Question

Following are the steps (algorithm) to obtain a solution for Queen Puzzle heuristically:

a, Divide n by 12 Remember the remainder (n is 8 for the eight queens puzzle)

b. Write a list of the odd numbers from 1 to n in order, if the remainder is 8, switch pairs (i.e. 3, 1, 7, 5. 11.9....)

c. if the remainder is 2, Switch the places of 1 and 3, then move 5 to the end of the list

Answer 1

Algorithm:

SOURCE CODE:

*Please follow the comments to better understand the code.

**Please look at the Screenshot below and use this code to copy-paste.

***The code in the below screenshot is neatly indented for better understanding.

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def get_solution(n):
    """
    return the value of the N-Queen problem solution
    """

    # STEP (a)  Divide n by 12 Remember the remainder
    remainder = n % 12

    # STEP (b)  Write a list of the odd numbers from 1 to n in order
    odd_numbers = [i for i in range(1, n + 1, 2)]
    if remainder == 8:
        # Switch Pairs
        for i in range(0, len(odd_numbers), 2):
            # SWAP
            odd_numbers[i], odd_numbers[i + 1] = odd_numbers[i + 1], odd_numbers[i]
    # STEP C
    elif remainder == 2:
        odd_numbers[0], odd_numbers[2] = odd_numbers[2], odd_numbers[0]
        # move 5 to the last
        num = odd_numbers.pop(4)
        odd_numbers.append(num)
    # STEP D
    elif remainder in (3, 9):
        one, three = odd_numbers[0], odd_numbers[2]
        odd_numbers.pop(0)
        odd_numbers.pop(1)
        # move to last
        odd_numbers.append(one)
        odd_numbers.append(three)

    # STEP E Append the even numbers from 2 to n in order
    even_numbers = [i for i in range(2, n + 1, 2)]
    final_arrangement = odd_numbers + even_numbers

    # STEP f if the remainder is 3 or 9. move 2 to the end of the list
    if remainder in (3, 9):
        two = final_arrangement.pop(1)
        final_arrangement.append(two)

    return final_arrangement


# TEST
if __name__ == '__main__':
    print('15 Queens solution is: ', get_solution(15))
    print('8 Queens solution is: ', get_solution(8))
    print('25 Queens solution is: ', get_solution(25))

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