Calculate potentialities of throwing a coin N instances in Python

The problem

On this problem, you’ll be given an integer n, which is the variety of instances that’s thrown a coin. You’ll have to return an array of strings for all the chances (heads[H] and tails[T]). Examples:

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

When completed type them alphabetically.

In C and C++ simply return a char* with all parts separated by, (with out house):
coin(2) ought to return "HH,HT,TH,TT"

INPUT:
0 < n < 18

Cautious with efficiency!! You’ll must move 3 primary check (n = 1, n = 2, n = 3), many medium exams (3 < n <= 10) and plenty of giant exams (10 < n < 18)

The answer in Python code

Possibility 1:

from itertools import product

def coin(n):
    return checklist(map(''.be part of, product(*(["HT"]*n))))

Possibility 2:

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

Possibility 3:

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

Check instances to validate our resolution

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