16. Range type#

Author: Tue Nguyen

16.1. Outline#

A range is an immutable sequence of evenly-spaced integers such as
- 0, 1, 2, 3, 4, …
- 2, 4, 6, 8, …
We use range to quickly make a sequence of integers (often used in a for loop)

A range object is created using range() function
Syntax
- range(stop)
- range(start, stop)
- range(start, stop, step)
The rule for start, stop, and step is the same as in Python slicing
- start is included
- stop is excluded
- step specifies the gap between jumps
A range is very similar to a tuple but
- It doesn’t contain actual elements
- Each element will be generated on-the-fly when being asked
- This helps save memory and increase performance
To see the actual elements of a range we need to convert it to a list or a tuple

Syntax 1: range(stop)

# Create a range from 0 to stop-1
r = range(10)
print(r)
print(type(r))

range(0, 10)
<class 'range'>

# See the actual elements
tuple(r)

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Syntax 2: range(start, stop)

# Create a range from 5 to 10
r = range(5, 11)
tuple(r)

(5, 6, 7, 8, 9, 10)

Syntax 3: range(start, stop, step)

# Create a range of even integers from 0 to 10
r = range(0, 11, 2)
tuple(r)

(0, 2, 4, 6, 8, 10)

Negative steps

# When step is negative, start must > stop
# Ex: create 5, 4, 3, 2, 1
tuple(range(5, 0, -1))

(5, 4, 3, 2, 1)

# If not, we will have an empty range
tuple(range(0, 5, -1))

()

a) Ex 1: ranges in list comp

# Generate a list of squares <= 100
[e**2 for e in range(11)]

[0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

# Generate a list of even squares <= 100
[e**2 for e in range(11) if e % 2 == 0]

[0, 4, 16, 36, 64, 100]

b) Ex 2: ranges in for loops

# Print out even numbers divisible by 7 and less than 100
for i in range(0, 100, 2):
    if i % 7 == 0:
        print(i)

First, using ranges saves typing as shown in the examples above
Second, using ranges save memory
- range(10) doesn’t produce 10 integers
- It is like a blueprint or instruction for Python on how to generate those integers
- This blueprint will yield one element at a time when being asked, for example, in each iteration of a for loop
- Thus, range(10) or range(100000) have the same (very small) size in the memory
Let’s see an example

# Compute the sum of first 1 million integers
total = 0
for i in range(1, 1000001):
    total += i
    
total

500000500000

Remarks

In the above example, we iterate through a range of the first 1 million integers
In each iteration, the range() function will yield an appropriate integer through variable i
And we add i to total to accumulate the sum (Note: total += i is equivalent to total = total + i)
Each integer is used only once, thus it is a waste of memory if we keep a list of 1 million integers sitting there through each iteration
Using a range is a better solution

What is a range?

A range is an immutable sequence of evenly-spaced integers
We use range to quickly make a sequence of integers (often used in a for loop or in a comprehension)

Create a range

We use range() to create a range
Syntax
- range(stop)
- range(start, stop)
- range(start, stop, step)
A range is very similar to a tuple but it doesn’t contains actual elements
- Instead, it is more like a blueprint or instruction for Python on how to generate integers
- The actual elements will be generated when being asked
- All ranges have the same size in memory

Why uses ranges?

To be updated