# How to Think Like a Computer Scientist: The PreTeXt Interactive Edition

## Section8.3The while Statement

There is another Python statement that can also be used to build an iteration. It is called the while statement. The while statement provides a much more general mechanism for iterating. Similar to the if statement, it uses a boolean expression to control the flow of execution. The body of while will be repeated as long as the controlling boolean expression evaluates to True.
The following figure shows the flow of control.
We can use the while loop to create any type of iteration we wish, including anything that we have previously done with a for loop. For example, the program in the previous section could be rewritten using while. Instead of relying on the range function to produce the numbers for our summation, we will need to produce them ourselves. To to this, we will create a variable called aNumber and initialize it to 1, the first number in the summation. Every iteration will add aNumber to the running total until all the values have been used. In order to control the iteration, we must create a boolean expression that evaluates to True as long as we want to keep adding values to our running total. In this case, as long as aNumber is less than or equal to the bound, we should keep going.
Here is a new version of the summation program that uses a while statement.
You can almost read the while statement as if it were in natural language. It means, while aNumber is less than or equal to aBound, continue executing the body of the loop. Within the body, each time, update theSum using the accumulator pattern and increment aNumber. After the body of the loop, we go back up to the condition of the while and reevaluate it. When aNumber becomes greater than aBound, the condition fails and flow of control continues to the return statement.
The same program in codelens will allow you to observe the flow of execution.
More formally, here is the flow of execution for a while statement:
1. Evaluate the condition, yielding False or True.
2. If the condition is False, exit the while statement and continue execution at the next statement.
3. If the condition is True, execute each of the statements in the body and then go back to step 1.
The body consists of all of the statements below the header with the same indentation.
This type of flow is called a loop because the third step loops back around to the top. Notice that if the condition is False the first time through the loop, the statements inside the loop are never executed.

### Warning8.3.1.

Though Python’s while is very close to the English “while”, there is an important difference: In English “while X, do Y”, we usually assume that immediately after X becomes false, we stop with Y. In Python there is not an immediate stop: After the initial test, any following tests come only after the execution of the whole body, even if the condition becomes false in the middle of the loop body.
The body of the loop should change the value of one or more variables so that eventually the condition becomes False and the loop terminates. Otherwise the loop will repeat forever. This is called an infinite loop. An endless source of amusement for computer scientists is the observation that the directions written on the back of the shampoo bottle (lather, rinse, repeat) create an infinite loop.
In the case shown above, we can prove that the loop terminates because we know that the value of aBound is finite, and we can see that the value of aNumber increments each time through the loop, so eventually it will have to exceed aBound. In other cases, it is not so easy to tell.

### Note8.3.2.

Introduction of the while statement causes us to think about the types of iteration we have seen. The for statement will always iterate through a sequence of values like the list of names for the party or the list of numbers created by range. Since we know that it will iterate once for each value in the collection, it is often said that a for loop creates a definite iteration because we definitely know how many times we are going to iterate. On the other hand, the while statement is dependent on a condition that needs to evaluate to False in order for the loop to terminate. Since we do not necessarily know when this will happen, it creates what we call indefinite iteration. Indefinite iteration simply means that we don’t know how many times we will repeat but eventually the condition controlling the iteration will fail and the iteration will stop. (Unless we have an infinite loop which is of course a problem.)
What you will notice here is that the while loop is more work for you — the programmer — than the equivalent for loop. When using a while loop you have to control the loop variable yourself. You give it an initial value, test for completion, and then make sure you change something in the body so that the loop terminates.
So why have two kinds of loop if for looks easier? The next section, Section 8.4 , shows an indefinite iteration where we need the extra power that we get from the while loop.

### Note8.3.3.

This workspace is provided for your convenience. You can use this activecode window to try out anything you like.

### Checkpoint8.3.4.

True or False: You can rewrite any for-loop as a while-loop.
• True
• Although the while loop uses a different syntax, it is just as powerful as a for-loop and often more flexible.
• False
• Often a for-loop is more natural and convenient for a task, but that same task can always be expressed using a while loop.

### Checkpoint8.3.5.

The following code contains an infinite loop. Which is the best explanation for why the loop does not terminate?
n = 10
while n > 0:
n = n + 1

• n starts at 10 and is incremented by 1 each time through the loop, so it will always be positive
• The loop will run as long as n is positive. In this case, we can see that n will never become non-positive.
• answer starts at 1 and is incremented by n each time, so it will always be positive
• While it is true that answer will always be positive, answer is not considered in the loop condition.
• You cannot compare n to 0 in while loop. You must compare it to another variable.
• It is perfectly valid to compare n to 0. Though indirectly, this is what causes the infinite loop.
• In the while loop body, we must set n to False, and this code does not do that.
• The loop condition must become False for the loop to terminate, but n by itself is not the condition in this case.

### Checkpoint8.3.6.

What is printed by this code?
n = 1
x = 2
while n < 5:
n = n + 1
x = x + 1
n = n + 2
x = x + n
print(n, x)

• 4 7
• Setting a variable so the loop condition would be false in the middle of the loop body does not keep the variable from actually being set.
• 5 7
• Setting a variable so the loop condition would be false in the middle of the loop body does not stop execution of statements in the rest of the loop body.
• 7 15
• After n becomes 5 and the test would be False, but the test does not actually come until after the end of the loop - only then stopping execution of the repetition of the loop.