Nested List Comprehension Explained

Nested list comprehensions offer a concise way to create complex lists dynamically using iterables. While their functionality can be understood through equivalent for loops, their systematic approach helps apply the concept across varying examples.

Syntax and Translation

Nested list comprehensions follow the syntax:

[exp2([exp1 for x in xSet]) for y in ySet]

Breaking this down, you'll find that for each element y in ySet, an inner list is created. Within this inner list, an expression exp1 is evaluated for each element x in xSet. Finally, the outer list comprehension evaluates exp2 using each inner list created.

Simplified Examples

• Flattened Comprehension:

[exp1 for x in xSet for y in ySet]

Equivalent for loop:

result = []
for x in xSet:
    for y in ySet:
        result.append(exp1)

• List of Lists Comprehension:

[[exp1 for x in xSet] for y in ySet]

Equivalent for loop:

result = []
for y in ySet:
    innerResult = []
    for x in xSet:
        innerResult.append(exp1)
    result.append(innerResult)

Systematic Application

To generalize, the following steps can be followed:

1. Start from the innermost for loop.
2. Create a new list using the expression within that for loop for each element in its iterable.
3. Move to the next for loop and use the list created in the previous step as the iterable.
4. Repeat steps 1-3 for each for loop in the comprehension.
5. Use the outer expression (exp2) to evaluate the final result.

Remember, the nesting of for loops occurs left-to-right, allowing for complex list transformations in a concise syntax.