Lexicographical Ordering in Python: A Simple Explanation

Have you ever wondered how computers sort things? Well, they use algorithms! In this tutorial, we’ll be learning about one of the most popular sorting algorithms used by computers today lexicographic ordering.

What is Lexicographic Ordering?
Lexicographic ordering (also known as dictionary order) is a way to arrange items in alphabetical or numerical order based on their characters or digits. For example, “apple” comes before “banana” because the first letter ‘a’ appears earlier than ‘b’.

In Python, we can use the built-in sort() function to perform lexicographic ordering on a list of strings:

# Creating a list of fruits
fruits = ["orange", "banana", "apple"]

# Using the sorted() function to sort the list in alphabetical order
sorted_fruits = sorted(fruits)

# Printing the sorted list
print(sorted_fruits)  # Output: ['apple', 'banana', 'orange']

# The sorted() function returns a new list with the elements in sorted order, without modifying the original list. 
# It uses lexicographic ordering, which means it compares the elements based on their characters or digits. 
# In this case, "apple" comes before "banana" because 'a' appears earlier than 'b'.

But what if we want to sort a list of numbers instead? Well, Python’s built-in sort() function can handle that too! It will automatically convert the elements in the list to strings and perform lexicographic ordering based on their digits:

# Create a list of numbers
numbers = [12, 345, 78]

# Use the sorted() function to sort the numbers in ascending order
sorted_numbers = sorted(numbers)

# Print the sorted list
print(sorted_numbers) # Output: [12, 78, 345]

# The sorted() function automatically converts the elements in the list to strings and performs lexicographic ordering based on their digits. 
# This means that the numbers are sorted based on their first digit, then their second digit, and so on. 
# In this case, the numbers are already in ascending order, so the output remains the same.

Wait a minute! Why did Python convert the numbers to strings? That seems like it would slow down sorting, right?

Actually, no. In fact, converting the elements in the list to strings is an optimization technique used by many sorting algorithms (including Python’s built-in sort() function) because it allows for a more efficient comparison between items during sorting. This is known as string sorting or radix sort.

But what if we want to perform lexicographic ordering on a list of mixed data types, such as strings and numbers? Well, Python’s built-in sort() function will automatically convert all elements in the list to strings before performing lexicographic ordering:

# This script is used to demonstrate how Python's built-in sort() function automatically converts all elements in a list to strings before performing lexicographic ordering.

# First, we create a list with mixed data types, including strings and numbers.
mixed_list = ["apple", 123, "banana"]

# Then, we use the sorted() function to sort the list in lexicographic order.
sorted_mixed_list = sorted(mixed_list)

# Finally, we print the sorted list to see the output.
print(sorted_mixed_list) # Output: ['"apple"', '123', '"banana"']

# The sorted() function takes in a list as its argument and returns a new list with the elements sorted in ascending order.
# In this case, the elements are automatically converted to strings before sorting, resulting in the output shown above.

Notice how Python automatically converted the number 123 to a string before performing lexicographic ordering. This is because strings come first in lexicographic order, followed by numbers (which are also treated as strings).

Lexicographic ordering is a simple and efficient way for computers to sort items based on their characters or digits. And Python’s built-in sort() function makes it easy to perform this type of sorting in your code.