Python Tutorial Part 1  >  Conditionals and recursion

Conditionals and recursion

The modulus operator

The modulus operator works on integers (and integer expressions) and yields
the remainder when the first operand is divided by the second. In Python, the
modulus operator is a percent sign (%). The syntax is the same as for other
>>> quotient = 7 / 3
>>> print quotient
>>> remainder = 7 % 3
>>> print remainder
So 7 divided by 3 is 2 with 1 left over.
The modulus operator turns out to be surprisingly useful. For example, you can
check whether one number is divisible by another if x % y is zero, then x is
divisible by y.
Also, you can extract the right-most digit or digits from a number. For example,
x % 10 yields the right-most digit of x (in base 10). Similarly x % 100 yields the
last two digits.
4.2 Boolean expressions
A boolean expression is an expression that is either true or false. One way to
write a boolean expression is to use the operator ==, which compares two values
and produces a boolean value:
38 Conditionals and recursion
>>> 5 == 5
>>> 5 == 6
In the first statement, the two operands are equal, so the value of the expression
is True; in the second statement, 5 is not equal to 6, so we get False. True and
False are special values that are built into Python.
The == operator is one of the comparison operators; the others are:
x != y # x is not equal to y
x > y # x is greater than y
x < y # x is less than y
x >= y # x is greater than or equal to y
x <= y # x is less than or equal to y
Although these operations are probably familiar to you, the Python symbols are
different from the mathematical symbols. A common error is to use a single equal
sign (=) instead of a double equal sign (==). Remember that = is an assignment
operator and == is a comparison operator. Also, there is no such thing as =< or

Logical operators

There are three logical operators: and, or, and not. The semantics (meaning)
of these operators is similar to their meaning in English. For example, x > 0 and
x < 10 is true only if x is greater than 0 and less than 10.
n%2 == 0 or n%3 == 0 is true if either of the conditions is true, that is, if the
number is divisible by 2 or 3.
Finally, the not operator negates a boolean expression, so not(x > y) is true if
(x > y) is false, that is, if x is less than or equal to y.
Strictly speaking, the operands of the logical operators should be boolean expressions,
but Python is not very strict. Any nonzero number is interpreted as
>>> x = 5
>>> x and 1
>>> y = 0
>>> y and 1

In general, this sort of thing is not considered good style. If you want to compare
a value to zero, you should do it explicitly.
4.4 Conditional execution
In order to write useful programs, we almost always need the ability to check
conditions and change the behavior of the program accordingly. Conditional
statements give us this ability. The simplest form is the if statement:
if x > 0:
print "x is positive"
The boolean expression after the if statement is called the condition. If it is
true, then the indented statement gets executed. If not, nothing happens.
Like other compound statements, the if statement is made up of a header and a
block of statements:
The header begins on a new line and ends with a colon (:). The indented statements
that follow are called a block. The first unindented statement marks the
end of the block. A statement block inside a compound statement is called the
body of the statement.
There is no limit on the number of statements that can appear in the body of an
if statement, but there has to be at least one. Occasionally, it is useful to have a
body with no statements (usually as a place keeper for code you haven't written
yet). In that case, you can use the pass statement, which does nothing.
4.5 Alternative execution
A second form of the if statement is alternative execution, in which there are two
possibilities and the condition determines which one gets executed. The syntax
looks like this:
if x%2 == 0:
print x, "is even"
print x, "is odd"

If the remainder when x is divided by 2 is 0, then we know that x is even, and
the program displays a message to that effect. If the condition is false, the second
set of statements is executed. Since the condition must be true or false, exactly
one of the alternatives will be executed. The alternatives are called branches,
because they are branches in the flow of execution.
As an aside, if you need to check the parity (evenness or oddness) of numbers
often, you might 'wrap' this code in a function:
def printParity(x):
if x%2 == 0:
print x, "is even"
print x, "is odd"
For any value of x, printParity displays an appropriate message. When you call
it, you can provide any integer expression as an argument.
>>> printParity(17)
17 is odd
>>> y = 17
>>> printParity(y+1)
18 is even

Chained conditionals

Sometimes there are more than two possibilities and we need more than two
branches. One way to express a computation like that is a chained conditional:
if x < y:
print x, "is less than", y
elif x > y:
print x, "is greater than", y
print x, "and", y, "are equal"
elif is an abbreviation of 'else if.' Again, exactly one branch will be executed.
There is no limit of the number of elif statements, but the last branch has to be
an else statement:
if choice == 'A':
elif choice == 'B':
elif choice == 'C':
print "Invalid choice."

