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nQueenProblem.py
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nQueenProblem.py
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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
def print_solution(board=[]):
""" Function to print the solution
"""
for i in range(len(board)):
for j in range(len(board[0])):
print "%s" % board[i][j],
print ""
def is_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
for i in range(col):
if board[row][i]:
return False
# Check upper diagonal on left side
i = row
j = col
while i >= 0 and j >= 0:
if board[i][j]:
return False
i -= 1
j -= 1
# Check lower diagonal on left side
i = row
j = col
while i < len(board) and j >= 0:
if board[i][j]:
return False
i += 1
j -= 1
return True
def solve_n_queen(board=[], col=0):
""" Recursive function to solve n queen
"""
# Base Case: When all queens are placed
if col >= len(board):
return True
# Place queens in all rows of this col and check
for i in range(len(board)):
# Check if queen can be placed in ith row of col
if is_safe(board, i, col):
# If safe then place queen on board
board[i][col] = 'X'
# recur to place rest of queens
if solve_n_queen(board, col+1) == True:
return True
board[i][col] = 0
return False
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]]
if solve_n_queen(brd, 0) == False:
print "Solution does not exist"
else:
print_solution(brd)