02 ds and algorithm session_02
-
Upload
yogeshjoshi362 -
Category
Technology
-
view
206 -
download
1
Transcript of 02 ds and algorithm session_02
Session 2Ver. 1.0
Data Structures and Algorithms
Write an algorithm to check whether a number is a prime number or not.
Exercise 1
Session 2Ver. 1.0
Data Structures and Algorithms
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”.
Exercise 1: Solution
Session 2Ver. 1.0
Data Structures and Algorithms
Exercise 2
Write an algorithm to generate the first 10 prime numbers.
Session 2Ver. 1.0
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
Session 2Ver. 1.0
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 1
3 2 1
4 3 2 1
5 4 3 2 1
Session 2Ver. 1.0
Data Structures and Algorithms
Exercise 3: Solution
1. Accept a number in the range of 1 - 9 from the user. Store it in a variable, num.
2. Declare an integer variable, i.
3. Set i = 1.
4. Repeat until i becomes greater than num: // To display // num
rowsa. 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
Session 2Ver. 1.0
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
1 2 1
1 2 3 2 1
1 2 3 4 3 2 1
1 2 3 4 5 4 3 2 1
Session 2Ver. 1.0
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:a. Set j = 0
b. Insert a space
c. Set j = j + 1
d. If j < n – i, go to step b // To display n – i spaces
e. Set j = 1
f. Display the value of j and insert a space
g. Set j = j + 1
h. If j < i, then go to step f // To display numbers from 1 to i
i. Set j = i – 1
Session 2Ver. 1.0
Data Structures and Algorithms
Exercise 4: Solution (Contd.)
j. Display the value of j and insert a space
k. Set j = j – 1
l. If j > 0, go to step j // To display numbers from i – 1 down // to 1
m. Give a line break
n. Set i = i + 1
Session 2Ver. 1.0
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”.
Session 2Ver. 1.0
Data Structures and Algorithms
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:a. If str[i] != substr[0], go to step b else go to step d
// To find the first matching character
b. Set i = i + 1
c. If (i < len1) go to step a
d. If i = len1, go to step e, else go to step g
e. Display “Substring not found in the string”
f. Exit
Exercise 5: Solution
Session 2Ver. 1.0
Data Structures and Algorithms
g. Set j = i // First character matched. Now match the // remaining characters
h. Set k = 0
i. If str[j] = substr[k], go to step j, else go to step m
j. Set j = j + 1
k. Set k = k + 1
l. If j < len1 and k < len2, go to step i
m. If k = len2, go to step n, else go to step p
n. Display “Substring found at position ” + (i + 1) + “ in the string”
o. Exit
p. Set i = i + 1
Exercise 5: Solution (Contd.)
Session 2Ver. 1.0
Data Structures and Algorithms
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.
Exercise 6
Session 2Ver. 1.0
Data Structures and Algorithms
Exercise 6: Solution
1. Accept two arrays, A1 and A2, each of size 10, from the user.
2. Declare an array, result, of size 20.
3. Set i = j = k = 0.
4. If (A1 [i] <= A2 [j]): // Insert the smaller element in the // result arraya. result [k] = A1 [i]
b. Set k = k + 1
c. Set i = i + 1
5. If (A1[i] > A2[j]): // Insert the smaller element in the // result arraya. result [k] = A2 [j]
b. Set k = k + 1
c. Set j = j + 1
Session 2Ver. 1.0
Data Structures and Algorithms
6. If (i < 10 and j < 10), go to step 4. // If none of the lists // has reached its end
7. 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
8. 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
9. Display result.
Exercise 6: Solution (Contd.)
Session 2Ver. 1.0
Data Structures and Algorithms
Write an algorithm to find the Highest Common Factor (HCF) of three numbers.
Exercise 7
Session 2Ver. 1.0
Data Structures and Algorithms
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 ):a. Display i // If i divides all the numbers, then HCF is i
b. Exit
Exercise 7: Solution
Session 2Ver. 1.0
Data Structures and Algorithms
7. Set i = i – 1.
8. Go to step 6.
Exercise 7: Solution (Contd.)
Session 2Ver. 1.0
Data Structures and Algorithms
Write an algorithm to multiply two 3 × 3 matrices.
Exercise 8
Session 2Ver. 1.0
Data Structures and Algorithms
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.
Algorithm 8: Solution
Session 2Ver. 1.0
Data Structures and Algorithms
12. If j < 3, go to step 6.
13. Set i = i + 1.
14. If i < 3, go to step 5.
15. Display result.
Algorithm 8: Solution (Contd.)
Session 2Ver. 1.0
Data Structures and Algorithms
Write a recursive algorithm to print the first n numbers in the Fibonacci series.
Algorithm 9
Session 2Ver. 1.0
Data Structures and Algorithms
Algorithm: Fibo (n)
1. If n = 1, return 0
2. If n = 2, return 1
3. Return (Fibo (n – 1) + Fibo (n – 2))
Algorithm 9: Solution