linear search and binary search
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The document outlines a lecture on search algorithms presented by Dr. Zia Ush Shamszaman, covering linear and binary search techniques. Linear search sequentially checks elements until a match is found, while binary search efficiently narrows down the search space in a sorted array by halving it at each step. The lecture also includes pseudocode for both algorithms along with their advantages and disadvantages.
![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
17-01-2020 8](https://image.slidesharecdn.com/l-13linearandbinarysearch-200121041434/85/linear-search-and-binary-search-8-320.jpg)
![Pseudocode
17-01-2020 20
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](https://image.slidesharecdn.com/l-13linearandbinarysearch-200121041434/85/linear-search-and-binary-search-20-320.jpg)
linear search and binary search
- 1. First Year BA (IT) CT1120 Algorithms Lecture 13 Dr. Zia Ush Shamszaman [email protected] 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 17-01-2020 2
- 3. Overview • Flashback • Introduction • Linear Search • Binary Search • Feedback and Assessment 317-01-2020
- 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. 17-01-2020 4
- 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. 17-01-2020 5
- 6. Graphical Illustration of LS 17-01-2020 6 Every item is checked but no match is found till the end of the data collection
- 7. Graphical Illustration of LS 17-01-2020 7 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 17-01-2020 8
- 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 17-01-2020 9
- 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 17-01-2020 10
- 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 17-01-2020 11
- 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 17-01-2020 12
- 13. Graphical Illustration of BS 17-01-2020 13
- 14. Graphical Illustration of BS 17-01-2020 14
- 15. Graphical Illustration of BS 17-01-2020 15
- 16. Graphical Illustration of BS 17-01-2020 16
- 17. Graphical Illustration of BS 17-01-2020 17
- 18. Graphical Illustration of BS 17-01-2020 18
- 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 17-01-2020 19
- 20. Pseudocode 17-01-2020 20 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. 17-01-2020 21
- 22. Next Lecture • Binary Search • Sorting 17-01-2020 22
- 23. References • https://www.tutorialspoint.com/ • https://www.hackerearth.com/ • www.khanacademy.org/computing/computer-science/algorithms 17-01-2020 23