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N-Queens problem.py
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N-Queens problem.py
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def is_safe(board, row, col, N):
# Check if a queen can be placed at board[row][col]
# Check the left side of the row
for i in range(col):
if board[row][i] == 1:
return False
# Check the upper diagonal on the left side
for i, j in zip(range(row, -1, -1), range(col, -1, -1)):
if board[i][j] == 1:
return False
# Check the lower diagonal on the left side
for i, j in zip(range(row, N, 1), range(col, -1, -1)):
if board[i][j] == 1:
return False
return True
def solve_n_queens_util(board, col, N):
# Base case: If all queens are placed, return True
if col >= N:
return True
# Recursive case: Try placing a queen in each row of the current column
for i in range(N):
if is_safe(board, i, col, N):
board[i][col] = 1
# Recursively check if the remaining queens can be placed
if solve_n_queens_util(board, col + 1, N):
return True
# If placing queen at board[i][col] doesn't lead to a solution, backtrack
board[i][col] = 0
# If no queen can be placed in this column, return False
return False
def solve_n_queens(N):
# Create an empty N x N chessboard
board = [[0] * N for _ in range(N)]
if not solve_n_queens_util(board, 0, N):
print("No solution exists.")
return
# Print the solution
for row in board:
print(' '.join(str(cell) for cell in row))
# Test the function with N = 4
solve_n_queens(4)