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Searching and Sorting Quiz 1

Question 1

Time: 00:00:00

What is the time complexity of given algorithm ?

void function (int n)

{

    int a = 0;

    for (int i = 0; i <= n; i++)

        for (int j = n / 2; j <= n; j++)

            for (int k = 1; k <= n; k = k * 2)

	            a++;

}

O((N^2)* (log N))

O(N^3)

O(N log N)

Constant

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First Outer loop and second loop runs n time so it’s time complexity is O(n*n) and the inner most loop is increasing in multiples of two so it’s time complexity is O(logn ). Hence total time complexity is O((N2)*(log N))

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Question 2

Time: 00:00:00

Bubble sort is a sorting algorithm used to sort the elements of an array .Here is that array arr={7,9,17,16}. How many iterations does it require to sort the given array?

Zero

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Bubble sort need 4 iteration to sort the given array . Eventhough first two elements are already sorted.

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Question 3

Time: 00:00:00

Which design technique is used to find all the pairs of shortest distance in a graph from the following algorithm?

Divide And Conquer

Greedy Algorithm

Backtracking

Dynamic Programming

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To find all the pairs of shortest distance in a graph Bellman-Ford algorithm is used.

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Question 4

Time: 00:00:00

Find the pivot element from the given input using median-of-three partitioning method.

8,7,9,3,6,2,4,1,0

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Left element=8, right element=0,

Centre=[position(left+right)/2]=6.

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Question 5

Time: 00:00:00

To sort an array of 3 million elements . Which of the following algorithm is best suited?

Bubble sort

Insertion sort

Merge sort

Quick sort

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The Quick sort is best suited to sort the array of 1 million elements. The practical implementations of Quick sort use randomised version. In practice randomised Quick sort algorithms rarely shows worst case behaviour and is almost always O(nlogn). And Quick sort requires little additional space and exhibits good cache locality.

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Question 6

Time: 00:00:00

What is the time complexity of the given algorithm ?

function (int n)

{

    int i = 1;

    while (i < n)

    {

        int j = n;

        while (j > 0)

	    j = j / 2;

        i = 2 * i;

    }

}

O(n)

O(log^2 n)

O(n^2)

O(n log n)

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Outer loop executes O(log n ) times and same as inner loop. So total time complexity is O(log n * log n) = O(log2 n).

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Question 7

Time: 00:00:00

Is Quick Sort a stable algorithm ?

False

True

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Quick sort is not a stable algorithm as it does not maintain the relative order of keys .

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Question 8

Time: 00:00:00

What is the run time complexity of heap sort algorithm?

O(N)

O(N^2)

O(N log N)

O(log N)

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The total time complexity of heap sort is mathematically found as O(N log N).

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Question 9

Time: 00:00:00

Recursion is similar to which of the following?

Goto statement

Loop

If-else

Switch Case

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Recursion is similar to a loop . Whatever programs we can make with recursion can also be possible through loops .

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Question 10

Time: 00:00:00

When elements of array are already in sorted array. Which of the following is the fastest sorting algorithm ?

Quick Sort

Merge Sort

Insertion Sort

Bubble Sort

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Merge Sort is the fastest stable sorting algorithm with worst-case complexity of O(n logn), but it requires extra space.

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