In the following C program fragment, j, k n and TwoLog_n are integer variables, and A is an array of integers. The variable n is initialized to an integer ≥ 3, and TwoLog_n is initialized to the value of 2*&lceil;log2(n)&rceil; C for (k = 3; k < = n; k++) A[k] = 0; for (k = 2; k < = TwoLog_n; k++) for (j = k + 1; j < = n; j++) A[j] = A[j] || (j % k); for (j = 3; j < = n; j++) if (!A[j]) printf("%d", j); The set of numbers printed by this program fragment is

{m | m ≤ n, (∃ i) [m = i!]} Here i! mean factorial of i

{m | m ≤ n, (∃ i) [m = i2]}

Let swap() be a function that swaps two elements using their addresses. Consider the following C function. C void fun(int arr[], int n) { for (int i = 0; i < n; i+=2) { if (i>0 && arr[i-1] > arr[i] ) swap(&arr[i], &arr[i-1]); if (i<n-1 && arr[i] < arr[i+1] ) swap(&arr[i], &arr[i + 1]); } } If an array {10, 20, 30, 40, 50, 60, 70, 80} is passed to the function, the array is changed to

{20, 10, 40, 30, 60, 50, 80, 70}

{10, 30, 20, 40, 60, 50, 80, 70}

{80, 70, 60, 50, 40, 30, 20, 10}

Top MCQs on Algorithms in DSA with Answers

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Question 1

Match the following and choose the correct answer for the order A, B, C, D

A. Strassen matrix multiplication	p. Decrease and Conquer
B. Insertion sort	q. Dynamic Programming
C. Guassian Elimination	r. Divide and Conquer
D. Floyd shortest path algorithm	s. Transform and Conquer

r, s, p, q
r, p, s, q
q, s, p, r
s, p, q, r

Question 2

In the following C program fragment, j, k n and TwoLog_n are integer variables, and A is an array of integers. The variable n is initialized to an integer ≥ 3, and TwoLog_n is initialized to the value of 2*⌈log2(n)⌉

for (k = 3; k < = n; k++)
    A[k] = 0;
for (k = 2; k < = TwoLog_n; k++)
    for (j = k + 1; j < = n; j++)
        A[j] = A[j] || (j % k);
for (j = 3; j < = n; j++)
    if (!A[j]) printf("%d", j);

The set of numbers printed by this program fragment is

{m | m ≤ n, (∃ i) [m = i!]} Here i! mean factorial of i
{m | m ≤ n, (∃ i) [m = i²]}
{m | m ≤ n, m is prime}
Last print never executes

Question 3

An n x n array v is defined as follows:

v[i, j] = i-j for all i, j, 1 <= i <= n, 1 <= j <= n

The sum of the elements of the array v is

0
n-1
n² - 3n + 2
n² (n+1)/2

Question 4

X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true?

k must be 1
k must be 0
k can take any value between 0 and 1 (d) None of the above
None of the above

Question 5

Suppose you are given an array s[1..n] and a procedure reverse (s, i, j) which reverses the order of elements in a between positions i and j (both inclusive). What does the following sequence do, where 1 <= k <= n:

reverse(s, 1, k) ;
reverse(s, k + 1, n);
reverse(s, l, n);

Rotates s left by k positions
Leaves s unchanged
Reverses all elements of s
None of the above

Question 6

Let swap() be a function that swaps two elements using their addresses. Consider the following C function.

void fun(int arr[], int n)
{
    for (int i = 0; i < n; i+=2)
    {
        if (i>0 && arr[i-1] > arr[i] )
            swap(&arr[i], &arr[i-1]); 
        if (i<n-1 && arr[i] < arr[i+1] )
            swap(&arr[i], &arr[i + 1]);
    }
}

If an array {10, 20, 30, 40, 50, 60, 70, 80} is passed to the function, the array is changed to

{20, 10, 40, 30, 60, 50, 80, 70}
{10, 30, 20, 40, 60, 50, 80, 70}
{10, 20, 30, 40, 50, 60, 70, 80}
{80, 70, 60, 50, 40, 30, 20, 10}

Question 7

Match the following

List-I

A. Prim’s algorithm for minimum spanning tree
B. Floyd-Warshall algorithm for all pairs shortest paths
C. Mergesort
D. Hamiltonian circuit

List-II

1. Backtracking
2. Greedy method
3. Dynamic programming
4. Divide and conquer

Codes:    A B C D

(a) 3 2 4 1
(b) 1 2 4 3
(c) 2 3 4 1
(d) 2 1 3 4

Question 8

Let a_n represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_n?

a_n–2 + a_n–1 + 2^n–2
a_n–2 + 2a_n–1 + 2^n–2
2a_n–2 + a_n–1 + 2^n–2
2a_n–2 + 2a_n–1 + 2^n–2

Question 9

Given below are some algorithms, and some algorithm design paradigms.

List-I
A. Dijkstra’s Shortest Path
B. Floyd-Warshall algorithm to compute all pairs shortest path
C. Binary search on a sorted array
D. Backtracking search on a graph

List-II
1. Divide and Conquer
2. Dynamic Programming
3. Greedy design
4. Depth-first search
5. Breadth-first search

Match the above algorithms on the left to the corresponding design paradigm they follow Codes:

    A B C D
(a) 1 3 1 5
(b) 3 3 1 5
(c) 3 2 1 4
(d) 3 2 1 5

Question 10

Suppose c = 〈c[0], ... , c[k – 1]〉 is an array of length k, where all the entries are from the set {0, 1}. For any positive integers a and n, consider the following pseudocode.

DOSOMETHING (c, a, n)
z ← 1
for i ← 0 to k – 1
    do z ← z² mod n
    if c[i] = 1
       then z ← (z × a) mod n
return z

If k = 4, c = 〈1, 0, 1, 1〉, a = 2 and n = 8, then the output of DOSOMETHING(c, a, n) is ____________.

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