a = [[1,1,1],[4,3,-1],[3,5,3]]
b = [1,6,4]
c = [[1,-3,7],[-2,6,1],[0,3,-2]]

def chechDeterminants(c):
    if c[0][0] == 0:
        print("Determinant is 0. Re-ordering")
        swap(c)
    elif c[0][0]*c[1][1]-c[0][1]*c[1][0] == 0:
        print("Determinant is 0. Re-ordering")
        swap(c)
    elif c[0][0]*c[1][1]*c[2][2]+c[0][1]*c[1][2]*c[2][0]+c[0][2]*c[1][0]*c[2][1]-c[0][2]*c[1][1]*c[2][0]-c[0][1]*c[1][0]*c[2][2]-c[0][0]*c[1][2]*c[2][1] == 0:
        print("Determinant is 0. Re-ordering")
        swap(c)
    else:
        LU(c)

def swap(c):
    secondRow = c[1]
    lastRow = c[2]
    c[1] = lastRow
    c[2] = secondRow
    print("Reordered Matrix B:")
    for i in range(len(c)):
        print(c[i])
    chechDeterminants(c)

def LU(a):

    n = len(a)

    L = [[0 for i in range(n)]for i in range(n)]
    for i in range(n):
        L[i][i] = 1

    U = [[0 for i in range(n)]for j in range(n)]
    for i in range(n):
        for j in range(n):
            if i == 0:
                U[i][j] = a[i][j]
            else:
                U[i][j] = 0

    for i in range(n):
        for j in range(n):
            if j == 0 and i > 0:
                L[i][j] = a[i][j]/U[0][0]
            else:
                if i == 1:
                    U[i][j] = a[i][j]-(L[i][0]*U[i-1][j])
                if i == 2:
                    if j == 1:
                        L[i][j] = (a[i][j]-(L[i][j-1]*U[i-2][j]))/U[i-1][j]
                    if j == 2:
                        U[i][j] = (a[i][j]-(L[i][j-2]*U[i-2][j])-(L[i][j-1]*U[i-1][j]))

    print("L Matrix")
    for i in range(len(L)):
        print(L[i])
    print("U Matrix")
    for i in range(len(U)):
        print(U[i])

    return L, U

def B(L,b,U):
    B = [0,0,0]
    n = len(b)
    for i in range(n):
        B[i] = b[i]/L[i][i]
        for j in range(n):
            if j != i:
                B[i] -= L[i][j]*B[j]
    print("B Matrix (LY)")
    print(B)

    X(U,B)

def X(U,B):
    X = [0,0,0]
    n = len(B)
    for i in range(n-1,-1,-1):
        X[i] = B[i]/U[i][i]
        for j in range(n):
            if j != i:
                X[i] += U[i][j]*X[j]
    print("Result!")
    print(X)

print("Matrix A:")
for i in range(len(a)):
    print(a[i])
L, U = LU(a)
B(L,b,U)
print("----------------")
print("Matrix B")
for i in range(len(c)):
    print(c[i])
chechDeterminants(c)