#Sets
U = {0,1,2,3,4,5,6,7,8,9}
P = {1,2,3,4}
Q = {4,5,6}
R = {3,4,6,8,9}

def set2bits(xs,us) :
    bs=[]
    for x in us :
        if x in xs :
            bs.append(1)
        else:
            bs.append(0)
    assert len(us) == len(bs)
    return bs

def union(set1,set2) :
    finalSet = set()
    bitList1 = set2bits(set1, U)
    bitList2 = set2bits(set2, U)

    for i in range(len(U)) :
        if(bitList1[i] or bitList2[i]) :
            finalSet.add(i)

    return finalSet

def intersection(set1,set2) :
    finalSet = set()
    bitList1 = set2bits(set1, U)
    bitList2 = set2bits(set2, U)

    for i in range(len(U)) :
        if(bitList1[i] and bitList2[i]) :
            finalSet.add(i)

    return finalSet

def compliment(set1) :
    finalSet = set()
    bitList = set2bits(set1, U)

    for i in range(len(U)) :
        if(not bitList[i]) :
            finalSet.add(i)

    return finalSet

def implication(a,b):
    return union(compliment(a), b)

###########################################################################################
######################         Problems 1-6         #######################################
###########################################################################################

#p \/ (q /\ r) = (p \/ q) /\ (p \/ r)
def prob1():
    return union(P, intersection(Q,R)) == intersection(union(P,Q), union(P,R))

#p /\ (q \/ r) = (p /\ q) \/ (p /\ r)
def prob2():
    return intersection(P, union(Q,R)) == union(intersection(P,Q), intersection(P,R))

#~(p /\ q) = ~p \/ ~q
def prob3():
    return compliment(intersection(P,R)) == union(compliment(P), compliment(R))

#~(p \/ q) = ~p /\ ~q
def prob4():
    return compliment(union(P,Q)) == intersection(compliment(P), compliment(Q))

#(p=>q) = (~q => ~p)
def prob5():
    return implication(P,Q) == implication(compliment(Q), compliment(P))

#(p => q) /\ (q => r)  =>  (p => r)
def prob6():
    return implication(intersection(implication(P,Q), implication(Q,R)), implication(P,R))


print("Problem 1: ", prob1())
print("Problem 2: ", prob2())
print("Problem 3: ", prob3())
print("Problem 4: ", prob4())
print("Problem 5: ", prob5())
print("Problem 6: ", prob6())

'''
Problem 1:  True
Problem 2:  True
Problem 3:  True
Problem 4:  True
Problem 5:  True
Problem 6:  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
'''

color2 = (60, 74, 172)
color1 = (19, 28, 87)

percent = 1.0
for i in range(101):
    resultRed = round(color1[0] + percent * (color2[0] - color1[0]))
    resultGreen = round(color1[1] + percent * (color2[1] - color1[1]))
    resultBlue = round(color1[2] + percent * (color2[2] - color1[2]))
    print((resultRed, resultGreen, resultBlue))
    percent -= 0.01

mydict = {'carl':40, 'alan':2, 'bob':1, 'danny':0}

# How to sort a dict by value Python 3>
sort = {key:value for key, value in sorted(mydict.items(), key=lambda kv: (kv[1], kv[0]))}
print(sort)

# How to sort a dict by key Python 3>
sort = {key:mydict[key] for key in sorted(mydict.keys())}
print(sort)

# Python program for implementation of Bogo Sort
import random

# Sorts array a[0..n-1] using Bogo sort
def bogoSort(a):
	n = len(a)
	while (is_sorted(a)== False):
		shuffle(a)

# To check if array is sorted or not
def is_sorted(a):
	n = len(a)
	for i in range(0, n-1):
		if (a[i] > a[i+1] ):
			return False
	return True

# To generate permuatation of the array
def shuffle(a):
	n = len(a)
	for i in range (0,n):
		r = random.randint(0,n-1)
		a[i], a[r] = a[r], a[i]

# Driver code to test above
a = [3, 2, 4, 1, 0, 5]
bogoSort(a)
print("Sorted array :")
for i in range(len(a)):
	print ("%d" %a[i]),

#Loop back to this point once code finishes
loop = 1
while (loop < 10):
#All the questions that the program asks the user
    noun = input("Choose a noun: ")
    p_noun = input("Choose a plural noun: ")
    noun2 = input("Choose a noun: ")
    place = input("Name a place: ")
    adjective = input("Choose an adjective (Describing word): ")
    noun3 = input("Choose a noun: ")
#Displays the story based on the users input
    print ("------------------------------------------")
    print ("Be kind to your",noun,"- footed", p_noun)
    print ("For a duck may be somebody's", noun2,",")
    print ("Be kind to your",p_noun,"in",place)
    print ("Where the weather is always",adjective,".")
    print ()
    print ("You may think that is this the",noun3,",")
    print ("Well it is.")
    print ("------------------------------------------")
#Loop back to "loop = 1"
    loop = loop + 1

def check_prop(fn, prop):
  return lambda obj: fn(obj[prop])
  
check_age = check_prop(lambda x: x >= 18, 'age')
user = {'name': 'Mark', 'age': 18}
check_age(user) # True