02 ds and algorithm session_02

Data Structures and Algorithms
Exercise 1

Write an algorithm to check whether a number is a prime
number or not.

Ver. 1.0 Session 2

Exercise 1: Solution

1. Accept a number from the user. Name it as num.
2. Declare an integer variable i.
3. Assign a value 2 to i.
4. Repeat until i > num/2:
a. If num % i = 0:
i. Display “The number is not prime”
ii. Exit
b. i = i + 1
5. Display “The number is prime”.

Ver. 1.0 Session 2

Exercise 2

Write an algorithm to generate the first 10 prime numbers.

Ver. 1.0 Session 2


1. Declare an integer variable, count, and assign the value 0 to
it.
2. Declare an integer variable, num, and assign the value 2 to
it.
3. Repeat until count becomes equal to 10:
a. If num is a prime number:
i. Display num
ii. Set count = count + 1
b. Set num = num +1

Ver. 1.0 Session 2

Exercise 3

Write an algorithm to accept a number between 1 and 9 and
display a pattern. For example, if the number entered is 5,
the following pattern should be displayed:

1
2 1
3 2 1
4 3 2 1
5 4 3 2 1

Ver. 1.0 Session 2


• Accept a number in the range of 1 - 9 from the user. Store it
in a variable, num.
• Declare an integer variable, i.
• Set i = 1.
• Repeat until i becomes greater than num: // To display
// num
rows
a. Declare an integer variable j
b. Set j = i
c. Display j and insert a space
d. Set j = j – 1
e. If j > 0 go to step c
f. Insert a line break
g. Set i = i + 1

Ver. 1.0 Session 2

Exercise 4

Write an algorithm to accept a number between 1 and 9 and
display a pyramid. For example, if the number entered is 5,
the following pyramid will be displayed:

1
1 2 1
1 2 3 2 1
1 2 3 4 3 2 1
1 2 3 4 5 4 3 2 1

Ver. 1.0 Session 2


1. Accept a number from the user in the range of 1-9. Store it
in a variable, n.
2. Set i = 1.
3. Repeat until i becomes greater than n:
• Set j = 0
• Insert a space
• Set j = j + 1
• If j < n – i, go to step b // To display n – i spaces
• Set j = 1
• Display the value of j and insert a space
• Set j = j + 1
• If j < i, then go to step f // To display numbers from 1 to i
• Set j = i – 1

Ver. 1.0 Session 2

Exercise 4: Solution (Contd.)

• Display the value of j and insert a space
• Set j = j – 1
• If j > 0, go to step j // To display numbers from i – 1 down
// to 1
• Give a line break
• Set i = i + 1

Ver. 1.0 Session 2

Exercise 5

Write an algorithm to accept two strings and check whether
the second string exists within the first string. For example,
if the first string is “concatenation” and the second string is
“cat”, the algorithm should display “Substring found at
position 4 in the string”. However, if the first string is
“concatenation” and the second string is “tent”, the algorithm
should display “Substring not found in the string”.

Ver. 1.0 Session 2


1. Accept a string value from the user. Store it in a variable, str.
2. Accept the substring to be searched in str. Store it in a
variable, substr.
3. Store the length of str in an integer variable, len1.
4. Store the length of substr in an integer variable, len2.
5. Set i = 0.
6. Repeat until i becomes equal to len1:
• If str[i] != substr[0], go to step b else go to step d
// To find the first matching character
• Set i = i + 1
• If (i < len1) go to step a
• If i = len1, go to step e, else go to step g
• Display “Substring not found in the string”
• Exit

Ver. 1.0 Session 2


• Set j = i // First character matched. Now match the
// remaining characters
• Set k = 0
• If str[j] = substr[k], go to step j, else go to step m
• Set j = j + 1
• Set k = k + 1
• If j < len1 and k < len2, go to step i
• If k = len2, go to step n, else go to step p
• Display “Substring found at position ” + (i + 1) + “ in the string”
• Exit
• Set i = i + 1

Ver. 1.0 Session 2

Exercise 6

Suppose you have two arrays of size 10 each containing
elements in ascending order. Write an algorithm to merge
the two arrays in such a way that the elements in the
resulting array are arranged in the ascending order.

Ver. 1.0 Session 2


• Accept two arrays, A1 and A2, each of size 10, from the
user.
• Declare an array, result, of size 20.
• Set i = j = k = 0.
• If (A1 [i] <= A2 [j]): // Insert the smaller element in the
// result array
a. result [k] = A1 [i]
b. Set k = k + 1
c. Set i = i + 1
• If (A1[i] > A2[j]): // Insert the smaller element in the
// result array
a. result [k] = A2 [j]
b. Set k = k + 1
c. Set j = j + 1

Ver. 1.0 Session 2


• If (i < 10 and j < 10), go to step 4. // If none of the lists
// has reached its
end
• Repeat until i equals 10: // If there are any elements left
// in A1, copy them to
result // array

a. result [k] = A1 [i]
b. Set k = k + 1
c. Set i = i + 1
• Repeat until j equals 10: // If there are any elements left in
// A2, copy them to the result
// array

a. result [k] = A2 [j]
Ver. 1.0 b. Set k = k + 1 Session 2

Exercise 7

Write an algorithm to find the Highest Common Factor
(HCF) of three numbers.

Ver. 1.0 Session 2


1. Accept three numbers from the user. Store them in
variables num1, num2, and num3.
2. Declare an integer variable, min.
3. Assign the value of the smallest number among num1,
num2, and num3 to min by executing the following steps:
a. Set min = num1
b. If (num2 < min), set min = num2
c. If (num3 < min), set min = num3
4. Declare an integer variable i.
5. Set i = min.
6. If ( num1 % i = 0 and num2 % i = 0 and num3 % i = 0 ):
• Display i // If i divides all the numbers, then HCF is i
• Exit

Ver. 1.0 Session 2


1. Set i = i – 1.
2. Go to step 6.

Ver. 1.0 Session 2

Exercise 8

Write an algorithm to multiply two 3 × 3 matrices.

Ver. 1.0 Session 2

Algorithm 8: Solution

1. Declare two 3 × 3 arrays, m1 and m2.
2. Accept the elements of the two matrices and store them in
m1 and m2.
3. Declare a 3 × 3 matrix, result, to store the result of
multiplication.
4. Set i = 0.
5. Set j = 0.
6. Set result [i, j] = 0.
7. Set k = 0.
8. result [i, j] + = m1 [i, k] × m2 [k, j].
9. Set k = k + 1.
10. If k < 3, go to step 8.
11. Set j = j + 1.

Ver. 1.0 Session 2

Algorithm 8: Solution (Contd.)

1. If j < 3, go to step 6.
2. Set i = i + 1.
3. If i < 3, go to step 5.
4. Display result.

Ver. 1.0 Session 2

Algorithm 9

Write a recursive algorithm to print the first n numbers in the
Fibonacci series.

Ver. 1.0 Session 2

Algorithm 9: Solution

Algorithm: Fibo (n)
2. If n = 1, return 0
3. If n = 2, return 1
4. Return (Fibo (n – 1) + Fibo (n – 2))

Ver. 1.0 Session 2

02 ds and algorithm session_02

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