## Introduction

List comprehensions provide a concise way to create lists. It is typically used to create new lists where each element is the result of some operations applied to each member of another sequence.

## List Comprehension

Assume we want to create a list of squares of the numbers from 1 to 10 using a for loop.

EXAMPLE for loop to create a list.

1squares = []
2for i in range(1,11):
3    squares.append(i**2)
4squares

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


List comprehension offers a more compact syntax when you want to create a new list based on the values of an existing list. Using a list comprehension, we can reproduce the above results as follows.

EXAMPLE List comprehension to create a list.

1[x**2 for x in range(1,11)]

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


More generally, a list comprehension consists of square brackets containing an expression followed by a for clause, with optional for or if clauses. The result will be a new list resulting from evaluating the expression in the context of the for and if clauses which follow it.

SYNTAX List Comprehension with an if clause.

1[expr for val in collection if condition]


The above is equivalent to the following for loop enclosing an if clause.

1result = []
2    for val in collection:
3        if condition:
4            result.append(expr)


As an example, imagine we are given a list of names from which we wish to extract only those that start with “J” and capitalize them. A for loop method will look like this:

EXAMPLE Filtering a list with a for loop.

1collection = ["Jane", "Peter", "Tom", "Julian", "Wendy", "Violet"]
2result = []
3for val in collection:
4    if val[0]== "J":
5        result.append(val.upper())
6result

['JANE', 'JULIAN']


On the other hand, a list comprehension will look like this.

EXAMPLE Filtering a list with a list comprehension.

1[val.upper() for val in collection if val[0]=="J"]

['JANE', 'JULIAN']


As another example, assume we want to create a list of perfect squares less than 200 (starting from 1). Using a while loop, we arrive at the following:

EXAMPLE Creating a list of perfect squares with a while loop.

1squares = []
2i = 1
3while i**2 < 200:
4    squares.append(i**2)
5    i +=1
6squares

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196]


On the other hand, using a list comprehension, we can write:

EXAMPLE Creating a list of perfect squares with a list comprehension.

1[x**2 for x in range(1,999) if (x**2) < 200]

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196]


In the above code, we are creating a new list using the expression x**2 where x comes from a (purposefully large) range object, subjected to the condition $x^2 < 200$.

We can also include conditions in the expression to manipulate the outcome. In the following example, given a list of names, those that start with “J” are set to 1 and the rest are set to 0. A simple sum() function will then return the number of names that start with “J”.

EXAMPLE Including a condition in the list comprehension expression.

1names = ["Jane", "Peter", "Tom", "Julian", "Wendy", "Violet"]
2io = [(1 if x[0]=="J" else 0 ) for x in names]
3print(io)
4print(sum(io))

[1, 0, 0, 1, 0, 0]
2


The expression may also be a Boolean expression. Let’s rework the above example with the expression now replaced by a Boolean expression.

1names = ["Jane", "Peter", "Tom", "Julian", "Wendy", "Violet"]
2io = [x[0]=="J" for x in names]
3print(io)
4print(sum(io))

[True, False, False, True, False, False]
2


### Nested List Comprehension

Imagine now we want to create matrix by using 2 for loops, one nested within the other.

EXAMPLE Create a matrix by using nested for loops.

1matrix = []
2for i in range(3):   # row
3    matrix.append([])
4    #print(matrix)
5    for j in range(5): # col
6        matrix[i].append(j)
7print(*matrix, sep='\n')

[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4]


Let’s reproduce the above results using a nested list comprehension which we will elaborate in 3 steps so that the reader can better understand.

Step 1 Create simple list comprehension.

1[i for i in range(3)] #Step 1: simple list comprehension

[0, 1, 2]


Step 2 Add an empty list as the expression.

1[[] for i in range(3)] # Step 2: add an empty list as the expression

[[], [], []]


Step 3 Write a for loop in the empty list.

1[[j for j in range(5)] for i in range(3)] # Step 3: populate the empty lists

[[0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4]]

Tip: To print a nested list in matrix format.

print(*list, sep = '\n')

1mat = [[j for j in range(5)] for i in range(3)] # from step 3
2print(*mat, sep='\n')

[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4]


Alternatively, we can also use a for loop to print the matrix.

1for row in mat:
2    print(f'{row}')

[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4]


As a final example, let’s create a 4 X 4 matrix of random integers from 10 to 99.

EXAMPLE Creating a $4 \times 4$ matrix of random integers.

1import random as rd
2A= [[j for j in list(rd.sample(range(10,100), 4))] for i in range(4)]
3# print out the result
4for row in A:
5    print(f'{row}')

[35, 47, 42, 91]
[89, 43, 60, 85]
[64, 86, 85, 62]
[86, 41, 31, 14]


EXAMPLE Count how many of the numbers generated are greater than 50.

1total=0
2for row2 in [[j>50 for j in row1]  for row1 in A]:
3    total += sum(row2)
4total

9


A more compact way.

1sum([sum(j>50 for j in row)  for row in A])

9


## Dictionary Comprehension

We also have dictionary comprehensions. In the following, we use a dict comprehension to group the scores of 6 students into either “PASS” or “FAIL”.

EXAMPLE Dictionary comprehension.

1scores = {"Carol":49, "Sammy":85, "Derrick":36, "Juan":81, "Wendy":79, "Tom":52}
2{k: "PASS" if v > 50  else "FAIL" for (k, v) in scores.items()}

{'Carol': 'FAIL',
'Sammy': 'PASS',
'Derrick': 'FAIL',
'Juan': 'PASS',
'Wendy': 'PASS',
'Tom': 'PASS'}


We may also include more than 2 categories in the expression.

EXAMPLE Dictionary comprehension with multiple categories.

1scores1 = {"Carol":68, "Sammy":85, "Derrick":62, "Juan":49, "Wendy":79, "Tom":86}
2{k:
3 "A" if v >85 else
4 "B" if v > 75 else
5 "C" if v >65 else
6 "D"
7 for (k, v) in scores1.items()}

{'Carol': 'C',
'Sammy': 'B',
'Derrick': 'D',
'Juan': 'D',
'Wendy': 'B',
'Tom': 'A'}


## Set Comprehension

Recall that a set has only unique elements. Therefore, the set comprehension always produces a set with unique elements even if the input list has duplicate elements.

EXAMPLE Set comprehension.

1currencies = ["sgd", "usd", "hkd", "eur", "aud", "inr", "rmb", "sgd", "eur"]
2{x.upper() for x in currencies}

{'AUD', 'EUR', 'HKD', 'INR', 'RMB', 'SGD', 'USD'}


EXAMPLE Set comprehension with an if clause.

1{x.upper() for x in currencies if x[2]=="d"} # only currencies that end with a "d".

{'AUD', 'HKD', 'SGD', 'USD'}