1. Chapter 9 slide 1 Introduction to Search Algorithms Search: locate an item in a list (array, vector, table, etc.) of information Two algorithms (methods): –Linear search –Binary search

2. Chapter 9 slide 2 Sequential Search Algorithm on Unordered Array set found to false set position to –1 set index to 0 while index < number of elts and found is false if list [index] is equal to search value (key) found = true position = index end If Add 1 to index end While return position

3. Chapter 9 slide 3 Linear Search Example Array numlist contains Searching for the the value 11, linear search examines 17, 23, 5, and 11 Searching for the the value 7, linear search examines 17, 23, 5, 11, 2, 29, and 3 17235112293

4. Chapter 9 slide 4 Sequential Search Tradeoffs Benefits –Easy algorithm to understand –Array can be in any order Disadvantage –Inefficient (slow): for array of N elements, examines N/2 elements on average for value in array, N elements for value not in array

5. Chapter 9 slide 5 Improved Sequential Search Algorithm on Ordered Array set found to false set position to –1 set index to 0 while index < number of items and list [index] <= key and found is false if list [index] is equal to search value (key) found = true position = index end If increment index end while return position

6. Chapter 9 slide 6 Sequential Search on Ordered Array: Tradeoffs Benefits –Still easy algorithm to understand –More efficient : for array of N elements, examines N/2 elements on average for value in array, N/2 elements for value not in array Disadvantage –Array MUST be in order

7. Chapter 9 slide 7 Binary Search Algorithm on Ordered Array 1.Divide a sorted array into three sections. –middle element –elements on one side of the middle element –elements on the other side of the middle element 2.If the middle element is the correct value, done. Otherwise, go to step 1, using only the half of the array that may contain the correct value. 3.Continue steps 1 and 2 until either the value is found or there are no more elements to examine.

8. Chapter 9 slide 8 Binary Search Example Array numlist2 contains Searching for the the value 11, binary search examines 11 and stops Searching for the the value 7, binary search examines 11, 3, 5, and stops 23511172329

9. Chapter 9 slide 9 Trace of Binary Search info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] 15 26 38 57 62 78 84 91 108 119 item = 45 first midPoint last info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] 15 26 38 57 62 78 84 91 108 119 first midPoint last LESS last = midPoint - 1 GREATERfirst = midPoint + 1

10. Chapter 9 slide 10 Trace continued info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] 15 26 38 57 62 78 84 91 108 119 item = 45 first, midPoint, last info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] 15 26 38 57 62 78 84 91 108 119 first, last midPoint LESS last = midPoint - 1GREATERfirst = midPoint + 1

11. Chapter 9 slide 11 Trace concludes info[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] 15 26 38 57 62 78 84 91 108 119 item = 45 last first first > last found = false

12. Chapter 9 slide 12 bool BinarySearch ( ArrayType info, ItemType& item, int length) // Purpose: To determine whether item is in the array info // Returns: If found, item’s key matches an element’s key in the list and a copy // of that element has been stored in item and returns true; otherwise, item is // unchanged and returns false { bool fount = false; int midPoint ; int first = 0; intlast = length - 1 ; bool moreToSearch = ( first <= last ) ; while ( moreToSearch && !found ) {midPoint = ( first + last ) / 2 ;// INDEX OF MIDDLE ELEMENT switch ( item.ComparedTo( info [ midPoint ] ) ) { case LESS : last = middle -1; break; // LOOK IN FIRST HALF NEXT case GREATER : first = middle+1; break; // LOOK IN SECOND HALF NEXT case EQUAL : found = true; // ITEM HAS BEEN FOUND item.Copy ( info[midPoint] ); } moreToSearch = ( first <= last ) ; } return found; }

13. Chapter 9 slide 13 Binary Search Tradeoffs Benefit –Much more efficient than linear search (For array of N elements, performs at most log 2 N comparisons) Disadvantage –Requires that array elements be sorted

14. Chapter 9 slide 14 Sequential Search Algorithm on Unordered Linked List set found to false set position to head while position != null and found is false if position->item.GetKey( ) == search value (key) found = true else position = position-> next; end while return position

15. Chapter 9 slide 15 Sequential Search Algorithm on Ordered Linked List set found to false set position to head while ( position != null and found is false and position->item.GetKey( ) <= search value (key)) if position->item.GetKey( ) == search value (key) found = true else position = position-> next; end while return position