Unsorted / Sorted Chains
Using Iterative/Recursive Sequential Search
Binary Search
Choosing a Search Method
The Efficiency of Searching methods
Adapted from Pearson Education, Inc.

4. 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
Adapted from Pearson Education, Inc.

5. Recursive Sequential Search of an Unsorted Array – Idea & Example 1
Basic idea:
Check if the item you want is the first one
If yes, you are done
If not, disregard that item and focus on the remaining items
Repeat the same until… ??
Adapted from Pearson Education, Inc.

6. Recursive Sequential Search of an Unsorted Array – Example 2
Adapted from Pearson Education, Inc.

7. Recursive Sequential Search of an Unsorted Array - Implementation
/** Searches the list for anEntry. */
public boolean contains (T anEntry)
{ return search (0, length - 1, anEntry);
} // end contains
/** Searches list[first] through list[last] for desiredItem.
@param first, last two integers >= 0 and < length
@param desiredItem the object to be found
@return true if desiredItem is found */
private boolean search (int first,int last,T desiredItem)
{ boolean found;
if (first > last)
found = false; // nothing left to search
else if (desiredItem.equals (list [first]))
found = true;
else found = search (first + 1, last, desiredItem);
return found;
} // end search
Trace it to search for 8
in this List = { 9, 5, 8, 4, 7 }
How often is this called at most?
Adapted from Pearson Education, Inc.

8. Iterative Sequential Search of a Unsorted Array vs. Sorted Array
What is the growth-rate?
Is the growth-rate different?
Unsorted Array
Sorted Array
public boolean contains (T anEntry) { for (int index = 0 ; index < numberOfEntries; index++) if(anEntry.equals (list [index])) return true; } // end for return false; } // end contains
public boolean contains (T anEntry) { int comp; for (int index = 0 ; index < numberOfEntries; index++) { comp = anEntry.compareTo (list [index])); if(comp == 0) return true; else if(comp < 0) return false; } // end for } // end contains
Adapted from Pearson Education, Inc.

9. Activity – Guess the number 
Higher / Lower
Correct / Incorrect
P1: Choose a number between
P2: Start guessing
P1: answer (Hi / Lo)
P3: keep a log:
Write down guess
Write down answer
P1: Choose a number between 1-100
P2: Start guessing
P1: answer ( / )
P3: keep a log:
Write down guess
Write down answer
Compare number of guesses until correct answer was reached
Adapted from Pearson Education, Inc.

10. Binary Search of a Sorted Array – Idea & Example
Basic idea:
Check if the item you want is the middle one
If yes, you are done
If not,
check if the item is less than the middle
if yes, repeat in lower half of the remaining array (disregard upper)
if not, repeat in upper half of the remaining array (disregard lowe
Repeat the same until…??
Adapted from Pearson Education, Inc.

11. Binary Search of a Sorted Array – Implementation
public boolean contains (T anEntry) { return binarySearch (0, length - 1, anEntry); } // end contains private boolean binarySearch (int first, int last, T desiredItem) { boolean found; int mid = (first + last) / 2; if (first > last) found = false; else if (desiredItem.equals (list [mid])) found = true; else if (desiredItem.compareTo (list [mid]) < 0) found = binarySearch (first, mid - 1, desiredItem); else found = binarySearch (mid + 1, last, desiredItem); return found; } // end binarySearch
Trace it to search for 8
in this List = { 2, 4, 5, 6, 8, 10, 12, 15, 18, 21, 24, 26}
How often are these called at most?
Adapted from Pearson Education, Inc.

12. Recursive Sequential Search of an Unsorted Chain – Self-Study
/** Searches the list for anEntry. */
public boolean contains (T anEntry)
{ return search (firstNode, anEntry);
} // end contains
/** Recursively searches a chain of nodes for desiredItem,
beginning with the node that current references. */
private boolean search (Node current, T desiredItem) {
boolean found;
if (current == null)
found = false;
else if (desiredItem.equals(current.data))
found = true;
else found = search (current.next, desiredItem);
return found;
} // end search
Trace it to search for 8
in this chain = { 9, 5, 8, 4, 7 }
How often is this called at most?
Adapted from Pearson Education, Inc.

13. Iterative Sequential Search of an Unsorted Chain vs. Sorted Chain
What is the growth-rate?
Is the growth-rate different?
Unsorted Chain
Sorted Chain
public boolean contains (T anEntry) { Node current = firstNode; while (current != null) if (anEntry.equals (current.data)) return true; current = current.next; } // end while return false; } // end contains
public boolean contains (T anEntry) { int comp; Node current = firstNode; while (current!=null) { comp = anEntry.compareTo (current.data)); if(comp == 0) return true; else if(comp < 0) return false; current = current.next; }// end while } // end contains
Adapted from Pearson Education, Inc.

14. Iterative Sequential Search of a Sorted Array vs. Sorted Chain
public boolean contains (T anEntry) { int comp; for (int index = 0 ; index < numberOfEntries; index++) { comp = anEntry.compareTo (list [index])); if(comp == 0) return true; else if(comp < 0) return false; } // end for } // end contains
public boolean contains (T anEntry) { int comp; Node current = firstNode; While (current!=null) { comp = anEntry.compareTo (current.data)); if(comp == 0) return true; else if(comp < 0) return false; current = current.next; }// end while } // end contains
Adapted from Pearson Education, Inc.

15. 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
What would the Big Oh be?
Adapted from Pearson Education, Inc.

16. Choosing a Search Method
Sequential search
Suitable for sorted and unsorted data
Suitable for array and chain
Suitable for smaller collections
Objects must have appropriate equals method
Binary search
Can NOT be used on unsorted data
Unsuitable for chain
Suitable for larger collections
Objects must have appropriate compareTo method
In both cases ask, “Search how often?”
Adapted from Pearson Education, Inc.

17. The time efficiency of searching
Adapted from Pearson Education, Inc.

18. Adapted from Pearson Education, Inc.
End
Chapter 18
Adapted from Pearson Education, Inc.