Python Programming
Python Programming
List comprehensions are a powerful, concise, and expressive way to create or transform lists in Python. They allow you to write cleaner and more efficient code compared to traditional looping and list manipulation methods. The first thing to note is that, although we call this construct "List Compehension", it doesn't just apply to lists and the same techniques can be used to construct other objects like sets.
List comprehensions are so named because they comprehend or encapsulate the entire process of creating and transforming a list in a single, concise expression. The term "comprehension" conveys the idea that the syntax is self-contained and provides a clear, high-level understanding of what the list will look like after execution.
Instead of explicitly writing out loops and conditionals in multiple steps (as you would in traditional looping), list comprehensions allow you to describe the process of list creation directly. This declarative style of programming emphasizes what you want (the resulting list) rather than how to get it (the step-by-step looping process).
The same principle applies to other comprehensions (e.g., set comprehensions, dictionary comprehensions, generator comprehensions), which all follow a similar syntax for creating those specific data structures.
In essence, the name reflects the clarity, readability, and compactness of this syntax. It allows you to express the intent behind the construction of a list (or other structures) comprehensively in one place. Here's our comprehensive guide to using and forming them:
List comprehensions are essentially an efficient alternative to constructing loops. The caveat with them is that it is easy to generate list comprehensions that rapidly become unreadable, so it is a balancing act of "coolness" versus practicality. List comprehensions follow this general syntax:
[expression for item in iterable if condition]
expression: The value to include in the resulting list.
item: A variable representing each element in the iterable.
iterable: The collection you're iterating over (e.g., a list, range, our DLList or any iterable).
condition (optional): Filters items; only include items that satisfy the condition.
# Traditional loop
result = []
for x in range(10):
if x % 2 == 0:
result.append(x)
# List comprehension
result = [x for x in range(10) if x % 2 == 0]
print(result) # Output: [0, 2, 4, 6, 8]
The simple use cases cover three actions:
squares = [x**2 for x in range(5)]
print(squares) # Output: [0, 1, 4, 9, 16]
even_numbers = [x for x in range(10) if x % 2 == 0]
print(even_numbers) # Output: [0, 2, 4, 6, 8]
uppercase = [char.upper() for char in "hello"]
print(uppercase) # Output: ['H', 'E', 'L', 'L', 'O']
uppercase = "".join([char.upper() for char in "hello"])
print(uppercase) # Output: HELLO
Nested list comprehensions allow you to work with multi-dimensional lists or generate nested structures. In these two examples we first generate a list of lists (a classic 2 dimensional grid) and then use the technique to flatten a list of lists.
This is reasonably straight forward. We are using the inner list as the row and generating it 3 times with the outer list. Although we are using the "x" to put a number in the cell - generated by the "range(3)" expression, there is no requirement for this to be the case. We just need the "for x in range(3)" to generate the 3 column cells of each row, and the x preceding the "for" could be any expression including a function call that returns the value we want to put in the cell (or even another comprehension list if we wanted a 3D (or higher dimension) grid.
grid = [[x for x in range(3)] for y in range(3)]
print(grid)
# Output: [[0, 1, 2], [0, 1, 2], [0, 1, 2]]
This next example does the reverse of the first, and takes a multi dimension grid and flattens it to a single dimension grid. It is a particularly interesting construct and deserves some close examination. The trick here is how the sublist variable is being used.
nested = [[1, 2], [3, 4], [5, 6]]
flat = [item for sublist in nested for item in sublist]
print(flat) # Output: [1, 2, 3, 4, 5, 6]
We will break down the execution of this comprehension because I don't think it is immediately obvious. To understand how this works think of it like this:
for sublist in nested
for item in sublist
add item
With list comprehension it is easy to get into the habit of thinking about them in reverse: ie. the left item being the inner action, but this is usually because that expression is placed where the item is located. When the "for" loops are chained like this and the item spot is occupied by something else, they are more just a flattened sequence of conventional "for" loops.
Outer Loop (for sublist in nested):
Iterates over each sublist in the nested list.
On each iteration, sublist will be one of the inner lists: [1, 2], [3, 4], or [5, 6].
Inner Loop (for item in sublist):
Iterates over each item in the current sublist.
For example:
When sublist = [1, 2], this loop will iterate over 1 and 2.
When sublist = [3, 4], this loop will iterate over 3 and 4.
And so on.
Expression (item):
This determines what gets added to the resulting list for each iteration.
