Question

1. Given a set of numbers: A = {1, 3, 5, 2, 8, 7, 9, 4 }.

Add each digit of your N-Number (e.g. N0 0 3 2 2 0 1 8) to each element of A

separately to get your own final array B. ( e.g. B={1,3,8,4,10,7,10,12} = {B1,B2,B3,B4,B5,B6,B7,B8}. )

a) Your set B = ?

b) Use merge-sort to sort the array B. Show each step.

c) How many “comparisons” for each algorithm above?

2. Use binary-search for finding the number 6 for the sorted array based on Question 1, show each step. (6 might not be in your sorted array.)

3. The time complexity equation of merger-sort is T(n) = 2* T(n/2) + n, where T(1) = C and C is a constant. Solve this equation by giving detailed steps. (Hint: See lecture notes).

4. How do we use linked-lists to represent adjacency-lists in a graph? Provide an example including at least 6 vertices and 8 edges.

Answer 1

1. A:1 3.5.2.8.7.9.0} | lat Us {o.1,21,0,0,1,2} | a) | 。 - {1,0,73,8 LL, 10,6 [urs all lol ill Lo 6 01 3 lo 白白向自西向立 11 6 ( 3c Sc 1 3 0 B $ 8 10 (L After sorting, 6. [1, 3,4,6,7,8, 10 , 11}

1. 2. In sorting a shows the number of compare- Son at that step. "val no. of comparisons - Ild+1+1/3+370 - 15 Array B= {1, 3, 4,6,7, 8, LO,&t} Value to search x = 6 Let index of B is ul 61718 101 st uTo 67 8 izi, j = 8 mld 3 (i) muid - 16 - 1141 B[4] z 6zx retween naid, 6 is at inder u in array B. 3. Tln) = 27(1/2) +n where t(1) 26 A TIM): 2/2017) + 2] +n . *(n) = 2²7 (2/2) +non > TA), (T(3) 3 + x + 1 T(m) = 237 (2/2) + ninin ntntn

after k function calls, fin నందం T(n) = 2 + ) + (n +n un to---k times) @ T(n) = 2*T (2/2) + kn - for 2 / 2 o ka logan By substituting ka logan in eq O, T (n) z 2 logan (1) + nlogn = noge? C + nlogn (alogo logoa d? EL T(L) = c J z ne tnlogna T(n) z 0 inlogn) To represent adjacency lists in a graph, we use an array of pointer that usest linked lists to show the adjacent neighbouro a nodes of a node. het a graph. GIVE) with 6 vertices 4.

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