10. Loops

  • if/else are great for having a block of code run when some condition is True

  • Sometimes we need a block to repeatedly run while some condition is True

10.1. Reusing and Updating Variables

  • Before we look at loops, consider the following code

 1a = 5
 2print(a)
 3
 4b = 6
 5print(a)
 6
 7a = a + b
 8print(a)
 9
10a = 3
11a = a + 1
12print(a)

Activity

What is the value of a at each print statement? In other words, a is printed out four times — what values are printed out?

  • The point being emphasized is that there is nothing stopping us from reusing variables

    • Assign a value to some variable

    • Update/change the value stored in that variable

  • A very common pattern for incrementing the value of some variable in programming is as follows

1a = a + 1

  • The above example will add one to whatever value is stored in a and then store that new value back to a

  • For example

    • If a starts with the value 5

    • Calculate a + 1, which is 6 in this example

    • Store the newly calculated value of 6 in a

  • This and similar patterns are so common that many programming languages have shorthand operators for this

1a += 1      # Effectively the same as a = a + 1

  • The above example is effectively identical to the previous

  • It means, add 1 to a and put the newly calculated value back into a

Activity

Start with a = 5.

  1. Figure out what a += 2 does.

  2. See what happens when you use a *= 2.

  3. Try other operators to see what works.

10.2. While loops

  • So far, if we need to run the same code multiple times, we repeat the code as many times as we need

    • For example, if I wanted to print("Hello, world!") five times, I need to write that print statement 5 times

  • The trouble with this is

    • It’s tedious

    • It doesn’t scale well

    • It’s prone to errors

    • It will not work for some variable number of times

      • For example, what if I want to print n times where n is some parameter to a function

  • This is where the while statement comes in

  • It will repeat some code while some condition is True

    • while some_condition:

    • The indented code will run while the condition is True

1counter = 0
2while counter < 10:
3    print(counter)
4    counter += 1

  • The above example will print out the numbers 0 – 9

    • We initialized a counter variable outside the loop

    • Before each iteration, Python checks the while condition

    • If the condition is True, the indented code runs

      • print out the value of counter

      • Increment counter

      • Repeat the loop until the condition is False

Warning

Off-by-one errors are very common when writing loops. For example, be careful about whether your stopping condition should include the final value or stop before it.

Starting with counter = 0:

  • while counter < 10: prints 0 through 9

    • Runs 10 times

  • while counter <= 10: prints 0 through 10

    • Runs 11 times

Activity

What would happen if counter += 1 was not included in the loop? Try to answer based on what you know. Confirm what happens by trying to run the code.

To stop the infinite loop, select the stop button in Colab.

A loop usually needs something inside to change, otherwise the condition may never become False.

10.2.1. Tracing Through A Function By Hand

  • Trace through the below code by hand for a few values of n

  • See if you can figure out what this function is doing

    • Note that n -= 1 is short hand for n = n - 1

1def trace_through_me_by_hand(n: int) -> int:
2    result = 1
3    while n > 1:
4        result = result * n
5        n -= 1
6    return result

  • while loops can get complex quickly

    • Comments here would have helped make the intent clearer

  • When tracing through the code, don’t try to do it all in your head

  • Create a table to keep track of the values

  • Below is an example with trace_through_me_by_hand(4)

n

result

4

1 -> 4

3

4 -> 12

2

12 -> 24

1

Stop

Activity

Write a function called int_sum(n) that takes a single integer n as a parameter and returns the sum of all the numbers between 0 and n inclusively (include n in the summation).

When you finish writing the function, do not run it right away — trace through the program by hand like with the trace_through_me_by_hand above.

Activity

Create a new function called int_sum_print that is the same as int_sum, however this function should print out the values of all the variables each time in the loop. Ideally this should be formatted similar to the table created with trace_through_me_by_hand, but do not worry too much about how the prints format the output.

10.3. Algorithm

Activity

  1. Write down (in English) an algorithm for calculating the sum of all the even numbers between 0 and n.

  2. Convert the algorithm into a Python function sum_even_numbers(n: int) -> int.

  3. Write some assert tests to verify correctness.

10.4. For Next Topic