Here, item is directly added to the flat list.
Here’s how the code processes the nested list:
First iteration (sublist = [1, 2]):
Inner loop: item = 1, then item = 2.
Adds 1 and 2 to the flat list.
Second iteration (sublist = [3, 4]):
Inner loop: item = 3, then item = 4.
Adds 3 and 4 to the flat list.
Third iteration (sublist = [5, 6]):
Inner loop: item = 5, then item = 6.
Adds 5 and 6 to the flat list.
In a cartesian product each item in the first list is combined with each item in the second list.
colours = ["red", "green", "blue"]
sizes = ["S", "M", "L"]
combinations = [(colour, size) for colour in colors for size in sizes]
print(combinations)
# Output: [('red', 'S'), ('red', 'M'), ('red', 'L'), ...]
To understand this comprehension we will again break it down into a conventional loop structure:
for colour in colours
for size in sizes
add (colour, size)
matrix = [[x if x % 2 == 0 else None for x in range(4)] for y in range(3)]
print(matrix)
# Output: [[0, None, 2, None], [0, None, 2, None], [0, None, 2, None]]
Here the inner loop is placed where the item for the outer loop is expected so the behaviour is different from the chaining example above. Again we will look at this as if it was written out in a conventional loop:
for y in range(3)
for x in range(4)
if x % 2 == 0
add x
else
add None
In this next example we both filter and transform the items to be placed in the list. The filtering is achieved by the "if" expression following the "for" expression, which ensures only those words satisfying the condition are included.
words = ["apple", "banana", "cherry", "date"]
filtered = [word.capitalize() for word in words if len(word) > 5]
print(filtered) # Output: ['Banana', 'Cherry']
Expressed as a conventional loop this would be:
for word in words
if len(word) > 5
add word.capitalize()
Here we demonstrate that the expression placed in the "item" location does not have to be an item, but can be a function (that obviously should return a value if you want something in the final list other than "None". Note that functions that don't return something explicitly will implicitly return "None" in python.
def square(x):
return x**2
result = [square(x) for x in range(5)]
print(result) # Output: [0, 1, 4, 9, 16]
Comprehensions, don't actually just apply to lists. Here we show a dictionary being created from two lists using a dictionary comprehension with the aid of the zip() function which takes two iterables and combines them in pairs of tuples. Note (as an aside) that zip() used with the * (unpack) operator will actually also unzip a list of tuples, but here we are using it to create a list of tuples, and then extract the key & value from the tuple for combining into a dictionary. So in this case, our list is generated by zip() as a list of tuple pairs from the two list arguments provided to it, which are then mined by the for loop to populate the dictionary items entry by entry.
keys = ["a", "b", "c"]
values = [1, 2, 3]
dictionary = {key: value for key, value in zip(keys, values)}
print(dictionary) # Output: {'a': 1, 'b': 2, 'c': 3}
Another example where we showing that comprehension applies to other generating other iterables, in this case sets.
unique_squares = {x**2 for x in range(-5, 5)}
print(unique_squares) # Output: {0, 1, 4, 9, 16, 25}
A generator in Python is a special type of iterator that allows you to produce values on-the-fly, one at a time, as they are requested. Generators are memory-efficient because they don't store all the values in memory at once; instead, they generate each value only when needed.
squares_gen = (x**2 for x in range(5))
print(list(squares_gen)) # Output: [0, 1, 4, 9, 16]
In this example, "squares_gen" is a generator object created using generator expression syntax (parentheses instead of square brackets like in list comprehensions). This generator will compute the squares of numbers from 0 to 4 lazily, meaning it calculates each square only when you request the value.
