python-programs/nQueenProblem.py at master · chinmayb/python-programs · GitHub

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# The N Queen is the problem of placing N chess queens on
# a NxN chessboard so that no two queens attack each other.
# Solution to the problem using Backtracking


defprint_solution(board=[]):
""" Function to print the solution
 """
foriinrange(len(board)):
forjinrange(len(board[0])):
print"%s"%board[i][j],
print""


defis_safe(board=[], row=0, col=0):
""" Function to check if queen can be placed in board[row][col].
 This function is called when 'col' queens are already placed in columns from 0 to -1.
 So we need to check only left side for attacking queen.
 """

# Check the row on left side
foriinrange(col):
ifboard[row][i]:
returnFalse

# Check upper diagonal on left side
i=row
j=col
whilei>=0andj>=0:
ifboard[i][j]:
returnFalse
i-=1
j-=1

# Check lower diagonal on left side
i=row
j=col
whilei<len(board) andj>=0:
ifboard[i][j]:
returnFalse
i+=1
j-=1
returnTrue


defsolve_n_queen(board=[], col=0):
""" Recursive function to solve n queen
 """

# Base Case: When all queens are placed
ifcol>=len(board):
returnTrue

# Place queens in all rows of this col and check
foriinrange(len(board)):
# Check if queen can be placed in ith row of col
ifis_safe(board, i, col):
# If safe then place queen on board
board[i][col] ='X'

# recur to place rest of queens
ifsolve_n_queen(board, col+1) ==True:
returnTrue
board[i][col] =0
returnFalse


if__name__=="__main__":
brd= [[0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0]]
ifsolve_n_queen(brd, 0) ==False:
print"Solution does not exist"
else:
print_solution(brd)