Solution to the N-Queens problem

N_Queens.py

# Three pretty print functions 
def print_row(length):
    for i in range(length):
        print('+-', end="")
    print('+')

def print_cell(array, length):
    for i in range(length):
        if i == array[0]:
            print('|*', end="")
        else:
            print('| ', end="")
    print("|")

def print_matrix(array):
    """Prints the queens n-matrix"""
    array = list(map(int, array))
    length = len(array)
    for i in range(length):
        print_row(length)
        print_cell(array[i:], length)
    print_row(length)
    print()

# Wrapper
def n_queens(row):
    permutations = []
    return _permute(row, 0, len(row)-1, permutations)

# Work is done here 
def _permute(row, start, end, permutations):
    """Permutes all of the Queen column positions and then checks
    if the Queen is in a valid position before appending it to the returned array"""
    
    if (start == end):
        isValid = True
        for i in range(len(row)-1):         # checks if in same row or diagonal
            if (row[i] == row[i+1]   or
                row[i] == row[i+1]+1 or
                row[i] == row[i+1]-1):
                isValid = False
        if isValid:
            string = ''.join(map(str, row))
            permutations.append(string)
    else:
        for i in range(start, end+1):
            row[start], row[i] = row[i], row[start]  # swap
            _permute(row, start+1, end, permutations)
            row[start], row[i] = row[i], row[start]  # swap
    return permutations

rows = list(range(5))
permutations = n_queens(rows)
for index, valid_solution in enumerate(permutations):
    print('Solution', index+1)
    print_matrix(valid_solution)