linear search and binary search

First Year BA (IT)
CT1120 Algorithms
Lecture 13
Dr. Zia Ush Shamszaman
z.shamszaman1@nuigalway.ie
1
School of Computer Science, College of Science and Engineering
17-01-2020

Information
•  Number of Lectures -12
–  When? Every Friday (12-1)
–  Where: AC201
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Overview
•  Flashback
•  Introduction
•  Linear Search
•  Binary Search
•  Feedback and Assessment
317-01-2020

Introduction
•  The definition of a search is the process of
looking for something.
•  In computer science
–  A search algorithm is an algorithm for finding
an item with specified properties among a
collection of items that coded into a computer
program.
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Linear Search (LS)
Linear Search involves checking all the
elements of the array (or any other
structure) one by one and in sequence
until the desired result is found.
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Graphical Illustration of LS
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Every item is checked but no match is found till the
end of the data collection

Graphical Illustration of LS
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Found a match at index 2

Linear Search Algorithm
•  Linear Search ( Array A, Value x)
•  Step 1: Set i to 1
•  Step 2: if i > n then go to step 7
•  Step 3: if A[i] = x then go to step 6
•  Step 4: Set i to i + 1
•  Step 5: Go to Step 2
•  Step 6: Print Element x Found at index i and go to step 8
•  Step 7: Print element not found
•  Step 8: Exit
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Pseudocode
•  procedure linear_search (list, value)
for each item in the list
if match item == value
return the item's location
end if
end for
end procedure
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Adv. & Disadv. Of LS
•  Advantages
–  Easiest to understand and implement
–  No sorting required
–  Suitable for small list sizes
–  Works fine for small number of elements
•  Disadvantages
–  Time inefficient as compared to other algorithms
–  Not suitable for large-sized lists
–  Search time increases with number of elements
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Binary Search (BS)
•  Binary Search is a Divide and Conquer algorithm
•  Binary search algorithm finds the position of a target value
within a sorted array
•  A more efficient approach than Linear Search because
Binary Search basically reduces the search space to half at
each step
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Binary Search
•  The algorithm begins by comparing the target value to the
value of the middle element of the sorted array
•  If they are equal the middle position is returned and the
search is finished
•  If the target value is less than the middle element's value,
then the search continues on the lower half of the array;
•  If the target value is greater than the middle element’s
value, then the search continues on the upper half of the
array
•  This process continues, eliminating half of the elements until
the value is found
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Graphical Illustration of BS
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Binary Search
•  With each test that fails to and a match, the search is
continued with one or other of the two sub-intervals,
each at most half the size
•  If the original number of items is N then after the
first iteration there will be at most N/2 items
remaining, then at most N/4 items, and so on
•  In the worst case, when the value is not in the list, the
algorithm must continue iterating until the list is empty
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Pseudocode
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Procedure binary_search
A ← sorted array
n ← size of array
x ← value to be searched
Set lowerBound = 1
Set upperBound = n
while x not found
if upperBound < lowerBound
EXIT: x does not
exists.
set midPoint =
lowerBound + ( upperBound -lowerBound )/2
if A[midPoint] < x
set lowerBound = midPoint + 1
if A[midPoint] > x
set upperBound = midPoint - 1
if A[midPoint] = x
EXIT: x found at location midPoint
end while
end procedure

Binary Search Algorithm
•  Step 1 − Start searching data from middle of the list.
•  Step 2 − If it is a match, return the index of the item,
and exit.
•  Step 3 − If it is not a match, probe position.
•  Step 4 − Divide the list and find the new middle.
•  Step 5 − If data is greater than middle, search in
higher sub-list.
•  Step 6 − If data is smaller than middle, search in lower
sub-list.
•  Step 7 − Repeat until match.
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Next Lecture
•  Binary Search
•  Sorting
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References
•  https://www.tutorialspoint.com/
•  https://www.hackerearth.com/
•  www.khanacademy.org/computing/computer-science/algorithms
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Feedback & Assessment
17-01-2020 24

linear search and binary search

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