Algorithm & Algorithm Complexity - Time

1. SANJIVANI K. B. P. POLYTECHNIC,
KOPARGAON
With NBA ACCREDIATED programs , Approved by AICTE, New Delhi,
Recognized by Govt. of Maharashtra, Affiliated to Maharashtra State Board of
Technical Education, Mumbai, ISO 9001:2015 Certified Institute
Name of Faculty: Prof. Vaibhav A. Parjane
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2. Topic to be Covered
Time Complexity
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Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane

3. Time Complexity :
1. Time complexity is the total time taken by the algorithm
to perform the intended task.
2. It is also known as frequency count.
3. Eg: consider the FOR LOOP
For ( i=0 ; i<n ; i++ )
Atleast once (1) + (n+1) + n
= 1 + (n+1) +n
= 2n + 2
true
false
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Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane

4. Time Complexity:
Ex: Consider the following algorithm to add two
numbers
𝐴𝑙𝑔𝑜_𝑎𝑑𝑑 (𝑎, 𝑏)
𝑺𝒕𝒆𝒑 𝟏. 𝑪 = 𝒂 + 𝒃;
𝑺𝒕𝒆𝒑 𝟐. 𝒓𝒆𝒕𝒖𝒓𝒏 𝑪;
Here, algorithm has only two simple statements so the
complexity of this algorithm is 2
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Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane

5. Example
void main ( )
{
int i , n , sum , x;
sum = 0;
printf(“Enter number of elements : ”);
scanf(“ %d” , &n);
for (i=0 ; i<n ; i++)
{
scanf(“ %d” , &x);
sum= sum + x;
}
printf(“sum = % d” , sum );
}
1. In the for loop, the condition
(i<n) will be executed (n+1)
times , and not ‘n’ times.
2. For all values of ‘i’ between 1
and n , the condition (i<n)
will evaluate to true and
when ‘i’ becomes (n+1) , the
condition (i<n) will evaluate
to false.
3. Thus the above instruction
will be executed (n+1) times.
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Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane

6. Calculation of computation time
Statement Frequency
sum = 0 1
printf(“Enter number of elements : ”); 1
scanf(“ %d” , &n); 1
for (i=0 1
i<n n + 1
i++ n
scanf(“ %d” , &x); n
sum= sum + x; n
printf(“sum = % d” , sum ); 1
=1 + 1 + 1 +1 + (n+1) + n + n + n + 1 =(6+4n)
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Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane

7. Example :
i=1;
while (i< = n)
{
x = x +1 ;
i = i + 1;
}
Statement Frequency
i=1; 1
while (i< = n) n +1
x = x +1 ; n
i = i + 1; n
=1 + (n+1) + n + n =(2+3n)
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Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane