Lab5

def reverse_relation(R):
    l = len(R)
    s = [[0 for j in range(l)] for i in range(l)]
    for i in range(0, len(R)):
        for j in range(0, len(R)):
            s[j][i] = R[i][j]
    return s


def analyze_relation(R):
    p1 = 0
    p2 = 0
    p3 = 0
    for i in range(0, len(R)):
        for j in range(0, len(R)):
            if (i == j) & (R[i][j] == True):
                p1 += 1
            if R[i][j] <= R[j][i]:
                p2 += 1
    if p1 == len(R):
        reflexive = True
    else:
        reflexive = False
    if p2 == len(R) * len(R):
        symmetric = True
    else:
        symmetric = False
    for i in range(0, len(R)):
        for j in range(0, len(R)):
            for x in range(0, len(R)):
                if ((R[i][j] & R[j][x]) <= R[i][x]):
                    p3 += 1
    if p3 == len(R) * len(R) * len(R):
        transitive = True
    else:
        transitive = False

    print("Рефлексивность:", reflexive)
    print("Симметричность:", symmetric)
    print("Транзитивность:", transitive)
    print("Сюръективность:", is_surjective(R))
    print("Инъективность:", is_injective(R))


def is_surjective(R):
    reverse_relation(R)
    for i in range(len(R)):
        if sum(R[i]) == 0:
            return False
    return True


def is_injective(R):
    for i in range(len(R)):
        for j in range(len(R)):
            if R[i][j] == 1 and sum([R[k][j] for k in range(len(R))]) > 1:
                return False
    return True

def print_relation(R):
    for row in R:
        print(list(map(int, row)))


A1 = ["Иванов", "Петров", "Сидоров", "Петечкин", "Васечкин"]
n1 = len(A1)

R1 = [[0 for _ in range(n1)] for _ in range(n1)]
R1_list = [("Иванов", "Петров"), ("Петров", "Сидоров"),
           ("Иванов", "Петечкин")]  # отношение задано перечислением своих элементов

for p in R1_list:
    ind1 = A1.index(p[0])
    ind2 = A1.index(p[1])
    R1[ind1][ind2] = 1

print_relation(R1)
analyze_relation(R1)
print("\n")

R1 = reverse_relation(R1)
print_relation(R1)
analyze_relation(R1)
print("\n")

A2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
n2 = len(A2)


# отношение задается предикатом - логическим условием

def F(x, y):
    return (x + y) % 2 == 0 # отношение: сумма x и y четна

R2 = [[0 for _ in range(n2)] for _ in range(n2)]
for i in range(n2):
    for j in range(n2):
        R2[i][j] = int(F(A2[i], A2[j]))

print_relation(R2)
analyze_relation(R2)
print("\n")

R2 = reverse_relation(R2)
print_relation(R2)
analyze_relation(R2)
print("\n")

A3 = [1, 2, 3, 4]
n3 = len(A3)

R3 = [[0 for _ in range(n3)] for _ in range(n3)]
R3_list = [(1, 1), (1, 4), (4, 1), (2, 2), (3, 3), (4, 4)]

for p in R3_list:
    ind1 = A3.index(p[0])
    ind2 = A3.index(p[1])
    R3[ind1][ind2] = 1

print_relation(R3)
analyze_relation(R3)
print("\n")

R3 = reverse_relation(R3)
print_relation(R3)
analyze_relation(R3)
print("\n")

A4 = ["a", "b", "c", "d", "e"]
n4 = len(A4)

R4 = [[0 for _ in range(n4)] for _ in range(n4)]
R4_list = [("a", "a"), ("a", "b"), ("a", "c"), ("b", "b"), ("b", "d"), ("c", "c"), ("d", "d"), ("e", "e")]

for p in R4_list:
    ind1 = A4.index(p[0])
    ind2 = A4.index(p[1])
    R4[ind1][ind2] = 1

print_relation(R4)
analyze_relation(R4)
print("\n")

R4 = reverse_relation(R4)
print_relation(R4)
analyze_relation(R4)
print("\n")

A5 = ["x", "y", "z"]
n5 = len(A5)

R5 = [[0 for _ in range(n5)] for _ in range(n5)]
print_relation(R5)
analyze_relation(R5)
print("\n")

R5 = reverse_relation(R5)
print_relation(R5)
analyze_relation(R5)