Category Hierarchy

def areLegalValues(values: list):
    if len(values) in [1,4,9,16,25]:
        for value in values:
            if value <= len(values):
                if value != 0 and values.count(value)>1:
                    return False
            else:
                return False
        return True
    return False

def isLegalRow(board: list, row: list):
    compareList = [ ]

    for r in range(len(board)):

        if r == row:

            for c in range(len(board[0])):
                #print(board[r][c])
                compareList.append(board[r][c])
    return areLegalValues(compareList)

def isLegalCol(board: list, col: list):
    compareList = [ ]
    for r in range(len(board)):
        for c in range(len(board[0])):
            if c == col:
                compareList.append(board[r][c])
                #print(compareList)
    return areLegalValues(compareList)

def isLegalBlock(board: list, block: list):
    compareList = [ ]
    N = int((len(board))**(1/2))
    blockRowNumber = int(block//N)
    blockColNumber = int(block%N)
    for row in range(blockRowNumber*N, blockRowNumber*N+N):
        #print(row)
        for col in range(len(board[0])):
            if col in range(blockColNumber*N, blockColNumber*N+N):
                #print(board[row][col])
                compareList.append(board[row][col])
                # print(compareList)
    return areLegalValues(compareList)

def isLegalSudoku(board: list):
    boardLength = len(board)
    for row in range(len(board)):
        if isLegalRow(board,row) != True:
            return False
        for col in range(len(board[0])):
            if isLegalCol(board,col) != True:
                return False
    for block in range(boardLength):
        if isLegalBlock(board, block) != True:
            return False
    return True

def solveSudoku(board: list):
    """takes in a sudoku board and solves the board through use of backtracking
    and returns the dectructively changed board"""
    checkZeroes = True
    for row in range(len(board)):
        for col in range(len(board[0])):
            if board[row][col] == 0:
                checkZeroes = False
    
    if checkZeroes == True:
        return board
    else:
        for row in range(len(board)):
            for col in range(len(board[0])):
                if board[row][col] == 0:
                    for number in range(1,len(board)+1):
                        board[row][col] = number
                        if isLegalSudoku(board) == True:
                            solution = solveSudoku(board)
                            if solution != None:
                                return solution
                        board[row][col] = 0
                    return None