Each condition is checked in order. If the first is false, the next is checked, and so
on. If one of them is true, the corresponding branch executes, and the statement
ends. Even if more than one condition is true, only the first true branch executes.
As an exercise, wrap these examples in functions called
compare(x, y) and dispatch(choice).

Nested conditionals

One conditional can also be nested within another. We could have written the
trichotomy example as follows:
if x == y:
print x, "and", y, "are equal"
if x < y:
print x, "is less than", y
print x, "is greater than", y
The outer conditional contains two branches. The first branch contains a simple
output statement. The second branch contains another if statement, which has
two branches of its own. Those two branches are both output statements, although
they could have been conditional statements as well.
Although the indentation of the statements makes the structure apparent, nested
conditionals become difficult to read very quickly. In general, it is a good idea to
avoid them when you can.
Logical operators often provide a way to simplify nested conditional statements.
For example, we can rewrite the following code using a single conditional:
if 0 < x:
if x < 10:
print "x is a positive single digit."
The print statement is executed only if we make it past both the conditionals,
so we can use the and operator:
if 0 < x and x < 10:
print "x is a positive single digit."
These kinds of conditions are common, so Python provides an alternative syntax
that is similar to mathematical notation:

if 0 < x < 10:
print "x is a positive single digit."
This condition is semantically the same as the compound boolean expression and
the nested conditional.

The return statement

The return statement allows you to terminate the execution of a function before
you reach the end. One reason to use it is if you detect an error condition:
import math
def printLogarithm(x):
if x <= 0:
print "Positive numbers only, please."
result = math.log(x)
print "The log of x is", result
The function printLogarithm has a parameter named x. The first thing it does is
check whether x is less than or equal to 0, in which case it displays an error message
and then uses return to exit the function. The flow of execution immediately
returns to the caller, and the remaining lines of the function are not executed.
Remember that to use a function from the math module, you have to import it.


We mentioned that it is legal for one function to call another, and you have seen
several examples of that. We neglected to mention that it is also legal for a
function to call itself. It may not be obvious why that is a good thing, but it
turns out to be one of the most magical and interesting things a program can do.
For example, look at the following function:
def countdown(n):
if n == 0:
print "Blastoff!"
print n

countdown expects the parameter, n, to be a positive integer. If n is 0, it outputs
the word, 'Blastoff!' Otherwise, it outputs n and then calls a function named
countdown'itself'passing n-1 as an argument.
What happens if we call this function like this:
>>> countdown(3)
The execution of countdown begins with n=3, and since n is not 0, it outputs the
value 3, and then calls itself...
The execution of countdown begins with n=2, and since n is not 0, it
outputs the value 2, and then calls itself...
The execution of countdown begins with n=1, and since n is
not 0, it outputs the value 1, and then calls itself...
The execution of countdown begins with n=0, and
since n is 0, it outputs the word, 'Blastoff!' and
then returns.
The countdown that got n=1 returns.
The countdown that got n=2 returns.
The countdown that got n=3 returns.
And then you're back in main (what a trip). So, the total output looks like
As a second example, look again at the functions newLine and threeLines:
def newline():
def threeLines():
Although these work, they would not be much help if we wanted to output 2
newlines, or 106. A better alternative would be this:

def nLines(n):
if n > 0:
This program is similar to countdown; as long as n is greater than 0, it outputs one
newline and then calls itself to output n-1 additional newlines. Thus, the total
number of newlines is 1 + (n - 1) which, if you do your algebra right, comes out
to n.
The process of a function calling itself is recursion, and such functions are said
to be recursive.

