#!/usr/bin/python3
# -*- coding: utf-8 -*-
"""
Created on Sat Dec 3 18:16:57 2016
@author: taylor@mst.edu
"""


# %% Iterative Factorial using loops (imperative), accumulate pattern
def fact_loop(n: int) -> int:
    """
    Computes the factorial of n, returns n.
    """
    total = 1
    for i in range(1, n + 1):
        total *= i
    return total


print(fact_loop(5))


# %% tail recursive factorial
def fact_rec_tail(n: int) -> int:
    """
    Computes the factorial of n, returns n.
    One way of defaulting value, which hides the details.
    """

    def loop(total: int, i: int) -> int:
        if i < n + 1:
            return loop(total * i, i + 1)
        else:
            return total

    return loop(1, 1)


print(fact_rec_tail(5))


# %% tail recursive factorial
def fact_rec_tail2(n: int, total: int = 1, i: int = 1) -> int:
    """
    Computes the factorial of n, returns n.
    Another way of defaulting values.
    """
    if i < n + 1:
        return fact_rec_tail2(n, total * i, i + 1)
    else:
        return total


print(fact_rec_tail2(5))