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Algorithms MCQ - Sorting and Searching

26 The number of possible commutative binary operations that can be defined on a set of n elements (for a given n) is

27 The number of swappings needed to sort the numbers 8, 22, 7, 9, 31, 19, 5, 13 in ascending order, using bubble sort is

28 The average successful search time taken by binary search on a sorted array of 10 items is

The 10 items i1, i2, ..., i10 may be arranged in a binary search tree as in Fig To get i5, the number of comparison needed is 1; for i2, it is 2; for i8 it is 2; for i1 it is 3, and so on. The average is (1+(2+2) +(3+3+3+3)+(4+4+4))/10, i.e., 2.9.

29 The average successful search time for sequential search on 'n' items is

If the search key matches the very first item, with one comparison we can terminate. If it is second, two comparisons , etc. So, average is (1+2+...+n)/n .i.e. (n+1)/2

30 The running time of an algorithm T(n), where 'n' is the input size, is given by T(n) = 8T(n/2) + qn, if n>1 Where p,q are constants. The order of this algorithm is

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Question:

The average time required to perform a successful sequential search for an element in an array A(1 : n) is given by

A. (n + 1)/2
B. log2n
C. n(n + 1)/2
D. n2

Correct answer: A

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