The above example doesn't really show the advantage of a generator particularly well because we immediately turn it into a list. Here is a better example that shows how the lazy eval behaviour of generators can be used:
squares_gen = (x**2 for x in range(5))
# Access values one by one using `next`
print(next(squares_gen)) # Output: 0 (computed on demand)
print(next(squares_gen)) # Output: 1 (computed on demand)
print(next(squares_gen)) # Output: 4 (computed on demand)
Let's say we want to calculate and print a list of all composite numbers (a number with factors other than 1 and itself) below a certain number with all their prime factors, but we don't want to include any numbers for who the factors are only 1 or itself (ie. only composite numbers should appear in the answer). To speed up the calculation we are not going to check factors higher than 1/2 of the composite number (if even) +1 or 1/3 (if odd) +1. We can use (a very complicated) list & tuple comprehension to achieve this (which took me quite a while to work out - so marvel at it!):
last_num=20
for var in [
(n, divisors)
for n in range(2, last_num)
if (divisors := [i for i in range(2, (n // (3 if (n % 2) else 2)) + 1)
if (not (n % i)) and all((i % j) for j in range(2, int(i**0.5) + 1))])
]:
print(var)
#Produces the output:
(4, [2])
(6, [2, 3])
(8, [2])
(9, [3])
(10, [2, 5])
(12, [2, 3])
(14, [2, 7])
(15, [3, 5])
(16, [2])
(18, [2, 3])
... etc
Walrus Operator (:=):
This uses Python's assignment expression (introduced in Python 3.8), often referred to as the "walrus operator." The assignment expression allows us to assign the result of a calculation as part of an expression and make the result of the assignment the result of the expression. In this case that means that we can test whether the result of the prime list calculation is [] (which would evaluate to False in the boolean expression) and thus mean that the tuple (n, divisors) was not included in the main list. If the result is anything other than [] it will be treated as True in the "if" clause and be included in the final list, because that value has been assigned to "divisors" which is the right hand term of the tuple.
The divisors list is computed once and stored, then used both in the tuple (n, divisors) and in the if condition.
This ensures that the computation is performed only once per n.
if divisors:
The if condition checks if divisors is non-empty. If it is empty, the tuple (n, divisors) is excluded from the final result.
So a number (i) is included as a factor of (n) if it meets two broad conditions, a) its modulo is 0 (not (n % i)) - which means i is a factor of n, and b) it is a prime factor (in that it is not divisible by any number less than i). That last part is accomplished by the expression after the "and", which we will look at next.
Checking the factor i is a prime is accomplished by the expression "all((i % j) for j in range(2, int(i**0.5) + 1))". We will break this down:
range(2, int(i**0.5) + 1):
Generates all integers j starting from 2 up to the square root of i (inclusive).
Why square root?
If a number i is divisible by any number greater than its square root, it would already have been divisible by a smaller factor earlier.
For example, for i = 36, if j = 6 divides 36, its pair factor 6 would have already been checked in the range [2, sqrt(36)].
i % j:
This computes the remainder when i is divided by j.
If i % j == 0, it means j is a factor of i.
all(...):
The all() function checks if all values in the provided iterable evaluate to True.
Here, (i % j) for each j in the range will return:
True if i is not divisible by j (remainder is non-zero).
False if i is divisible by j (remainder is zero).
Overall Logic:
The expression evaluates to True only if i is not divisible by any number in range(2, int(i**0.5) + 1). In other words:
If no j in that range divides i, then i is prime.
A list comprehension can be used to generate the Fibonacci sequence, but since the Fibonacci sequence relies on the values of previous terms, we'll need to maintain a running list or use a generator function.
We will first consider a solution that modifies the list inside the comprehension:
n = 10 # Number of Fibonacci terms to generate
fibonacci = [0, 1]
[fibonacci.append(sum(fibonacci[-2:])) for _ in range(2, n)]
print(fibonacci) # Output: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
Seed Values:
The first two values of the Fibonacci sequence are 0 and 1.
These are initialized as [0, 1].
List Comprehension:
Generates the rest of the Fibonacci sequence using fibonacci[-2:], which retrieves the last two values from the list and calculates their sum.
Iterates n-2 times since the first two values are already present.
The "for _ in ..." indicates that we are not interested in the actual value produced from the range(2,n), rather we are simply using the for loop to trigger the fibonacci.append(sum(sum(fibonacci[-2:])) to do its calculation n-2 times.
The comprehension creates a list of "Nones" from the .apply() which are discarded as the list is built through .append()
This approach is compact but modifies the running fibonacci list during the comprehension.
If you prefer not to modify the list inside the comprehension, you can use a generator function to give a slightly cleaner solution that separates the logic from the comprehension:
def generate_fibonacci(n):
a, b = 0, 1
for _ in range(n):
yield a
a, b = b, a + b
fibonacci = [x for x in generate_fibonacci(10)]
print(fibonacci) # Output: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
The generate_fibonacci() function is a generator that produces the Fibonacci sequence lazily, meaning it calculates each term on-the-fly as requested. It uses the yield keyword to return one Fibonacci number at a time (similar to an iterator - see the iterators in the BPC DLList library), making it memory-efficient and suitable for generating sequences with potentially large numbers of terms.
