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Q.1: Complete the following: a. F(n)=12n 5 +4n 3 is O(…………) b. F(n)= 5n 2 + 3n l

ID: 3821634 • Letter: Q

Question

Q.1: Complete the following:

a. F(n)=12n5+4n3                        is O(…………)

b. F(n)= 5n2 + 3n log n + 2n 5 is O(…………)

c. F(n)= 3 log n + 2                    is O(…………)

e. F(n)= 2n + 100 log n is O(…………)

Which function grows faster: …………………………..

Q.2: Prove the following:

            a. 3n log n + 2n is (n log n)            For n ……..

           

Q.3. Use the master method to give tight asymptotic bounds for the following recurrences.

a. T(n)= 2T(n/4) + 1.

b. T(n)= 2T(n/4) + n2.

Q. 4. Use Dijkstra’s algorithm to find the length of the shortest path between the vertices a and z in this weighted graph.

The shortest path is: ……………………………………………………..

10 Z 3 6 d e 8 c 1 4 2

Explanation / Answer

HI, I have answered all parts of Q1.

Please repost ohter questions in separate post.

In Big-O notation, we generally ignore lower order terms and conastant terms.

Q.1: Complete the following:

a. F(n)=12n^5+ 4n^3

   ignoring 4n^3 and 12 from 12n^5

   O(n^5)

b. F(n)= 5n^2 + 3n log n + 2n^5
  
   O(n^5)

c. F(n)= 3 log n + 2

   O(logn)

e. F(n)= 2n + 100 log n
   O(n)

Please let me know if you have any double in Q1