La résolution de la n-reine de puzzle

Je viens de résoudre le nqueen problème en python. La solution sorties le nombre total de solutions pour placer n reines sur un échiquier nXn mais en essayant avec n=15 prend plus d'une heure pour obtenir une réponse. Quelqu'un peut-il prendre un coup d'oeil au code et de me donner des conseils sur l'accélération de ce programme...... Un novice en python programmeur.

#!/usr/bin/env python2.7
##############################################################################
# a script to solve the n queen problem in which n queens are to be placed on
# an nxn chess board in a way that none of the n queens is in check by any other
#queen using backtracking'''
##############################################################################
import sys
import time
import array
solution_count = 0
def queen(current_row, num_row, solution_list):
if current_row == num_row:
global solution_count 
solution_count = solution_count + 1
else:
current_row += 1
next_moves = gen_nextpos(current_row, solution_list, num_row + 1)
if next_moves:
for move in next_moves:
'''make a move on first legal move of next moves'''
solution_list[current_row] = move
queen(current_row, num_row, solution_list)
'''undo move made'''
solution_list[current_row] = 0
else:
return None
def gen_nextpos(a_row, solution_list, arr_size):
'''function that takes a chess row number, a list of partially completed 
placements and the number of rows of the chessboard. It returns a list of
columns in the row which are not under attack from any previously placed
queen.
'''
cand_moves = []
'''check for each column of a_row which is not in check from a previously
placed queen'''
for column in range(1, arr_size):
under_attack =  False
for row in range(1, a_row):
'''
solution_list holds the column index for each row of which a 
queen has been placed  and using the fact that the slope of 
diagonals to which a previously placed queen can get to is 1 and
that the vertical positions to which a queen can get to have same 
column index, a position is checked for any threating queen
'''
if (abs(a_row - row) == abs(column - solution_list[row]) 
or solution_list[row] == column):
under_attack = True
break
if not under_attack:
cand_moves.append(column)
return cand_moves
def main():
'''
main is the application which sets up the program for running. It takes an 
integer input,N, from the user representing the size of the chessboard and 
passes as input,0, N representing the chess board size and a solution list to
hold solutions as they are created.It outputs the number of ways N queens
can be placed on a board of size NxN.
'''
#board_size =  [int(x) for x in sys.stdin.readline().split()]
board_size = [15]
board_size = board_size[0]
solution_list = array.array('i', [0]* (board_size + 1))
#solution_list =  [0]* (board_size + 1)
queen(0, board_size, solution_list)
print(solution_count)
if __name__ == '__main__':
start_time = time.time()
main()
print(time.time() 

OriginalL'auteur | 2011-01-27