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This particular Assignment references the syllabus chosen for the subject of Computer Application, for the July 2023 - January 2024 session. The code for the assignment is MCS-31 and it is often used by students who are enrolled in the MCA Degree.
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Q1: For a problem P, two algorithms A and B have time complexities T1(n) = 5n2 and T2 (n) = 100nlogn respectively. Find the range for n, the size of instance of the given problem P, for which A is more efficient than B.
Q2: Solve the following recurrence equations:
(i) T(n) = 2T(n/2) + 0(n)
(ii) T(n) = T(n - 1) + 0(n)
Q3: Write a recursive function in C language to calculate the sum of all digits in a long integer provided as input.
Q4: Show stepwise sorting of elements using Heapsort algorithm to the following max heap.
Q5: Write a Turing machine to recognize the language of all strings of even length over the alphabet {a, b}.
Q6: Define ambiguity in Context-Free Grammar (CFG). Prove that the following grammar is ambiguous.
E →>E+E/E*E/a
Q7: Use Prim's algorithm to construct a minimum spanning tree for the following graph. (use starting node A)
Q8: Discuss the relationship between class P, NP, NP complete and NP Hard problems with suitable example of each class.
Q9: Define fractional Knap-Sack problem, and give a greedy algorithm to solve this problem efficiently.
Q10: Give an algorithm for topological sort. Obtain a topological ordering for the following graph:
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