![scalescale
Linear Search
Pseudocode
Using Iteration
Require: list a, size of list n, desired item x
for i=0 to n-1 do
if a[i]=x then
return i
end if
i=i+1
end for
if i=n then
return false
end if
Aditya Kumar 20142028 Search Algorithms](https://image.slidesharecdn.com/presentation-150923205222-lva1-app6891/85/Search-Algprithms-7-320.jpg)
![scalescale
Binary Search
Pseudocode (using recursion)
BinarySearch(list[], min, max, key)
if max <min then
return false
else
mid = (max+min) / 2
if list[mid] >key then
return BinarySearch(list[], min, mid-1, key)
else if list[mid] <key then
return BinarySearch(list[], mid+1, max, key)
else
return mid
end if
end if
Aditya Kumar 20142028 Search Algorithms](https://image.slidesharecdn.com/presentation-150923205222-lva1-app6891/85/Search-Algprithms-18-320.jpg)
![scalescale
Binary Search
Pseudocode (using iteration)
BinarySearch(list[], min, max, key)
while min ≤ max do
mid = (max+min) / 2
if list[mid] >key then
max = mid-1
else if list[mid] <key then
min = mid+1
else
return mid
end if
end while
return false
Aditya Kumar 20142028 Search Algorithms](https://image.slidesharecdn.com/presentation-150923205222-lva1-app6891/85/Search-Algprithms-19-320.jpg)
Search Algprithms
- 1. scalescale Search Algorithms Technical Writing(CS1305) Assignment Aditya Kumar 20142028 MNNIT Allahabad August 2015 Aditya Kumar 20142028 Search Algorithms
- 2. scalescale Introduction In computer science, a search algorithm is an algorithm for finding an item with specified properties among a collection of items which are coded into a computer program. The program then looks for clues to give us back exactly what we want. Aditya Kumar 20142028 Search Algorithms
- 3. scalescale Introduction In computer science, a search algorithm is an algorithm for finding an item with specified properties among a collection of items which are coded into a computer program. The program then looks for clues to give us back exactly what we want. We are going to cover two search algoritms in this presentation: linear and binary. Aditya Kumar 20142028 Search Algorithms
- 4. scalescale Linear Search Linear search is a method for finding a particular value in a list that checks each element in sequence until the desired element is found or the list is exhausted Aditya Kumar 20142028 Search Algorithms
- 5. scalescale Linear Search Linear search is a method for finding a particular value in a list that checks each element in sequence until the desired element is found or the list is exhausted It is the simplest search algorithm A special case of brute-force search Average time complexity: O(n) Aditya Kumar 20142028 Search Algorithms
- 6. scalescale Linear Search continued Figure: Graphical illustration of linear search Aditya Kumar 20142028 Search Algorithms
- 7. scalescale Linear Search Pseudocode Using Iteration Require: list a, size of list n, desired item x for i=0 to n-1 do if a[i]=x then return i end if i=i+1 end for if i=n then return false end if Aditya Kumar 20142028 Search Algorithms
- 8. scalescale Linear Search Pseudocode Using Recursion LinearSearch(list, size, value) if size=0 then return false else if first item of list=value then return location of first item else return LinearSearch(list, remaining size, value) end if Aditya Kumar 20142028 Search Algorithms
- 9. scalescale Linear Search Advantages and Disadvantages Advantages Easiest to understand and implement No sorting required Suitable for small list sizes Aditya Kumar 20142028 Search Algorithms
- 10. scalescale Linear Search Advantages and Disadvantages Advantages Easiest to understand and implement No sorting required Suitable for small list sizes Disadvantages Time inefficient as compared to other algorithms Not suitable for large-sized lists Aditya Kumar 20142028 Search Algorithms
- 11. scalescale Binary Search Binary search algorithm finds the position of a target value within a sorted array Aditya Kumar 20142028 Search Algorithms
- 12. scalescale Binary Search Binary search algorithm finds the position of a target value within a sorted array It can be classified as a divide-and-conquer search algorithm Average time complexity: O(log n) Aditya Kumar 20142028 Search Algorithms
- 13. scalescale Binary Search Overview The algorithm begins by comparing the target value to the value of the middle element of the sorted array Aditya Kumar 20142028 Search Algorithms
- 14. scalescale Binary Search Overview 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 Aditya Kumar 20142028 Search Algorithms
- 15. scalescale Binary Search Overview 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; or if the target value is greater than the middle element’s value, then the search continues on the upper half of the array Aditya Kumar 20142028 Search Algorithms
- 16. scalescale Binary Search Overview 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; or 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 or the array is exhausted Aditya Kumar 20142028 Search Algorithms
- 17. scalescale Binary Search continued Figure: Graphical illustration of binary search Aditya Kumar 20142028 Search Algorithms
- 18. scalescale Binary Search Pseudocode (using recursion) BinarySearch(list[], min, max, key) if max <min then return false else mid = (max+min) / 2 if list[mid] >key then return BinarySearch(list[], min, mid-1, key) else if list[mid] <key then return BinarySearch(list[], mid+1, max, key) else return mid end if end if Aditya Kumar 20142028 Search Algorithms
- 19. scalescale Binary Search Pseudocode (using iteration) BinarySearch(list[], min, max, key) while min ≤ max do mid = (max+min) / 2 if list[mid] >key then max = mid-1 else if list[mid] <key then min = mid+1 else return mid end if end while return false Aditya Kumar 20142028 Search Algorithms
- 20. scalescale Binary Search Performance With each test that fails to find a match, the search is continued with one or other of the two sub-intervals, each at most half the size Aditya Kumar 20142028 Search Algorithms
- 21. scalescale Binary Search Performance With each test that fails to find 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 Aditya Kumar 20142028 Search Algorithms
- 22. scalescale Binary Search Performance With each test that fails to find 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; this take at most floor(log2 N + 1) iterations, where floor() rounds down its argument to an integer Aditya Kumar 20142028 Search Algorithms
- 23. scalescale Binary Search Performance With each test that fails to find 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; this take at most floor(log2 N + 1) iterations, where floor() rounds down its argument to an integer Thus binary search runs in logarithmic time Aditya Kumar 20142028 Search Algorithms
- 24. scalescale Binary Search Advantages and Disadvantages Advantages Excellent time efficiency Suitable for large list sizes Aditya Kumar 20142028 Search Algorithms
- 25. scalescale Binary Search Advantages and Disadvantages Advantages Excellent time efficiency Suitable for large list sizes Disadvantages Can only be implemented on a sorted array Not suitable for small sizes, where linear search would be faster, as sorting takes up a considerable amount of time Aditya Kumar 20142028 Search Algorithms
- 26. scalescale Binary Search Language Support Many standard libraries provide a way to do a binary search: C provides bsearch() in its standard library C++’s STL provides the functions binary search(), lower bound() and upper bound() Java offers a set of overloaded binarySearch() static methods in the class Arrays in the standard java.util package for performing binary searches on Java arrays Python provides the bisect module Aditya Kumar 20142028 Search Algorithms
- 27. scalescale End Thank you Aditya Kumar 20142028 Search Algorithms