cs235-hw2-quotient using

# cs235
# Yuxiao Wang
# hw2
# question 3


def quotient(X,R):
    return {frozenset({y for y in X if (x,y) in R}) for x in X}

def flight(X,R):
    return len(quotient(X,R))



# Test!
C = {'Iceland', 'USA', 'Canada', 'Mexico', 'Australia', 'Norway', 'Sweden', 'Finland'}
D = {('USA', 'Canada'), ('USA', 'Mexico'), ('Norway', 'Sweden'), ('Sweden', 'Finland')}


S1={(x, x) for x in C} 
D=D.union(S1)

# reflective
S1={(x, x) for x in C} 
#symmetricity: 
S2={(y, x) for (x,y) in D}
#and transitivity: 
S3={(x, z) for x in C for z in C for y in C if ((x,y) in D and (y,z) in D)} 
# equ 
D=D.union(S1).union(S2).union(S3)


print("Equivenlence D now is: \n",D,"\n")
print("You can visit all the countries in each of these set in one car ride: \n"
      ,quotient(C,D),"\n")
print("Minimum number of flights you need to visit all the countries is:\n"
      ,flight(C,D),"\n")