Chapter 5: Going Back Again

5.1 Repeating Steps

Many algorithms are built on the concept of a loop where you repeat some steps of the algorithm multiple times. For example:

• On a shampoo bottle, it says “Lather, rinse, and repeat”.
• In our “guess the number” algorithm, we have to keep on guessing until we guess the number right.
• In adding and subtracting algorithms you learned in grade school you must keep going for every digit of the number.

With loops we will be able to write programs that do these kinds of things, and repeat some part of the program over again.

As a first example, consider the “guess the number” game. We could in theory just use if statements to guess all the numbers:

if input("Did you guess 1? ") == "yes":
    print("Got it!")
elif input("Did you guess 2? ") == "yes":
    print("Got it!")
elif input("Did you guess 3? ") == "yes":
    print("Got it!")
elif input("Did you guess 4? ") == "yes":
    print("Got it!")
elif input("Did you guess 5? ") == "yes":
    print("Got it!")
elif input("Did you guess 6? ") == "yes":
    print("Got it!")
elif input("Did you guess 7? ") == "yes":
    print("Got it!")
elif input("Did you guess 8? ") == "yes":
    print("Got it!")
elif input("Did you guess 9? ") == "yes":
    print("Got it!")
elif input("Did you guess 10? ") == "yes":
    print("Got it!")

However, this is clearly kind of repetitive. It also isn’t sustainable, if we wanted to write a program that would guess a number from 1 to 100, that would be a lot of typing! Instead we should use a loop.

5.2 While Loops

The simplest loop in Python is the while loop. The while loop looks a lot like an if statement. It starts with the word while, and then it has a condition, followed by a colon. Then there are some statements indented over. These statements are called the loop body.

The following is a simple example of a program with a while loop:

Program 5.1

number = 1
while number <= 10:
    print(number)
    number = number + 1

The way a while loop works is sort of similar to an if statement too. When this program is run, we start by setting the number variable to 1. Next we check if that variable is less than or equal to 10. If so we do the statements indented under the loop.

The difference is that, after we’re done those statements, we go back to the top. It will check the condition another time. If it’s still true, it does the loop again. It will keep on doing it over and over again until the condition is false.

In this particular case, the program will find that the condition is true the first time, so it will print the number, and then add one to it. Now the number is 2. This is still less than or equal to 10, so it does the loop body again. It keeps going on like this until the number variable is bigger than 10. So the output will be this:

1
2
3
4
5
6
7
8
9
10

We can now use a while loop to implement the simple version of the “guess a number” game as follows:

Program 5.2

# start by asking for 1
number = 1
answer = input("Did you guess 1?")

# keep doing the loop until the answer is yes
while answer != "yes":
    number = number + 1
    answer = input("Did you guess " + str(number) + "?")

# when we are done the loop it means we got it
print("Got it!")

This program will keep looping until the user enters “yes”. At that point, the condition becomes false and so the loop exits.

There’s quite a bit going on in this code, so let’s go through it.

• First, we need to ask them the first question: whether their number was 1 or not. We do this so that the variable answer is defined for the start of the loop.
• We then have the loop condition which checks if their answer was not “yes”. If it wasn’t we go into the loop. If it was, then we got it on the first try, and skip over the whole loop.
• Inside the loop body, we add 1 to the number variable. This is how we change the thing we guess from 1, to 2, to 3, etc.
• We also ask them if the latest number is their guess or not. Doing so is a little tricky. Unlike print, the input function doesn’t let us pass it numbers, only a string. So we have to convert number to a string with the str function, and join it to the rest of the question.
• The code after the while loop, which prints “Got it!”, will only happen once the condition becomes false. For this program that means that answer was yes.

5.3 Example: Checking Input

We’ve talked about how to use if statements to check if user input is valid. For instance, this program will check if the user enters a negative number for their age:

# program that checks for bad data once
age = int(input("How old are you? "))

if age < 0:
    print("Hey, your age can't be negative!")
    age = int(input("How old are you for real? "))

print("You are", age, "years old.")

However, if someone puts in a negative number twice in a row, then the bad input will still get through. We could of course repeat the check again to make really sure:

# (silly) program that checks for bad data twice
age = int(input("How old are you? "))

if age < 0:
    print("Hey, your age can't be negative!")
    age = int(input("How old are you for real? "))

if age < 0:
    print("Hey, your age STILL can't be negative!")
    age = int(input("How old are you for real? "))

print("You are", age, "years old.")

Of course now, they can put in a negative number three times. Clearly this is not a great way of approaching this. A better way would be to use a loop. In this case, we will want to keep on asking them, over and over again, until they eventually put in valid data. Maybe this is the first try, or maybe it’s the hundredth.

We can do it by simply replacing if with while. Now, the program will keep asking the user for data until it is greater than or equal to 0. Now the program looks like this:

Program 5.3

# program that checks for bad data over and over
age = int(input("How old are you? "))

while age < 0:
    print("Hey, your age can't be negative!")
    age = int(input("How old are you for real? "))

print("You are", age, "years old.")

