#################################################
#  Author:
#  Date:
#  harder_functions.py
#################################################

def close_enough(a,b):
    """This is free code. You can use it to check for "equality
of floating-point numbers.  Consider floats x and y to be equal
here if they are within 1e-6 of each other."""
    return abs(a-b)<1e-6
##############END FREE CODE######################################


###################Problem 1################
def rectangle(m, n):
    """Precondition: m and n are nonnegative integers.
Postcondition:  prints a rectangle of *s to the screen that 
has m rows and n columns"""
    pass

###################Problem 2################
def power(base, exp):
    """prec:  base is a number, exp is an integer`
postc: computes base**exp from scratch (no using libraries
or built-in functions).  Pay attention to the case where exp < 0!"""
    return 1
###################Problem 3################
def convert_to_binary(n):
    return ""
###################Problem 4################
def sum_of_digits(n):
    """precondition: n is an integer
postcondition:  returns the sum of the digits of n.  You should
be able to take negative input; in such cases disregard the - sign.  """
    return 0
###################Problem 5################
def super_summer(f, n):
    """precondition: f is a function that is defined for all nonnegative
integers.
postcondition:  returns sum(f(k), k = 1..n) """
    return 0
###################Problem 6################
def reverse_string(x):
    """prec: x is a string
    postc:  return a string containing x is reverse."""
    return ""
###################Problem 7################
def sum_from(n, x):
    """prec:  n is an integer, x is a list of integers.
postc: returns a sublist of x whose sum is n if it exists
and the graveyard object None otherwise.  """
    return None

def main():
    print("###################Problem 1################")
    print("You should get a rectangle with 5 rows, 10 columns.")
    rectangle(5,10)
    print("###################Problem 2################")
    base = 4.5
    exp = 3
    y = 91.125
    print(f"Case base = {base}, exp = {exp}:", end="")
    print("PASS" if close_enough(power(base, exp), y) else "FAIL")
    base = 4.5
    exp = -3
    y = 0.010973936899862825
    print(f"Case base = {base}, exp = {exp}:", end="")
    print("PASS" if close_enough(power(base, exp), y) else "FAIL")
    print("###################Problem 3################")
    print("###################Problem 4################")
    print("###################Problem 5################")
    print("###################Problem 6################")
    print("###################Problem 7################")

main()