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.

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Session 2

Data Structures and Algorithms Exercise 1: Solution 1. 2. 3. 4.

Accept a number from the user. Name it as num. Declare an integer variable i. Assign a value 2 to i. 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”.

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Session 2

Data Structures and Algorithms Exercise 2 Write an algorithm to generate the first 10 prime numbers.

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Session 2

Data Structures and Algorithms Exercise 2: Solution 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

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Session 2

Data Structures and Algorithms 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 3 4 5

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1 2 3 4

1 2 3

1 2

1

Session 2

Data Structures and Algorithms Exercise 3: Solution • • • •

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. b. c. d. e. f. g.

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Declare an integer variable j Set j = i Display j and insert a space Set j = j – 1 If j > 0 go to step c Insert a line break Set i = i + 1 Session 2

Data Structures and Algorithms 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

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1 2

1 2 3

1 2 3 4

1 2 3 4 5

1 2 3 4

1 2 3

1 2

1

Session 2

Data Structures and Algorithms Exercise 4: Solution 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: • • • • • • • • •

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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

Session 2

Data Structures and Algorithms Exercise 4: Solution (Contd.) • • • • •

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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

Session 2

Data Structures and Algorithms 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”.

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Session 2

Data Structures and Algorithms Exercise 5: Solution 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: • • • • • • Ver. 1.0

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 Session 2

Data Structures and Algorithms Exercise 5: Solution (Contd.)

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•

Set j = i

• • • • • • • • •

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

// First character matched. Now match the // remaining characters

Session 2

Data Structures and Algorithms 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.

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Session 2

Data Structures and Algorithms Exercise 6: Solution • • • •

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

Data Structures and Algorithms Exercise 6: Solution (Contd.) •

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

•

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

Session 2

Data Structures and Algorithms Exercise 7 Write an algorithm to find the Highest Common Factor (HCF) of three numbers.

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Session 2

Data Structures and Algorithms Exercise 7: Solution 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 ): • •

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Display i Exit

// If i divides all the numbers, then HCF is i

Session 2

Data Structures and Algorithms Exercise 7: Solution (Contd.) 1. Set i = i – 1. 2. Go to step 6.

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Session 2

Data Structures and Algorithms Exercise 8 Write an algorithm to multiply two 3 × 3 matrices.

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Session 2

Data Structures and Algorithms 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

Data Structures and Algorithms Algorithm 8: Solution (Contd.) 1. 2. 3. 4.

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

Session 2

Data Structures and Algorithms Algorithm 9 Write a recursive algorithm to print the first n numbers in the Fibonacci series.

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Session 2

Data Structures and Algorithms 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

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– 2))

Session 2