unit 1 SIXTH.pptx Algorithm Complexity Time
Download as PPTX, PDF2 likes15 views
The document is an educational outline from Sanjivani K.B.P. Polytechnic that discusses time complexity in computer algorithms. It covers definitions, examples of algorithm execution times, and frequency counts for various operations. The text is structured to provide both theoretical and practical insights for students in the department of computer technology.
unit 1 SIXTH.pptx 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 1
- 2. Topic to be Covered Time Complexity 2 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 3 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 4 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. 5 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) 6 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) 7 Sanjivani K. B. P. Polytechnic, Kopargaon Department of Computer Technology Prof. Vaibhav A. Parjane