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1. 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

2. Information
• Number of Lectures -12
– When? Every Friday (12-1)
– Where: AC201
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3. Overview
• Flashback
• Introduction
• Linear Search
• Binary Search
• Feedback and Assessment
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4. 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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5. 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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6. Graphical Illustration of LS
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Every item is checked but no match is found till the
end of the data collection

7. Graphical Illustration of LS
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Found a match at index 2

8. 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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9. 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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10. 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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11. 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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12. 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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13. Graphical Illustration of BS
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14. Graphical Illustration of BS
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15. Graphical Illustration of BS
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16. Graphical Illustration of BS
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17. Graphical Illustration of BS
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18. Graphical Illustration of BS
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19. 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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20. 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

21. 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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22. Next Lecture
• Binary Search
• Sorting
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23. References
• https://www.tutorialspoint.com/
• https://www.hackerearth.com/
• www.khanacademy.org/computing/computer-science/algorithms
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24. Feedback & Assessment
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