import numpy as np

A = [[1, 2 / 3, 2, 5 / 2, 5 / 3, 5],
     [3 / 2, 1, 3, 10 / 3, 3, 9],
     [1 / 2, 1 / 3, 1, 4 / 3, 7 / 8, 5 / 2],
     [2 / 5, 3 / 10, 3 / 4, 1, 5 / 6, 12 / 5],
     [3 / 5, 1 / 3, 8 / 7, 6 / 5, 1, 3],
     [1 / 5, 1 / 9, 2 / 5, 5 / 12, 1 / 3, 1]]

B = [[1, 2 / 5, 3, 7 / 3, 1 / 2, 1],
     [5 / 2, 1, 4 / 7, 5 / 8, 1 / 3, 3],
     [1 / 3, 7 / 4, 1, 1 / 2, 2, 1 / 2],
     [3 / 7, 8 / 5, 2, 1, 4, 2],
     [2, 3, 1 / 2, 1 / 4, 1, 1 / 2],
     [1, 1 / 3, 2, 1 / 2, 2, 1]]

C = [[1, 17 / 4, 17 / 20, 8 / 5, 23 / 6, 8 / 3],
     [4 / 17, 1, 1 / 5, 2 / 5, 9 / 10, 2 / 3],
     [20 / 17, 5, 1, 21 / 10, 51 / 10, 10 / 3],
     [5 / 8, 5 / 2, 10 / 21, 1, 5 / 2, 11 / 6],
     [6 / 23, 10 / 9, 10 / 51, 2 / 5, 1, 19 / 30],
     [3 / 8, 3 / 2, 3 / 10, 6 / 11, 30 / 19, 1]]


def koczkodaj(mtx):
    maxOfVal = 0
    for x in range(len(mtx)):
        for y in range(len(mtx)):
            if x == y:
                continue
            for z in range(len(mtx)):
                if y == z:
                    continue
                inKocz = min(abs(1 - (mtx[x][z] * mtx[z][y]) / mtx[x][y]), abs(1 - mtx[x][y] / (mtx[x][z] * mtx[z][y])))
                if inKocz > maxOfVal:
                    maxOfVal = inKocz

        return maxOfVal


def checkValInKocz(n, k):
    return 1 - ((1 + pow(4 * (n - 1) * (n - k - 2), 1 / 2)) / (2 * (n - 1)))


# ########### A

print("Matrix A:")
print("Koczkodaj Index: ", koczkodaj(A))
print("Checked Value(max index value): ", checkValInKocz(6, 2))

n = 6
k = 2

A1 = [[1, 2 / 3, 2, 5 / 2],
      [3 / 2, 1, 3, 10 / 3],
      [1 / 2, 1 / 3, 1, 4 / 3],
      [2 / 5, 3 / 10, 3 / 4, 1]]

B1 = [[5 / 3, 5],
      [3, 9],
      [7 / 8, 5 / 2],
      [5 / 6, 12 / 5]]

for i in range(n - k):
    for j in range(n - k):
        if i != j:
            A1[i][j] *= -1 / (n - 1)

Wk = [3, 1]
B1 = np.matmul(B1, Wk)
b = B1 * 1 / (n - 1)
W = np.matmul(np.linalg.inv(A1), b)
res = np.concatenate((W, Wk), axis=None)

print("Final ranking: ", res)

# ########### B

print("\nMatrix B:")
print("Koczkodaj Index: ", koczkodaj(B))
print("Checked Value(max index value): ", checkValInKocz(6, 3))

n = 6
k = 3

A1 = [[1, 2 / 5, 3],
     [5 / 2, 1, 4 / 7],
     [1 / 3, 7 / 4, 1]]

B1 = [[7 / 3, 1 /2, 1],
     [5 / 8, 1 / 3, 3],
     [1 / 2, 2, 1 / 2]]

for i in range(n - k):
    for j in range(n - k):
        if i != j:
            A1[i][j] *= -1 / (n - 1)

Wk = [2, 1 / 2, 1]
B1 = np.matmul(B1, Wk)
b = B1 * 1 / (n - 1)
W = np.matmul(np.linalg.inv(A1), b)
res = np.concatenate((W, Wk), axis=None)

print("Final ranking: ", res)

# ########### C

print("\nMatrix C:")
print("Koczkodaj Index: ", koczkodaj(C))
print("Checked Value(max index value): ", checkValInKocz(6, 2))

n = 6
k = 2

reshapedC = [[1, 23 / 6, 17 / 20, 8 / 3, 17 / 4, 8 / 5],
             [6 / 23, 1, 10 / 51, 19 / 30, 10 / 9, 2 / 5],
             [20 / 17, 51 / 10, 1, 10 / 3, 5, 21 / 10],
             [3 / 8, 30 / 19, 3 / 10, 1, 3 / 2, 6 / 11],
             [4 / 17, 9 / 10, 1 / 5, 2 / 3, 1, 2 / 5],
             [5 / 8, 5 / 2, 10 / 21, 11 / 6, 5 / 2, 1]]

A1 = [[1, 23 / 6, 17 / 20, 8 / 3],
     [6 / 23, 1, 10 / 51, 19 / 30],
     [20 / 17, 51 / 10, 1, 10 / 3],
     [3 / 8, 30 / 19, 3 / 10, 1]]

B1 = [[17 / 4, 8 / 5],
     [10 / 9, 2 / 5],
     [5, 21 / 10],
     [3 / 2, 6 / 11]]

for i in range(n - k):
    for j in range(n - k):
        if i != j:
            A1[i][j] *= -1 / (n - 1)

Wk = [2, 5]
B1 = np.matmul(B1, Wk)
b = B1 * 1 / (n - 1)
W = np.matmul(np.linalg.inv(A1), b)
res = np.concatenate((W, Wk), axis=None)
print("Final ranking: ", res)