How do Nested List Comprehensions in Python Work and What are Their Equivalents in Loop Form?

Understanding Nested List Comprehension

List comprehensions offer a concise and elegant syntax for manipulating collections in Python. By combining nested for loops, one can construct complex data structures with ease. Here's a detailed breakdown of how nested list comprehensions work:

Consider the given list comprehension:

<code class="python">[(min([row[i] for row in rows]),max([row[i] for row in rows])) 
for i in range(len(rows[0]))]</code>

This code is equivalent to the following loop:

<code class="python">result = []
for i in range(len(rows[0])):
  innerResult = []
  for row in rows:
    innerResult.append(row[i])
  innerResult2 = []
  for row in rows:
    innerResult2.append(row[i])
  tuple = (min(innerResult), max(innerResult2))
  result.append(tuple)</code>

In general, a nested list comprehension of the form:

<code class="python">[exp2([exp1 for x in xSet]) for y in ySet]</code>

can be translated to:

<code class="python">result = []
for y in ySet:
  innerResult = []
  for x in xSet:
    innerResult.append(exp1)
  exp2Result = exp2(innerResult)
  result.append(exp2Result)</code>

For simpler cases, such as:

<code class="python">[exp1 for x in xSet for y in ySet] </code>

it is equivalent to:

<code class="python">result = [] 
for x in xSet:
  for y in ySet: 
    result.append(exp1)</code>

whereas,

<code class="python">[[exp1 for x in xSet] for y in ySet]</code>

is equivalent to:

<code class="python">result = []
for y in ySet:
  innerResult = []
  for x in xSet:
    innerResult.append(exp1)
  result.append(innerResult)</code>

It's important to note that the nesting of for loops in a single list comprehension is always from left to right. For example:

<code class="python">[item for item in row for row in matrix] </code>

This code will not work because the inner loop variable 'row' is not defined in the outer loop. The correct form is:

<code class="python">[item for row in matrix for item in row] </code>

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