Perform the Bubble Sort Algorithm on the Array - IT/Computer Science Assignment Help

Assignment Task:

TASK:

Question 1 (18 marks) a) An algorithm takes 1 seconds to handle a data set of 1,000 items. How long does it take the algorithm to handle a similar data set of 100,000 items?

i) If the complexity is O(n)

ii) If the complexity is O(1)

iv) If the complexity is O(log n) [6 marks]

b) Suppose we apply the binary search to search for a given element in an array that has 1,000 elements.

i) In the worst case, how many comparisons does it take to search for an element that is in the array?

ii) In the best case, how many comparisons does it take to search for an element that is in the array? [4 marks]

3 c) Describe the following functions in terms of the Big-Oh notation. i) f(n) = n + 3log n ii) f(n) = 3 + 2n + n 3 [4 marks]

d) Consider the following method which computes an . In terms of the Big-Oh notation, what is the efficiency of the method? Justify your answer with the sequence of recursive calls for power(a, 16). public static double power(double a, int n) // n is a non-negative integer { if (n== 0) { return 1; } else if ( n % 2 == 0) // n is even { double p = power(a, n/2); return p * p; } else // n is odd { double p = power(a, n/2); return p * p * a; } } [4 marks] 4

Question 2 (24 marks) a) a: 10 8 2 6 4 Perform the bubble sort algorithm on the array above, and show the array after each pass. The tracing can be done in any way you like. [8 marks] b)

a: 10 8 2 6 4 Perform the selection sort algorithm on the array above, and show the array after each pass. The tracing can be done in any way you like. [8 marks]

c) a: 10 8 2 6 4 Perform the insertion sort algorithm on the array above, and show the array after each pass. The tracing can be done in any way you like.

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