Assignment 2: Problem Solving Example

Unit 1 > Assignment 1 > problem solving

Let's start with the outer while loop that reads an integer from the user each time:

In pseudocode first:

    read an integer n
    while n > 0:
        compute number of divides
        read another integer into n

Which we can flesh out as:

n = int(input('Enter an integer: '))

while n > 0:
    # Compute and print number of divides.
    n = int(input('Enter an integer: '))

Notice how we've combined function calls. We could have written

n = int(input('Enter an integer: '))

n_str = input('Enter an integer: ')
n = int(n_str)

The first call prompts the user and gets a string. The second converts the string into an integer.

A1.1 Exercise: Write up the above in my_demo_problem1.py and test out the while loop.

Next, we want to successively divide by 2 (using integer division):

The pseudocode for that part could be:

    count = 0
    while n > 1:
        # divide by 2, increment count
    print(count)

In more detail:

    count = 0
    while n > 1:
        n = n // 2
        count += 1
    print('Number of divides for n=', n, ': ', count, sep='')

We can now include this in our outer while-loop as:

n = int(input('Enter an integer: '))

while n > 0:
    # Compute and print number of divides.
    count = 0
    while n > 1:
        n = n // 2
        count += 1
    print('Number of divides for n=', n, ': ', count, sep='')
    # Get the next one.
    n = int(input('Enter an integer: '))

print('Thank you!')

A1.2 Exercise: Does this work? Write up the above in my_demo_problem2.py and find out. Then explain what went wrong in your assignment2.pdf.

A1.3 Exercise: In my_demo_problem3.py fix the problem by rewriting the inner while-loop so that the output is correct (as shown in the problem description).

That solves the problem. However, we'll now explore a few alternative ways of writing the code:

First, let's write the dividing part in a function:

def num_divides(n):
    count = 0
    while n > 1:
        n = n // 2
        count += 1
    return count

n = int(input('Enter an integer: '))

while n > 0:
    count = num_divides(n)
    print('Number of divides for n=', n, ': ', count, sep='')
    n = int(input('Enter an integer: '))

print('Thank you!')

A1.4 Exercise: Write up the above in my_demo_problem4.py and explain in assignment2.pdf why we were able to use the same variable n in the function.

Finally, noticing that we get input once outside and then again inside the loop, we could ask: can we rewrite the outer loop so that we get input only inside the loop?

That is, can the outer loop structure look like this:

while n > 0:
    n = int(input('Enter an integer: '))
    # Do stuff ...

A1.5 Exercise: In my_demo_problem5.py show that this can indeed be done, using a break statement. Use the function num_divides() as given to you above.