IGNOU BCS 42 SOLVED ASSIGNMENT

Ques 1.

 Prove the following proposition using induction:

P(n): 1² + 2² + 3² + 4² + ... ... ... ... . + n² = n(n+1)(2n+1) / 6

Ques 2.

. For the function defined by f(n) = 2n³ + 3n² + 1 and g(n) = 2n² +3, show that

(i) f(n) = Ω(g(n))

(ii) g(n) != Ω(f(n))

(iii) n³ = Ω(g(n))

(iv) f(n) != Ω(n⁴)

Ques 3.

Solve the following recurrence Using Recursion tree method

(i) T(n) = 3T(n/3) + n

(ii) T(n) = 2T(n/2) + n²

(iii) T(n) = T(n/2) + T(n/4) + T(n/8) + n

Ques 4.

Insertion sort

Ques 5.

 Binary sort

Ques 6.

Binary search

Ques 7.

) Merge sort

Ques 8.

 Apply Kruskal's Algorithm on the following graph to find minimum cost spanning tree

Ques 9.

Q8. Explain DFS and BDS Graph traversal algorithms with the help of a suitable example.

Ques 10.

 Prove the following proposition using induction:

P(n): 1² + 2² + 3² + 4² + ... ... ... ... . + n² = n(n+1)(2n+1) / 6

Ques 11.

. For the function defined by f(n) = 2n³ + 3n² + 1 and g(n) = 2n² +3, show that

(i) f(n) = Ω(g(n))

(ii) g(n) != Ω(f(n))

(iii) n³ = Ω(g(n))

(iv) f(n) != Ω(n⁴)

Ques 12.

Solve the following recurrence Using Recursion tree method

(i) T(n) = 3T(n/3) + n

(ii) T(n) = 2T(n/2) + n²

(iii) T(n) = T(n/2) + T(n/4) + T(n/8) + n

Ques 13.

Insertion sort

Ques 14.

 Binary sort

Ques 15.

Binary search

Ques 16.

) Merge sort

Ques 17.

 Apply Kruskal's Algorithm on the following graph to find minimum cost spanning tree

Ques 18.

Q8. Explain DFS and BDS Graph traversal algorithms with the help of a suitable example.

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