Initialization (a, b = 0, 1):
a and b represent the first two numbers in the Fibonacci sequence.
Initially, a = 0 (the first Fibonacci number), and b = 1 (the second Fibonacci number).
Loop (for _ in range(n)):
The loop runs n times, where n is the number of Fibonacci numbers to generate.
Each iteration calculates the next term in the sequence and yields it.
yield a:
The yield statement produces the current value of a (the current Fibonacci number).
Instead of returning all the Fibonacci numbers at once, yield pauses the function and lets the caller retrieve one value at a time.
Update (a, b = b, a + b):
After yielding the current value of a, the values of a and b are updated:
a takes on the value of b (the next Fibonacci number).
b becomes a + b (the next term in the sequence).
Repeats:
The process repeats for n iterations, generating the next Fibonacci number during each loop iteration.
yield:Memory Efficiency:
Unlike a list, the generator doesn’t store all Fibonacci numbers in memory. It calculates and yields one value at a time.
Lazy Evaluation:
Values are computed only when they are needed.
Infinite Generation:
You could modify the function to generate an infinite Fibonacci sequence by removing the range(n) loop condition and using a while True loop.
You use the generator by iterating over it or by calling next() explicitly:
fib_gen = generate_fibonacci(5)
for num in fib_gen:
print(num)
# Output: 0, 1, 1, 2, 3
fib_gen = generate_fibonacci(5)
print(next(fib_gen)) # Output: 0
print(next(fib_gen)) # Output: 1
Let's say we want to generate characters and numbers supplied in a string as a larger scale 3 by 5 pixel art grid. We can use list comprehension and string manipulation to generate this very efficiently:
# This code creates a simple representation of letters,
# numbers 0-9 and some symbols using a grid of characters.
# Each charcter is represented by a list of strings, where
# each string represents a row in the grid. Missing keys
# are handled by a custom dictionary class.
# The dictionary entries look up a row pattern which is a
# list of strings, where each string represents a row in the grid for that character.
#Dictionary class to handle missing keys
class Default(dict):
def __missing__(self, key):
return "33333"
#Pattern lookup table for characters
#The dictionary entries look up a row pattern which is a list of strings,
#where each string represents a row in the grid.
#Row Patterns: [" #","# ","# #","###","## "," ##"," # "," "]
PatternKey = Default({
"0":"32223", "1":"66666", "2":"30313", "3":"30303", "4":"22300",
"5":"31303", "6":"31323", "7":"30000", "8":"32323", "9":"32303",
"A":"32322", "B":"32423", "C":"32123", "D":"42224", "E":"31313",
"F":"31411", "G":"32125", "H":"22322", "I":"36663", "J":"50023",
"K":"22422", "L":"11113", "M":"23322", "N":"24422", "O":"62226",
"P":"32311", "Q":"62225", "R":"42422", "S":"51304", "T":"36666",
"U":"22223", "V":"22226", "W":"22232", "X":"22622", "Y":"22366",
"Z":"30613", "!":"66676", " ":"77777", "?":"30676", ".":"77776"})
print(s:=input().upper())
print( "\n".join([" ".join([
[" #","# ","# #","###","## "," ##"," # "," "]
[int(PatternKey[column][row])] for column in s]) for row in range(5)]))
It produces the following output:
1234 ABCD!
# ### ### # # ### ### ### ## #
# # # # # # # # # # # # # #
# ### ### ### ### ## # # # #
# # # # # # # # # # # #
# ### ### # # # ### ### ## #
This code is a masterpiece of efficiency, blending dictionary lookups, list comprehension, and even the walrus operator (:=) into a slick, minimalistic ASCII art generator! (Alright, I know I am biased because I wrote it...) Let's break it down and appreciate its elegance:
The Default class extends Python’s built-in dict and overrides __missing__() to return a default value when an undefined key is accessed.
If a character isn't found in PatternKey, "33333" is returned, ensuring the code never crashes due to missing characters.
class Default(dict):
def __missing__(self, key):
return "33333"
Why is this cool? This makes the dictionary fault-tolerant—even if a user enters an unsupported character, the program will still function gracefully.
PatternKey stores grid patterns for numbers, letters, and symbols.
