diff --git a/backtracking/n_queens.py b/backtracking/n_queens.py index bbf0ce44f..0f237d95e 100644 --- a/backtracking/n_queens.py +++ b/backtracking/n_queens.py @@ -17,40 +17,39 @@ def is_safe(board: list[list[int]], row: int, column: int) -> bool: This function returns a boolean value True if it is safe to place a queen there considering the current state of the board. - Parameters : - board(2D matrix) : board - row ,column : coordinates of the cell on a board + Parameters: + board (2D matrix): The chessboard + row, column: Coordinates of the cell on the board - Returns : + Returns: Boolean Value """ - for i in range(len(board)): - if board[row][i] == 1: - return False - for i in range(len(board)): - if board[i][column] == 1: - return False - for i, j in zip(range(row, -1, -1), range(column, -1, -1)): - if board[i][j] == 1: - return False - for i, j in zip(range(row, -1, -1), range(column, len(board))): - if board[i][j] == 1: - return False - return True + + n = len(board) # Size of the board + + # Check if there is any queen in the same row, column, + # left upper diagonal, and right upper diagonal + return ( + all(board[i][j] != 1 for i, j in zip(range(row, -1, -1), range(column, n))) + and all( + board[i][j] != 1 for i, j in zip(range(row, -1, -1), range(column, -1, -1)) + ) + and all(board[i][j] != 1 for i, j in zip(range(row, n), range(column, n))) + and all(board[i][j] != 1 for i, j in zip(range(row, n), range(column, -1, -1))) + ) def solve(board: list[list[int]], row: int) -> bool: """ - It creates a state space tree and calls the safe function until it receives a - False Boolean and terminates that branch and backtracks to the next + This function creates a state space tree and calls the safe function until it + receives a False Boolean and terminates that branch and backtracks to the next possible solution branch. """ if row >= len(board): """ - If the row number exceeds N we have board with a successful combination + If the row number exceeds N, we have a board with a successful combination and that combination is appended to the solution list and the board is printed. - """ solution.append(board) printboard(board) @@ -58,9 +57,9 @@ def solve(board: list[list[int]], row: int) -> bool: return True for i in range(len(board)): """ - For every row it iterates through each column to check if it is feasible to + For every row, it iterates through each column to check if it is feasible to place a queen there. - If all the combinations for that particular branch are successful the board is + If all the combinations for that particular branch are successful, the board is reinitialized for the next possible combination. """ if is_safe(board, row, i): @@ -77,14 +76,14 @@ def printboard(board: list[list[int]]) -> None: for i in range(len(board)): for j in range(len(board)): if board[i][j] == 1: - print("Q", end=" ") + print("Q", end=" ") # Queen is present else: - print(".", end=" ") + print(".", end=" ") # Empty cell print() -# n=int(input("The no. of queens")) +# Number of queens (e.g., n=8 for an 8x8 board) n = 8 board = [[0 for i in range(n)] for j in range(n)] solve(board, 0) -print("The total no. of solutions are :", len(solution)) +print("The total number of solutions are:", len(solution))