Chapter 9 slide 1 Introduction to Search Algorithms Search: locate an item in a list (array, vector,...
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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
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Transcript of Chapter 9 slide 1 Introduction to Search Algorithms Search: locate an item in a list (array, vector,...
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
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 Whilereturn position
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
17 23 5 11 2 29 3
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
Chapter 9 slide 5
Improved Sequential Search Algorithm on Ordered Arrayset 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 whilereturn position
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
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.
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
2 3 5 11 17 23 29
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
GREATER first = midPoint + 1
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 - 1
GREATER first = midPoint + 1
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
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; int last = 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;}
Chapter 9 slide 13
Binary Search Tradeoffs
• Benefit – Much more efficient than linear search(For array of N elements, performs at mostlog2N comparisons)
• Disadvantage – Requires that array elements be sorted
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
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