Each character is mapped to a string of digits, where each digit represents a row index in a predefined set of ASCII patterns:
PatternKey = Default({
"A": "32322", "B": "32423", "C": "32123", # Letters
"0": "32223", "1": "66666", "2": "30313", # Numbers
"!": "66676", " ": "77777", "?": "30676" # Symbols
})
Why is this cool? Instead of defining each character manually, it compresses representation into short, easy-to-read row patterns.
:=)
print(s := input().upper())
The := operator assigns the user input (input()) to s, while simultaneously passing it to print().
This eliminates redundancy and makes the code ultra-compact.
Why is this cool? It reduces clutter and performs assignment + usage in one step!
Now comes the powerhouse of the program—a nested list comprehension that constructs and prints the ASCII representation.
print("\n".join([" ".join([
[" #","# ","# #","###","## "," ##"," # "," "]
[int(PatternKey[column][row])]
for column in s]) for row in range(5)]))
Breaking It Down:
Outer List Comprehension: Iterates over five rows, each corresponding to a row in the ASCII pattern.
Inner List Comprehension: Iterates over each character in the input string (s).
Index Lookup: PatternKey[column][row] retrieves the predefined row index for each character.
Row Mapping: The index is used to fetch the correct ASCII representation.
Why is this cool? It transforms character encoding into ASCII art in a single elegant expression—no explicit loops needed!
I asked AI if it could improve it and its response was:
"This is Python at its best—concise, efficient, and creative.
Uses dictionaries for fast lookup
Handles missing keys gracefully
Employs list comprehension for ultra-clean processing
Leverages the walrus operator for assignment efficiency
Encodes data in a compressed format for compactness
This isn't just code—it’s a showcase of Python's expressive power! "
Hah! So there!
Next we will look at two approaches using comprehensions for checking a sudoku board. Essentially a Sudoku board is a grid consisting of 9 rows by 9 columns made up of the numbers 1 - 9 inclusive. In a valid board no integer may appear more than once in any given row, column or in 3 by 3 squares tiled across the board. There are 9 such tiles on a board. The aim of the two programs is to check a board comprising 9 rows of 9 digit strings for compliance with the rules just stated. We will use two different approaches:
The core problem to be solved is to be able to establish that a given group of numbers has 1 and only 1 occurrence of each digit from 1 - 9. The two programs employ fundamentally different approaches to this problem. The first counts the number of instances of each number from 1 - 9 over a given sequence of numbers (like a row or a column) and tests that this equals 1, while the second makes use of the fact that a set can only have one instance of particular number and then measures the length of the resulting set comprised of each number in a given sequence (eg. row or column, etc.) - which must be 9 if the sequence is valid.
The zip() function used in the first program takes multiple iterables and produces a list of tuples joining the corresponding nth element of each iterable into a single tuple. In a list of lists, where each row is a list, the effect is to rotate the matrix by 90 degrees turning columns into tuples and making a list of tuples. The tuples can then be treated like rows and iterated.
Firstly we consider the list comprehension approach:
# This code checks if a given Sudoku board is valid using list comprehension and count.
sudokuIn1 = [
"295743861", "431865927", "876192543",
"387459216", "612387495", "549216738",
"763524189", "928671354", "154938672"
]
sudokuIn2 = [
"195743862", "431865927", "876192543",
"387459216", "612387495", "549216738",
"763524189", "928671354", "254938671"
]
sudokuInT = sudokuIn2 #sudokuIn1 #Input("Gimme Sudoku (sep row with space):").split()
def is_valid_sudoku1(board):
#Check number of rows
dataSafe = (len(board) == 9)
try:
#Convert text to int cells above 0 (len will < 9 if any cells are 0)
sboard = [[int(ch) for ch in row if int(ch) > 0] for row in board]
#Check number of columns - if it passes this evry cell is between 1 and 9 inclusive
dataSafe &= all([len(row) == 9 for row in sboard])
#Check for duplicates in rows
dataSafe &= all([([row.count(ch) for ch in range(1, 10)].count(1) == 9) for row in sboard])
#Check for duplicates in columns - zip of the rows returns tuples of columns
#effectively rotating the matrix by 90 degrees
dataSafe &= all([([row.count(ch) for ch in range(1, 10)].count(1) == 9) for row in zip(*sboard)])
#Split the board into a list of 3 * 3 mini boards
# This creates a list of lists, where each inner list represents a mini board.
#First we segment the board vertically into 3 sections of 3 rows each.