Stack diagrams for recursive functions

In Section 3.11, we used a stack diagram to represent the state of a program during
a function call. The same kind of diagram can help interpret a recursive function.
Every time a function gets called, Python creates a new function frame, which
contains the function's local variables and parameters. For a recursive function,
there might be more than one frame on the stack at the same time.
This figure shows a stack diagram for countdown called with n = 3:
n 3
n 2
n 1
n 0
As usual, the top of the stack is the frame for main . It is empty because we
did not create any variables in main or pass any arguments to it.
The four countdown frames have different values for the parameter n. The bottom
of the stack, where n=0, is called the base case. It does not make a recursive
call, so there are no more frames.
As an exercise, draw a stack diagram for nLines called with n=4.

Infinite recursion

If a recursion never reaches a base case, it goes on making recursive calls forever,
and the program never terminates. This is known as infinite recursion, and it is
generally not considered a good idea. Here is a minimal program with an infinite
def recurse():
In most programming environments, a program with infinite recursion does not
really run forever. Python reports an error message when the maximum recursion
depth is reached:
File "<stdin>", line 2, in recurse
(98 repetitions omitted)
File "<stdin>", line 2, in recurse
RuntimeError: Maximum recursion depth exceeded
This traceback is a little bigger than the one we saw in the previous chapter.
When the error occurs, there are 100 recurse frames on the stack!
As an exercise, write a function with infinite recursion and run it in
the Python interpreter.

Keyboard input

The programs we have written so far are a bit rude in the sense that they accept
no input from the user. They just do the same thing every time.
Python provides built-in functions that get input from the keyboard. The simplest
is called raw input. When this function is called, the program stops and waits
for the user to type something. When the user presses Return or the Enter key,
the program resumes and raw input returns what the user typed as a string:
>>> input = raw_input ()
What are you waiting for?
>>> print input
What are you waiting for?
Before calling raw input, it is a good idea to print a message telling the user
what to input. This message is called a prompt. We can supply a prompt as an
argument to raw input:

>>> name = raw_input (" your name? ") your name? Arthur, King of the Britons!
>>> print name
Arthur, King of the Britons!
If we expect the response to be an integer, we can use the input function:
prompt = " the airspeed velocity of an unladen swallow?\n"
speed = input(prompt)
The sequence \n at the end of the string represents a newline, so the user's input
appears below the prompt.
If the user types a string of digits, it is converted to an integer and assigned to
speed. Unfortunately, if the user types a character that is not a digit, the program
>>> speed = input (prompt) the airspeed velocity of an unladen swallow?
What do you mean, an African or a European swallow?
SyntaxError: invalid syntax
To avoid this kind of error, it is generally a good idea to use raw input to get a
string and then use conversion functions to convert to other types.


modulus operator: An operator, denoted with a percent sign (%), that works on
integers and yields the remainder when one number is divided by another.
boolean expression: An expression that is either true or false.
comparison operator: One of the operators that compares two values: ==, !=,
>, <, >=, and <=.
logical operator: One of the operators that combines boolean expressions: and,
or, and not.
conditional statement: A statement that controls the flow of execution depending
on some condition.
condition: The boolean expression in a conditional statement that determines
which branch is executed.
compound statement: A statement that consists of a header and a body. The
header ends with a colon (:). The body is indented relative to the header.
block: A group of consecutive statements with the same indentation.
body: The block in a compound statement that follows the header.
nesting: One program structure within another, such as a conditional statement
inside a branch of another conditional statement.
recursion: The process of calling the function that is currently executing.
base case: A branch of the conditional statement in a recursive function that
does not result in a recursive call.
infinite recursion: A function that calls itself recursively without ever reaching
the base case. Eventually, an infinite recursion causes a runtime error.
prompt: A visual cue that tells the user to input data.