How to Generate Combinations in Python

from itertools import combinations

items = ['A', 'B', 'C', 'D']

pairs = list(combinations(items, 2))
print(pairs)

triplets = list(combinations(items, 3))
print(triplets)

from itertools import combinations_with_replacement

items = ['A', 'B', 'C']

result = list(combinations_with_replacement(items, 2))
print(result)

from itertools import combinations

def subsets_of_size(items, k):
    """Generate all subsets of exactly size k."""
    return [set(combo) for combo in combinations(items, k)]

print(subsets_of_size([1, 2, 3, 4], 2))

from itertools import combinations

players = ["Alice", "Bob", "Charlie", "Diana"]

for player1, player2 in combinations(players, 2):
    print(f"{player1} vs {player2}")

Alice vs Bob
Alice vs Charlie
Alice vs Diana
Bob vs Charlie
Bob vs Diana
Charlie vs Diana

from itertools import combinations

numbers = [1, 2, 3, 4, 5]
target = 7

pairs = [(a, b) for a, b in combinations(numbers, 2) if a + b == target]
print(pairs)

[(2, 5), (3, 4)]

def generate_combinations(items, r):
    """Generate combinations using pick/skip recursion."""
    if r == 0:
        return [[]]
    if not items:
        return []
    
    first, rest = items[0], items[1:]
    
    with_first = [[first] + combo for combo in generate_combinations(rest, r - 1)]
    
    without_first = generate_combinations(rest, r)
    
    return with_first + without_first

print(generate_combinations(['A', 'B', 'C'], 2))

[['A', 'B'], ['A', 'C'], ['B', 'C']]

def combinations_iterative(items, r):
    """Generate combinations iteratively using indices."""
    n = len(items)
    if r > n:
        return []
    
    indices = list(range(r))
    result = [tuple(items[i] for i in indices)]
    
    while True:
        for i in range(r - 1, -1, -1):
            if indices[i] != i + n - r:
                break
        else:
            return result
        
        indices[i] += 1
        for j in range(i + 1, r):
            indices[j] = indices[j - 1] + 1
        
        result.append(tuple(items[i] for i in indices))
    
    return result

from math import comb  # Python 3.8+

print(comb(5, 2))  # 10 combinations of 5 items taken 2 at a time
print(comb(10, 3)) # 120 combinations

from math import factorial

def count_combinations(n, r):
    return factorial(n) // (factorial(r) * factorial(n - r))

10
120

from itertools import combinations

def all_combinations(items):
    """Generate combinations of all sizes."""
    result = []
    for r in range(1, len(items) + 1):
        result.extend(combinations(items, r))
    return result

print(all_combinations(['A', 'B', 'C']))

[('A',), ('B',), ('C',), ('A', 'B'), ('A', 'C'), ('B', 'C'), ('A', 'B', 'C')]

from itertools import combinations, permutations

items = ['A', 'B', 'C']

print(list(combinations(items, 2)))

print(list(permutations(items, 2)))