Python program to get all subsets of given size of a Set

We are given a set, and our task is to get all subsets of a given size. For example, if we have s = {1, 2, 3, 4} and need to find subsets of size k = 2, the output should be [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)].

Using itertools.combinations

We can use itertools.combinations(iterable, r) to generate all possible subsets (combinations) of size "r" from the given set without repetition. It returns an iterator of tuples where each tuple represents a unique subset.

from itertools import combinations
s = {1, 2, 3, 4}
k = 2

# Get all subsets of size k
subsets = list(combinations(s, k))
print("Subsets of size", k, ":", subsets)

Subsets of size 2 : [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]

Explanation:

• Combinations(s, k) function generates all possible 2-element subsets from the set {1, 2, 3, 4}, returning an iterator of tuples.
• List(combinations(s, k)) converts the iterator to a list and the result is printed, displaying all subsets of size 2.

Using bit manipulation

Using bit manipulation we can represent each subset of a set as a binary number where each bit indicates whether an element is included. By iterating through all binary numbers of length equal to set's size we can filter subsets of the desired size.

s = {1, 2, 3, 4}
k = 2

s = sorted(s)  # Ensure consistent ordering
n = len(s)
res = []

for i in range(1 << n):  # Iterate through all possible combinations
    subset = [s[j] for j in range(n) if (i & (1 << j))]
    if len(subset) == k:
        res.append(subset)

print("Subsets of size", k, ":", res)

Subsets of size 2 : [[1, 2], [1, 3], [2, 3], [1, 4], [2, 4], [3, 4]]

Explanation:

• We iterate through all possible binary numbers of length equal to the size of the set (1 << n gives 2^n possibilities), each bit in the binary representation of i determines whether the corresponding element is included.
• The expression (i & (1 << j)) checks if the j-th bit is set, meaning the element should be part of the subset.
• We collect subsets of size k and append them to the result list and Sorting s ensures a consistent lexicographic order of subsets.

Using list comprehensions

List comprehensions can be used to efficiently filter and collect subsets of a given size by iterating over all possible combinations. They offer a concise readable way to generate subsets without explicitly using loops or conditionals.

s = {1, 2, 3, 4}
k = 2

s = list(s)
n = len(s)
res = [[]]

# Iteratively build subsets
for ele in s:
    ns = [s + [ele] for s in res]
    res.extend(ns)

# Filter subsets of size `k`
sub = [s for s in res if len(s) == k]

print("Subsets of size", k, ":", sub)

Subsets of size 2 : [[1, 2], [1, 3], [2, 3], [1, 4], [2, 4], [3, 4]]

Explanation:

• Loop iterates over each element creating new subsets by appending element to all existing subsets (s + [ele]), effectively generating all possible subsets.
• list comprehension [s for s in res if len(s) == k] is used to filter and collect only those subsets with size k