Linear Search

Searching Algorithms
Linear Search

Data Search − Consider an inventory of 1 million(106) items of a
store. If the application is to search an item, it has to
search an item in 1 million(106) items every time slowing
down the search. As data grows, search will become slower.
This is why searching algorithms are important
Need for Searching Algorithms

1. Linear search or sequential 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.
2. The list need not be ordered.
3. It is very simple and works as follows: We keep on comparing
each element with the element to search until the desired
element is found or list ends.
Linear search

This is the array we are going to perform linear search
Let’s search for the number 3. We start at the beginning
and check the first element in the array.
Example

Is the first value 3? No, not it. Is it the next
element?
Is the second value 3?
Not there either. The next element?

Is the third value 3?
Not there either. Next?
Is the fourth value 3? Yes!
We found it!!! Now you understand the idea of
linear searching; we go through each element,
in order, until we find the correct value.

Linear search - Pseudocode:
# Input: Array D, integer key
# Output: first index of key in D, or -1 if not found
For i = 0 to last index of D:
if D[i] equals key:
return i
return -1

Time Complexity
In the linear search problem, the best case occurs when Target is
present at the first location. The number of operations in the
best case is constant (not dependent on n). So time complexity in
the best case would be O(1)
Best case Analysis

Time Complexity
For Linear Search, the worst case happens when the element to be
searched is not present in the array or it is present at the end of
the array.
In this scenario the search() compares it with all the elements of
array one by one. Therefore, the worst case time complexity of
linear search would be O(n).
Worst case Analysis

Time Complexity
The key is equally likely to be in any position in the array
If the key is in the first array position: 1 comparison
If the key is in the second array position: 2 comparisons ...
If the key is in the ith postion: i comparisons ...
So average all these possibilities:
(1+2+3+...+n)/n = [n(n+1)/2] /n = (n+1)/2 comparisons.
The average number of comparisons is (n+1)/2 = O(n).
Average case Analysis

Time Complexity
In average case analysis, we take all possible inputs and calculate
computing time for all of the inputs. Sum all the calculated values and
divide the sum by total number of inputs.
We must know distribution of cases. For the linear search problem, let us
assume that all cases are uniformly distributed (including the case of
target not being present in array).
Average case Analysis

Space Complexity
This type of search requires only a single unit of memory to store the
element being searched. This is not relevant to the size of the input
Array.
Hence, the Space Complexity of Linear Search is O(1).

1. What is the best case for linear search?
a) O(nlogn)
b) O(logn)
c) O(n)
d) O(1)
2. What is the worst case for linear search?
a) O(nlogn)
b) O(logn)
c) O(n)
d) O(1)
QUIZ
1. D
2. C

3. What is the best case and worst case complexity of ordered linear
search?
a) O(nlogn), O(logn)
b) O(logn), O(nlogn)
c) O(n), O(1)
d) O(1), O(n)
4. Which of the following is a disadvantage of linear search?
a) Requires more space
b) Greater time complexities compared to other searching algorithms
c) Not easy to understand
d) Not easy to implement
3. D
4. B

5. The array is as follows: 1,2,3,6,8,10. At what time the element 6
is found? (By using linear search algorithm)
a) 4th call
b) 3rd call
c) 6th call
d) 5th call
5. A

Linear Search

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Linear Search