from typing import List
"""
Module for calculating the determinant of a 3x3 matrix.
Functions:
    neg_odd_vals(lst: List[int]) -> List[int]:
        Returns a new list where every value at an odd index is negated.
    det3x3(M: List[List[int]]) -> int:
        Calculates and returns the determinant of a 3x3 matrix M using Laplace expansion along the first row.
        Requires an external module 'determinate2x2' with a function 'det2x2' for 2x2 determinants.
        
NOTE: You call determinate3x3.det3x3(M) to find the determinate of matrix M.  If M is not a 3x3 matrix, you 
will receive an AssertionError: "Matrix is not 3x3"
        
"""
import modules.determinate2x2 as determinate2x2
import copy


def neg_odd_vals(lst: List[int])-> List[int]:
    return [-val if i % 2 == 1 else val for i, val in enumerate(lst)]

def det3x3(M: List[List[int]])->int:
    assert len(M) == 3 and len(M[0]) == 3, "Matrix is not 3x3"
    # Matrix M with row 0 and col 0 removed
    N = copy.deepcopy(M)
    N[1].remove(N[1][0]) 
    N[2].remove(N[2][0])
    A = [N[1], N[2]]

    #Matrix M with row 0 and col 1 removed
    N = copy.deepcopy(M)
    N[1].remove(N[1][1]) 
    N[2].remove(N[2][1])
    B = [N[1], N[2]]

    #Matrix M with row 0 and col 2 removed
    N = copy.deepcopy(M)
    N[1].remove(N[1][2])
    N[2].remove(N[2][2])    
    C = [N[1], N[2]]
 
    # List M[0] with every odd index value set to its negative
    N0 = neg_odd_vals(N[0])
    
    # Sum of determinates A, B, C times their respective multipliers
    det0 = N0[0]*determinate2x2.det2x2(A)
    det1 = N0[1]*determinate2x2.det2x2(B)
    det2 = N0[2]*determinate2x2.det2x2(C)
    return det0 + det1 + det2