The document discusses two search algorithms: linear search and binary search. Linear search sequentially checks each element of a list to find a target value, with average time complexity of O(n). Binary search works on a sorted list by comparing the target to the middle element and recursively searching half of the list, providing logarithmic time complexity of O(log n). Both algorithms are illustrated with pseudocode and their advantages of efficient searching for large and small lists respectively are contrasted.

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Search Algorithms
Technical Writing(CS1305) Assignment
Aditya Kumar
20142028
MNNIT Allahabad
August 2015
Aditya Kumar 20142028 Search Algorithms

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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

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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

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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

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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

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Linear Search
continued
Figure: Graphical illustration of linear search
Aditya Kumar 20142028 Search Algorithms

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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

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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

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Linear Search
Advantages and Disadvantages
Advantages
Easiest to understand and implement
No sorting required
Suitable for small list sizes
Aditya Kumar 20142028 Search Algorithms

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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

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Binary Search
Binary search algorithm finds the position of a target
value within a sorted array
Aditya Kumar 20142028 Search Algorithms

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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)
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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

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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

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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

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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

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Binary Search
continued
Figure: Graphical illustration of binary search
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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
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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
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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
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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
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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

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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

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Binary Search
Advantages and Disadvantages
Advantages
Excellent time efficiency
Suitable for large list sizes
Aditya Kumar 20142028 Search Algorithms

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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
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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
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End
Thank you
Aditya Kumar 20142028 Search Algorithms