Below is an example run of this program, where the user messes up by entering a negative age a few times in a row:

How old are you? -5
Hey, your age can't be negative!
How old are you for real? -2
Hey, your age can't be negative!
How old are you for real? -7
Hey, your age can't be negative!
How old are you for real? -1000
Hey, your age can't be negative!
How old are you for real? 27
You are 27 years old.

5.4 Infinite Loops

One danger when creating loops is that the condition might never become true. For example, there’s a mistake in the program below which causes this:

number = 1

while number < 10:
    print(number)
    numer = number + 1

print("All done!")

Here we mistyped “number” as “numer”. So when we run the addition, it doesn’t change number to be bigger. Instead it makes a new variable. Because of our typo, the variable number never reaches 10, so the condition stays false forever. This is called an infinite loop and is a common programming mistake.

If you run this program, it will never stop running. It will just continue on forever. Or until you stop it, which is probably what you will want to do. You can do this in Thonny by hitting the stop button (), or by choosing “Stop/Restart backend” from the “Run” menu.

5.5 Example: Running Total

Let’s write a program that will compute a running total of numbers. The way this will work is that you will put in numbers to the program, and it will add them all together, and show you the sum after each one. You can then stop the program by entering a 0 (there’s no reason to add 0 normally since it won’t change anything).

Below is an example of a run of this program, so you can see how it should work before we dive into some code:

What's the first number? 7
Running total is 7
Next: 12
Running total is 19
Next: -5
Running total is 14
Next:  2
Running total is 16
Next:  0
The total is 16

The code which solves this problem is given below:

Program 5.4

# get the first number
number = int(input("What's the first number? "))
total = number

# keep going until they enter 0
while number != 0:
    print("Running total is", total)
    number = int(input("Next: "))
    total = total + number

# print the final result
print("The total is", total)

We start by getting the first number from the user. The number variable is used to store the thing they just entered. The total variable is used to keep track of the running sum. It starts as the same as the number first entered.

The condition for this while loop is number != 0. So we will keep going as long as the number they entered wasn’t 0.

Inside the loop, we do a few things. First we print out the total so the user can see it change for each number they enter. Then we get the next number. Lastly we add it to the total variable.

After the loop, we just print out the total sum.

This kind of program would be impossible to write without a loop of some kind. Even if we wanted to copy and paste a bunch of code, we couldn’t because we don’t know ahead of time how many numbers the user will want to add.

5.6 For Loops

There is another type of loop in Python called a for loop. A for loop is similar to a while loop in that it lets you do some piece of code over and over again. But it is different in that it loops through every element in a sequence of some kind.

The only type of sequence we have seen so far is a string. A string is a sequence of characters (which could be letters, digits, punctuation, etc.). Below is a for loop that just prints each character one by one:

Program 5.5

name = input("What's your name? ")

for letter in name:
    print(letter)

The for loop looks a bit different from the while loop. Instead of the condition, we have the word for followed by a variable name. The variable name above is letter. Then we have the word in, followed by the sequence we are using. In this case, that’s the string name.

When you run a for loop, it makes the variable (letter in this case) equal to each thing in the sequence one-by-one. It then runs the loop body on it. So if we enter, let’s say “Amy” as the name, then it will first set letter to “A”. It will then run the loop body on “A”. Next it will run the loop body again, but with letter equal to “m”. Lastly it will run the loop body with letter as “y”. Then it will stop.

The result of running this program can be seen below:

What's your name? Amy
A
m
y

The result of this program is that it prints the name out vertically.

Every for loop could be replaced by a while loop that does the same thing. In the example above, we could have written a while loop to count up to the length of the string, and used indices to get the letters out.

But for loops have a few benefits when looping through a sequence:

• It’s much harder to accidentally make an infinite for loop.
• For loops are a little easier to read. They make our intention of looping through a sequence more obvious.

5.7 The range Function

For loops can be used to loop through any sequence. A string is just one type of sequence. There are several others in Python. The next one that we will look at is a range.

The range function is used to create a sequence of numbers. For example, we could use range to make a sequence of numbers from 1 through 10. Or a sequence of numbers from 25 down to 5. We can then combine range with a for loop to write code that does something for each number in the sequence.

If we pass range 1 number, it will give us a sequence from 0 up to (but not including) that number. For example, if we pass 10:

for i in range(10):
    print(i)

Then range will give us a sequence of numbers going from 0 through 9. Instead of starting at 1, range starts at 0 — just like string indices ¹. If we run this program, we will get:

0
1
2
3
4
5
6
7
8
9

Just like the for loop with a string, this for loop sets our variable (called i) to each thing in the sequence one by one. It then runs the loop body once for each value.

If we don’t want to start on 0, we can also pass range a starting point. To do that, we have to pass two numbers. The first is the start and the second is 1 past the ending point.

