8. Understanding the while loop

A set of Python statements can be executed repeatedly using a while loop. This chapter examines the syntax of the while loop using some simple examples.

8.1. A simple while loop

Type the following code at the Python prompt:

>>> while (1 < 2):
...     print 'hello'
...     print 'world'
...

The Python print statement can be used for displaying a message on the screen; the message should be in single (or double) quotations. Both the print statements should be indented properly. You should type an empty line after the last print statement. You will see that Python keeps on printing the two messages hello and world repeatedly!

The general format of a while loop is:

while (condition):
   body

The body can be either a single statement or multiple statements, all properly indented (just like the body of a function or an if-else statement). Python first checks the condition and if it is found to be true, the body gets executed. Once again, Python checks the condition and if it is found to be true, the body is executed again. This process repeats until the condition becomes false. If the condition never becomes false, Python will keep on repeating this process infinitely. In the above example, the condition is:

1 < 2

and the body is composed of two statements:

print 'hello'
print 'world'

Python first checks the condition - 1 is definitely less than 2, so the condition is true and the body (the two print statements) gets executed. Python once again checks the condition - again, 1 is less than 2, condition is true and so the body gets executed. 1 is never going to be bigger than 2, so the condition will never become false and as a result, Python will never stop executing the loop! If you wish, you can type Ctrl-c (hold down the Ctrl key and press c) to forcibly terminate the loop.

8.2. A loop which terminates

Here is a while loop which does something a bit more interesting than printing hello and world:

>>> i = 0
>>> while (i < 5):
...      print i
...      i = i + 1
...

The condition is initially true - i has the value 0 and zero is less than 5. So the body gets executed. The print statement displays the value of i on the screen. The next statement is:

i = i + 1

You should read this as: i assigned to i plus 1. The logic is:

New value of i is old value of i plus one.

So, the value of i becomes 1. Python once again checks the condition - it’s true (because 1 is less than 5). So the body gets executed again. The value of i is printed(this time, the value is 1). The next statement(i = i + 1) changes the value of i to 2. The condition gets checked once more. Again, it is true (2 is less than 5). So the body gets executed once more. The print statement displays 2 on the screen (value of i is now 2) and the value of i gets changed to 3 in the next statement. This process repeats until the value of i becomes 5. At this point, the condition becomes false and the loop terminates. Here is what you will see on the screen:

0
1
2
3
4

8.3. Finding HCF using Euclid’s method

The term algorithm is commonly used in computer programming. It refers to a precise set of rules for solving a problem. A very famous numerical algorithm exists to find out the highest common factor (also called the greatest common divisor) of two numbers. The algorithm was invented by Euclid; it’s therefore called the Euclid’s algorithm.

Here is how the algorithm works. Say you wish to find out the HCF of two numbers A and B. Simply repeat the following steps until both numbers become equal:

• If A is greater than B, change A to A-B and do not modify B
• If B is greater than A, change B to B-A and do not modify A

The value of A (and B) when both become equal will be the Highest Common Factor!

Let’s try this out with two numbers, A=18 and B=42.

B is greater than A, so B becomes 24 and A remains as 18. So, we have:

A = 18, B = 24

If we repeat this process, we get:

A = 18, B = 6
A = 12, B = 6
A = 6,  B = 6

Finally, both A and B become equal (both have value 6). The HCF of 18 and 42 is 6.

You can try out this procedure on different pairs of numbers and verify that it works perfectly!

Even better, you can write a loop in Python to discover the HCF:

>>> a = 18
>>> b = 42
>>> while (a <> b):
...    if (a > b):
...       a = a - b
...    else:
...       b = b - a
...
>>> a
6
>>> b
6
>>>

Initially, a and b are not equal, so the condition “a <> b” (remember, ‘<>’ is the not equal to operator) is true. As b is greater then a, the else part of the if-else statement gets executed and value of b changes to 24 while a remains unchanged. In the next iteration of the loop, b becomes 6 and a remains as 18. This process repeats until both a and b become equal. At that point, the loop terminates. Now, if you examine the value of a and b, you will see that both are 6.

A small problem with this approach is that any time you wish to calculate the HCF of two numbers, you have type the whole loop all over again. This is difficult. The next section shows how this problem can be solved.

8.4. Defining a function to compute HCF of two numbers

Look at the following Python program:

>>> def hcf(a, b):
...     while (a <> b):
...        if (a > b):
...            a = a - b
...        else:
...            b = b - a
...     return a
...
>>> hcf(18, 42)
6
>>> hcf(15,20)
5
>>>

The only change is that we are now writing the loop within a function called hcf (the name of the function doesn’t really matter. You can call it by any name you like). Now whenever you wish to find out hcf of two numbers, you just have to call the function hcf with those two numbers as parameters. Say you call:

hcf(15,20)

Within the function, a will assume the value 15 and b will assume the value 20. The while loop will terminate when a and b both become equal to 5. Once the while loop is over, the return statement will transmit the value 5 as value of the function hcf(15,20).