# ---------------------------------------------------------
# CSCI 246, Python Assignment
# Your name
# Last Modified: March ??, 2022
# ---------------------------------------------------------


# Place the missing functions here.


# ---------------------------------------------------------
# print_set
# ---------------------------------------------------------
# original_set: a string that represents a set, e.g. "{1, 2}"
# power_set, a list of strings that represents the power set of
#            the original set in any order, e.g. ["", "1", "12", "2"]
# ---------------------------------------------------------
# Print out a numbered list of each subset.  Match the
# format of the sample output transcript exactly.
# ---------------------------------------------------------

def print_set(original_set, power_set):
    print("The power set of", original_set, "consists of")
    counter = 1
    for subset in power_set:
        print(str(counter) + ". {" + subset + "}")
        counter += 1
    print("----------------")

# ---------------------------------------------------------
# relation_properties
# ---------------------------------------------------------
# max_label: The label of the highest point, e.g. 3
#            Assume that points 0, 1, ... max_label exist
# points: A list of lists that shows all ordered pairs in the relation,
#         e.g. [[0,1], [2,3]] is a relation consisting of 2 points
# ---------------------------------------------------------
# Determine whether a relation is (1) reflexive, (2) symmetric
# and/or (3) transitive.  These three concepts are introduced
# in section 8.2.  Match the format of the sample output transcript.
# ---------------------------------------------------------

def relation_properties(max_label, points):
    print("Data Set:", points)
    print("Reflexive:", reflexive(max_label, points))
    print("Symmetric:", symmetric(max_label, points))
    print("Transitive:", transitive(max_label, points))
    print("----------------")

# ---------------------------------------------------------
# main
# ---------------------------------------------------------
# The main program to test the following functions that you
# write: (1) power_set, (2) hamming, (3) reflexive, (4) symmetric
# and (5) transitive.  Note that we will test your solution with
# a different main function so be sure that your solution is
# fully general.  Match the format of the sample output transcript.
# ---------------------------------------------------------

def main():
    # Power Sets are introduced in section 6.1
    # The power_set function can return the power set of its input in any order.
    print_set("{x,y,z}", power_set("xyz"))

    # Hamming Distance is introduced in section 7.1
    print("The Hamming distance between 64 and 63 =", hamming(64, 63))
    print("The Hamming distance between 4 and 4 =", hamming(4,4))
    print("----------------")
   
    relation_properties(3, [[0,0], [0,1], [0,3], [1,0], [1,1], [2,2], [3,0], [3,3]])
    relation_properties(3, [[0,0], [0,2], [0,3], [2,3]])
    relation_properties(3, [[0,1], [2,3]])
   
# ---------------------------------------------------------

main()