Calculate Possibilities of Throwing a Coin N Times in Python

The challenge

In this challenge, you will be given an integer n, which is the number of times that is thrown a coin. You will have to return an array of strings for all the possibilities (heads[H] and tails[T]). Examples:

coin(1) should return {"H", "T"}
coin(2) should return {"HH", "HT", "TH", "TT"}
coin(3) should return {"HHH", "HHT", "HTH", "HTT", "THH", "THT", "TTH", "TTT"}

When finished sort them alphabetically.

In C and C++ just return a char* with all elements separated by, (without space):
coin(2) should return "HH,HT,TH,TT"

INPUT:
0 < n < 18

Careful with performance!! You’ll have to pass 3 basic test (n = 1, n = 2, n = 3), many medium tests (3 < n <= 10) and many large tests (10 < n < 18)

The solution in Python code

Option 1:

from itertools import product

def coin(n):
    return list(map(''.join, product(*(["HT"]*n))))

Option 2:

def coin(n): return [x + v for x in coin(n-1) for v in 'HT'] if n - 1 else ['H','T']

Option 3:

memo = {1 : ["H", "T"]}
for j in range(2, 18):
    b = memo[j-1]
    total = set()
    for i in b:
        total.add("T"+i)
        total.add(i+"T")
        total.add("H"+i)
        total.add(i+"H")
    memo[j] = sorted(total)
    
def coin(n):
    return memo[n]

Test cases to validate our solution

test.describe("Basic Tests")
test.assert_equals(coin(1),["H","T"])
test.assert_equals(coin(2),["HH", "HT", "TH", "TT"])
test.assert_equals(coin(3),["HHH", "HHT", "HTH", "HTT", "THH", "THT", "TTH", "TTT"])