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This mock test of Divide And Conquer (Basic Level) - 2 for Computer Science Engineering (CSE) helps you for every Computer Science Engineering (CSE) entrance exam.
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QUESTION: 1

Which of the following is useful in implementing heap sort?

Solution:

For implementation of function call in heap sort, stack is used.

QUESTION: 2

Following algorithm (s) can be used to sort n integers in the range [1 ... n^{3}] in O(n) time?

Solution:

Radix sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys which share same position and value. So it take O(n) time.

QUESTION: 3

The recurrence relation that arises in relation with the complexity of binary search is

Solution:

Binary search only half of the array.

So,

QUESTION: 4

Which one of the following statements is false?

Solution:

Connected components of a graph can be computed in linear time by using either breadth- first search or depth-first search.

QUESTION: 5

Merge sort uses

Solution:

A merge sort is comparisbn based sorting algorithm and divide-and-conquer algorithm.

QUESTION: 6

For merging two sorted lists of sizes m and n into a sorted list of size m + n, we required comparisons of

Solution:

The number of comparisons required in the worst case is O(m + n).

QUESTION: 7

Quicksort is run on two inputs shown below to sort in ascending order:

(i) 1 , 2 , 3 .... n .

(ii) n, n - 1, n - 2 , .... 2, 1

Let C_{1}, and C_{2} be the number of comparisons made for the inputs (i) and (ii) respectively. Then,

Solution:

Both of given cases are Quicksort Worst cases problem, so comparisons are equal.

QUESTION: 8

Let T(n) be the function defined by T(1) = 1, T(n) Which of the following statements is true?

Solution:

Use Master Theorem

QUESTION: 9

A sorting technique is called stable if

Solution:

A sorting algorithm is called stable if it keeps elements with equal keys in the same relative order in the output as they were in the input.

For example in the following input the two 4’s are indistinguishable. 1,4_{a}, 3, 4_{b}, 2 and so the output of a stable sorting algorithm must be:

1, 2, 3, 4_{a}, 4_{b}

Bubble sort, merge sort, counting sort, insertion sort are stable sorting algorithms.

QUESTION: 10

If one uses straight two-way merge sort algorithm to sort the following elements in ascending order:

20,47, 15,8,9,4,40,30, 12, 17

Then the order of these elements after second pass of the algorithm is

Solution:

Given: 20, 47, 15, 8, 9, 4, 40, 30, 12, 17

2-way merge sort so group of 2 is taken at once.

2nd pass:

The order of elements after second pass of the algorithm is 8, 15, 20, 47, 4, 9, 30, 40, 12, 17.

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