#Then we segment the board horizontally into 3 sections of 3 columns each for each 3 row segment
#creating 9 lists of 3 tuples representing the columns of the mini boards.
minisboards = [list(zip(*[sboard[i:i+3] for i in range(0, 9, 3)][k]))[j:j+3]
for j in range(0, 9, 3) for k in range(0,3)]
#print(minisboards)
# Flatten each mini board into a single list (to remove the tuples),
# making miniboards a list of 9 lists.
# This is done to check for duplicates in each mini board.
minisboards = [[item for sublist in minisboards[h] for item in sublist]
for h in range(0, 9)]
dataSafe &= all([([row.count(ch) for ch in range(1, 10)].count(1) == 9)
for row in minisboards])
except :
dataSafe = False
return dataSafe
print(f"Sudoku board is {'valid' if is_valid_sudoku1(sudokuInT) else 'invalid'}")
I have commented this code pretty heavily to explain what is happening, so I recommend you read the comments. Essentially, I am using the same test throughout, which is to take a sequence of 9 elements in a row and count how many times each number from 1-9 appears in the sequence, generating a list of "1"s for in the correct scenario where each number appears once. We then count the number of 1's in the list which should come to 9, if the sequence being tested is correct.
The "minisboards" is created as a list of lists of tuples, by segmenting the board into groups of 3 rows, then applying zip() to rotate each set of 3 rows and then segment that into 3 sub-boards creating a 3 by 3 matrix represented by a list of tuples where each tuple is a 3 member set of the original columns. The expression [item for sublist in minisboards[h] for item in sublist], is literally the list flattening example shown earlier in this paper, which turns the list of tuples into a simple list of 9 numbers, to which I then apply our row number counting strategy used throughout the program.
Secondly we consider the set comprehension approach:
# This code checks if a given Sudoku board is valid using sets comprehension.
sudokuIn1 = [
"295743861", "431865927", "876192543",
"387459216", "612387495", "549216738",
"763524189", "928671354", "154938672"
]
sudokuIn2 = [
"195743862", "431865927", "876192543",
"387459216", "612387495", "549216738",
"763524189", "928671354", "254938671"
]
sudokuInT = sudokuIn1 # Change input source as needed
def is_valid_sudoku2(board):
"""Checks if a given Sudoku board is valid."""
if len(board) != 9 or any(len(row) != 9 for row in board):
return False # Ensure 9x9 structure
try:
sboard = [[int(ch) for ch in row] for row in board]
except ValueError:
return False # Invalid non-integer values
# Check rows, columns, and 3x3 grids using sets to ensure uniqueness
# Row validation
if any([len(set(sboard[i])) != 9 for i in range(9)]): return False
# Column validation
if any([len(set(row[i] for row in sboard)) != 9 for i in range(9)]): return False
# 3x3 grid validation
if any([len(set(sboard[i][j] for i in range(x, x+3) for j in range(y, y+3))) != 9
for y in range(0, 9, 3) for x in range(0, 9, 3)]): return False
return True
# Print result
print(f"Sudoku board is {'valid' if is_valid_sudoku2(sudokuInT) else 'invalid'}")
The expression set(sboard[i][j] for i in range(x, x+3) for j in range(y, y+3)) is a set comprehension. It works the same as the list comprehension but generates a set, rather than a list. In this case it makes a single set from the 9 elements in a 3 by 3 tile on the board. The idea with using sets is that a member can appear only once in a set so if a number is added twice it will appear only once can thus we can check for all 9 numbers by adding all members in the sequence to the set and then counting the set membership using len() which should equal 9 if everything is correct. In this case we look to see if the len() is NOT 9 for each set, adding that boolean result to a list and then use the boolean test "any()" to see if any of the results in the list returned "True", in which case we have a failed condition and failed sudoku board.
Nested or overly complex list comprehensions can be hard to read. When dealing with multiple conditions or loops, consider breaking the logic into smaller pieces.
List comprehensions are faster than traditional loops for smaller datasets, but they may consume more memory since they eagerly create lists. Use generators if memory usage is a concern.
List comprehensions should focus on creating new lists. Avoid side effects like modifying global variables or printing within the comprehension.
Concise: Single-line syntax simplifies common list operations.
Expressive: Can combine filtering, transformations, and nesting in one statement.
Versatile: Can be used with other iterable types like sets, dictionaries, and generators.
Readable: Improves readability for simple cases, but can become opaque with excessive complexity.
List comprehensions are invaluable for Python development.
