1.11. Exercises for Lecture 1#

1.11.1. Exercise 1.1#

  • Write a program that reads an integer given as input from the user and determines whether it is divisible by 2, 3, 5, or 7.

  • Encapsulate the check into a function taking as input two numbers, and write a program that asks the user to insert two numbers and checks whether the first is divisible by the other one (and vice-versa).

1.11.2. Exercise 1.2#

  • Write a program that, given the three sides of a triangle, determines whether the triangle is acute-angled, rectangular-angled or obtuse-angled.

1.11.3. Exercise 1.3#

  • Write a program that, by using a while loop, returns the Fibonacci sequence up to the n-th term and stores it in a python list.

1.11.4. Exercise 1.4#

  • Write a program that, by using a for loop, returns the Fibonacci sequence up to the n-th term and stores it in a python dictionary, where the key represents the index of each element and value its actual value.

1.11.5. Exercise 1.5#

  • Define a function that returns the Fibonacci sequence up to the n-th term.

    Hint

    The function prototype could be

    def fibonacci (n) :
    """A function that calculates the Fibonacci sequence up to the n-th term

    Args:
        n (int): the n-th term of the sequence

    Returns:
        list: a list with the Fibonacci sequence
    """

  • Test the function with a main program, filling a list with the elements of the sequence.

  • Create a new list containing only the elements with even index in the list.

  • Create a new list containing only the elements with odd index in the list.

  • Move the function in a library and import it in the main program.

1.11.6. Exercise 1.6#

  • By writing a suitable program and functions, verify whether the value of variables passed to a function get modified in the main program, if they are changed inside the function.

  • Perform the check for the various types described during the lecture.

1.11.7. Exercise 1.7#

  • Write a python program that determines the solution of second-order equations

1.11.8. Exercise 1.8#

  • Write a python program that finds the list of prime integer numbers smaller than 100, starting by knowing that 2 is a prime number

1.11.9. Exercise 1.9#

  • Write a python program that finds the decomposition in prime factors of a positive integer number, implementing the algorithm in a function encapsulated in a python module

  • Write a test function, in the library, that checks the correctness of the procedure for all numbers from 1 to 100