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Add nqueens csp #1238

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60 changes: 60 additions & 0 deletions csp-nqueens.py
Original file line number Diff line number Diff line change
@@ -0,0 +1,60 @@
import numpy as np


# 3 constraints
# no queens on the same row
# no queens on the same col
# no queens on the same diagonal


def is_safe_row(board,n):
for row in range(n):
if sum(board[row,:]) > 1: # if there is a row with more than one queen, then its sum will be more than 1s
return False
return True

def is_safe_col(board,n):
for col in range(n):
if sum(board[:,col]) > 1 :
return False
return True

def is_safe_diag(board,n):
diags = []
for i in range(-n+1,n):
# if the index i is negative, take the upper ith diagonal
# if the index i is positive, the the lower ith diagonal
diags.append(board.diagonal(i))

diags.extend(board.diagonal(i) for i in range(n-1,-n,-1))
for x in diags:
if len(x)>1:
if sum (x)>1:
return False
return True


def nqueens (board, queen, n):
if is_safe_row(board,n) and is_safe_col(board,n) and is_safe_diag(board,n):
if board.sum()==n:
return True

for row in range (0,n):
board[row,queen] = 1
print(f'Queen: {row}')
if is_safe_row(board,n) and is_safe_col(board,n) and is_safe_diag(board,n):
if nqueens(board, queen+1,n):
return True
board[row,queen] = 0
else:
board[row,queen] = 0
return False


if __name__ == '__main__':
n = 4
board = np.zeros((n, n))
if nqueens(board, 0, n):
print(board)
else:
print('Cannot find a solution for ',n,' queens.')