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MCS031- SOLVED ASSIGNMENT 2016-17IGNOU MCA 3rd SEM

1.
Discuss some real world problems, to which the techniques given below are applicable
(i) Divide & Conquer
(ii) Dynamic Programming
(iii) Greedy Approach










2.
Two algorithms A1 and A2 run on the same machine. The running time of A1 is 100 n and running time of A2 is 2n. For what value of n2, A1 runs faster than A2 ? If running time of A1 is changed to 100 n30, then what could be the possible value of n. You can use any spreadsheet software to plot the graph nVS A1 &A2 running time, to analyse the results.








3.
Use Principle of Mathematical induction to show that the polynomial P(X) = X3 – X, is divisible by 6, where X is a non-negative integer.









4.
Verify the expression n! = 0(nn).








5.
Determine the complexity of following sorting algorithms
(i) Quick sort
(ii) Merge sort
(iii) Bubble sort
(iv) Heap sort
Show all steps, performed to determine the complexity, with suitable example for each.








6.
Find the product of two numbers X1 = 732912 and X2 = 1026732 by using Karatsuba's Method.







7.
Write Strassen's Algorithm ? What are the limitation of Strassen's Algorithim. Apply Strassen's Algorithm to multiply two matrices A1 & A2 given below










8.
Perform following tasks
(a) Write Kleene closure of {aa, b}
(b) Find regular expression for language {⋀, a, abb, abbbb, ….}










9.
Write short note on NP complete and NP Hard problems, give suitable example for each.










10.
Discuss the following with suitable example
(i) Halting problem,
(ii) Turing machine,
(iii) Push down automata.



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