For example, if we want to make a range of numbers from 5 through 10, including both end points, we could do it like this:

for i in range(5, 11):
    print(i)

This program will print the numbers from 5 to 10:

5
6
7
8
9
10

Lastly, we can pass three numbers into range. The first two are the same as before. The last number we pass in will be used as step between each. For example, if we want to go through even numbers from 2 through 10, we could pass a step of 2:

for i in range(2, 11, 2):
    print(i)

This gives us the following:

2
4
6
8
10

The step is just the amount that you add to each number to go on to the next one.

We could also pass a negative number for the step to go backwards:

for i in range(10, 0, -1):
    print(i)

This gives us the following:

10
9
8
7
6
5
4
3
2
1

5.8 Example: Temperature Table

As an example of a for loop with a range, let’s write a program which gives us a table of Celsius temperatures with their equivalent Fahrenheit temperatures. Rather than read in one, and print out the other, we will just print a whole table. That way the user can see how the two relate.

One part of this is converting one temperature from Fahrenheit to Celsius. We can do this by subtracting 32 from the Fahrenheit temperature and then multiplying by ⁵⁄₉.

The next part is doing this for a bunch of temperatures. To be helpful, let’s make the range of temperatures start at the lowest Fahrenheit temperature it’s likely to be. Here in Virginia, it’s rare that it gets below 0°, or above 100° Fahrenheit. We can therefore use 0 as the starting point to range, and 101 as the ending point (remember it has to be just past the value we want to end at.

It will also be nicer if we don’t print every temperature from 0° to 100°. 100 lines of output will probably be too much. Instead, we will go in increments of 5°. To do this, we can just pass 5 for the last thing to range.

The program, then, is given below:

Program 5.6

# loop from 0 to 100, going 5 at a time
for far in range(0, 101, 5):
    # do the conversion, and round it
    cel = (far - 32) * 5/9
    cel = round(cel, 2)

    # print one line of the table
    print(far, "degrees F =", cel, "degrees C")

Here our loop variable is called far (short for Fahrenheit). It is given all the values in the sequence of numbers we make with range. First it’s 0, then 5, then 10, all the way to 100.

For each time through the loop, we do all of the commands on the loop body. This converts to a Celsius temperature, rounds it, and prints out the two temperatures that are equivalent.

The output from this program is given below:

0 degrees F = -17.78 degrees C
5 degrees F = -15.0 degrees C
10 degrees F = -12.22 degrees C
15 degrees F = -9.44 degrees C
20 degrees F = -6.67 degrees C
25 degrees F = -3.89 degrees C
30 degrees F = -1.11 degrees C
35 degrees F = 1.67 degrees C
40 degrees F = 4.44 degrees C
45 degrees F = 7.22 degrees C
50 degrees F = 10.0 degrees C
55 degrees F = 12.78 degrees C
60 degrees F = 15.56 degrees C
65 degrees F = 18.33 degrees C
70 degrees F = 21.11 degrees C
75 degrees F = 23.89 degrees C
80 degrees F = 26.67 degrees C
85 degrees F = 29.44 degrees C
90 degrees F = 32.22 degrees C
95 degrees F = 35.0 degrees C
100 degrees F = 37.78 degrees C

There are other types of sequences that for loops work with. We will see a few more as we go. We will also see lots more examples of solving problems with loops. Almost all algorithms use looping in some fashion.

5.9 Comprehension Questions

1. What is the purpose of writing loops in a program?
2. How is a while loop different from an if statement in Python?
3. What is an infinite loop? Are they usually a good thing?
4. How are for loops different than while loops?
5. What is the purpose of the range function?
6. When would you choose to use a for loop vs. a while loop?

5.10 Programming Exercises

1. Write a program that reads in a number from the user, and a message. The pro- gram should then print the message out “number” many times. For example, if they enter 3 and “Hello”, then the program should print “Hello” three times.

2. Write a program which will let the user print the length of strings, for as many as they want. It should ask them to enter a string and then print the length of it. It should keep doing this until they enter an empty string (with a length of 0). Then the program should end.

3. Your younger sibling is working on learning their times tables. They want help with specific numbers, so have asked you to write a program to print one column of a times table. For example, if they want help with 7, your program would print:

       7 * 1 = 7
       7 * 2 = 14
       7 * 3 = 21
       ...
       7 * 10 = 70

   Your program should read in the number they want the times table column of (7 of this case). It should then output this column showing the products of the number with 1 through 10. f

4. Write a sum calculator. Begin by asking the user how many numbers they wish to enter. Then write a loop that executes that many times. Each time, read in a number from the user and add it to a running tally. At the end, print out the sum of all the numbers they entered.

5. Ask the user to enter a number and then tell them how many digits are in that number. This can be done by dividing the number by 10 until the number is less than 1, counting how many divisions you did to make that happen.

6. The Fibonacci series is a sequence of numbers. The first two numbers in the series are both 1. Each number after that is the sum of the previous two numbers. So the series starts as “1, 1, 2, 3, 5, 8, 13, 21…”. Write a program to print the first 50 numbers in the series.

Footnotes

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