1. Cs212: DataStructures
Lecture 3: Searching

2. Lecture Contents searching Sequential search algorithm.
Binary search algorithm.

3. Search Algorithms Search Algorithms Sequential Search Binary Search
Searching , the process used to find the location of a target among a list of objects.
In this chapter, we will study searches that work with arrays
Search Algorithms
Sequential Search
Binary Search

4. Search Algorithms Sequential search. Binary search.
It’s not requires an ordered list.
Binary search.
It requires an ordered list.

5. 1/ Sequential (Linear) Search
Search an array or list by checking items one at a time.
Sequential search is usually very simple to implement, and is practical when the list has only a few elements, or when performing a single search in an unordered list.
Look at every element : This is a very straightforward loop comparing every element in the array with the target(key).
Eighter we find it,
or we reach the end of the list!

6. Locating data in unordered list.

7. Sequential Search Algorithm
The searching algorithm requires three parameters:
The list.
An index to the last element in the list.
The target.

8. Sequential Search Algorithm
algorithm SeqSearch (val list <array>, val last <index>, val target <keyType>) Locate the target in an unordered list of size elements. PRE list must contain at least one element. last is index to last element in the list. target contains the data to be located. POST if found – matching index stored in Location. if not found – (-1) stored in Location RETURN Location<integer>

9. Sequential Search Algorithm
looker = 0
loop (looker < last AND target not equal list(looker))
looker = looker + 1
if (target == list[looker] )
Location= looker
else
Location = -1
End If
return Location
end SeqSearch

10. Recursive sequential search (1)
Algorithm sequentialSearch (item<integer>,list<array>, listSize<integer>) Pre item contains a value, listSize contains the actual size of the array list Post find the location of item in list Return either the item found and its location is returned or not and -1 returned if (listSize == 0) return -1 if (list[listSize-1] == item) return listSize-1 else return sequentialSearch (item, list, listSize-1) End sequentialSearch

11. 2/ Binary search algorithm
Search a sorted array by repeatedly dividing the search interval in half.
A fast way to search a sorted array is to use a binary search.

12. Binary search algorithm
Calculate the middle element
Test the data in the element at the middle of the array.
Target < middle element
Target > middle element
it is in the first half before middle
it is in the second half after middle
Calculate the middle element
Calculate the middle element
Test the data in the element at the middle of the array.
Test the data in the element at the middle of the array.
Target < middle
Target < middle
Target > middle
Target > middle
it is in the
first half!
it is in the
second half!
it is in the
first half!
it is in the
second half! . . . .
If the middle element equals to the Target , the algorithm stops

13. mid=(first+last)/2 target < A[mid] last = mid -1 target == A[mid]
first = mid +1
target < A[mid]
last = mid -1
target == A[mid]

14. target < A[mid]
last = mid -1
target > A[mid]
first = mid +1
target > A[mid]
first = mid +1
target < A[mid]
last = first  not found stop

15. Recursive Binary search algorithm
algorithm RecBinarySearch (val First<index>, val last <index>,val target <keyType>) Locate the target in an ordered list of size elements. PRE list must contain at least one element. First is index to first element in the list. last is index to last element in the list. target contains the data to be located. POST if found – matching index stored in Location if not found – (-1) stored in Location RETURN Location<integer>

16. Recursive search algorithm
m := if target = am then Location= m else if (first=last) then Location= -1 else if (target < am) then Location =binarySearch(first, m-1, target) else if (target > am) then Location=binarySearch(m+1, last, target ) Return Location End RecBinarySearch
base cases
recursive calls

17. Example [4] [3] [2] [1] [0] 20 11 7 5 3 BinarySearch (0,4,20)
20 >7 then
binarySearch(3 , 4,20)
Return 4
Return 4
BinarySearch (3,4,20)
M=3+4/2=3
20 >11 then
binarySearch(4 , 4,20)
Recursive call
Return 4
BinarySearch (4,4,20)
M=4+4/2=2
20 == 20
Recursive call

18. Binary search algorithm (iterative)
Algorithm BinarySearch (list<array>, key <integer>, listSize<integer> ) Search an ordered list using Binary Search PRE list must contain at least one element. listSize is the actual size of the list. key contains the data to be located. POST if found – matching index stored in Location if not found (-1) stored in Location RETURN Location<integer>

19. Binary search in iterative algorithm
first=0
last=listSize-1
while (first<= last)
{ mid =
if ( list [mid] == key)
return mid
else if (list[mid] < key)
first = mid + 1
else
last = mid - 1 }
return -1
End BinarySearch

20. End Of Chapter
References:
Text book, chapter2: Searching