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91 lines
2.6 KiB
Python
91 lines
2.6 KiB
Python
"""
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The nqueens problem is of placing N queens on a N * N
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chess board such that no queen can attack any other queens placed
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on that chess board.
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This means that one queen cannot have any other queen on its horizontal, vertical and
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diagonal lines.
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"""
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from __future__ import annotations
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solution = []
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def isSafe(board: list[list[int]], row: int, column: int) -> bool:
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"""
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This function returns a boolean value True if it is safe to place a queen there
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considering the current state of the board.
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Parameters :
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board(2D matrix) : board
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row ,column : coordinates of the cell on a board
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Returns :
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Boolean Value
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"""
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for i in range(len(board)):
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if board[row][i] == 1:
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return False
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for i in range(len(board)):
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if board[i][column] == 1:
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return False
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for i, j in zip(range(row, -1, -1), range(column, -1, -1)):
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if board[i][j] == 1:
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return False
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for i, j in zip(range(row, -1, -1), range(column, len(board))):
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if board[i][j] == 1:
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return False
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return True
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def solve(board: list[list[int]], row: int) -> bool:
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"""
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It creates a state space tree and calls the safe function until it receives a
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False Boolean and terminates that branch and backtracks to the next
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possible solution branch.
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"""
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if row >= len(board):
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"""
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If the row number exceeds N we have board with a successful combination
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and that combination is appended to the solution list and the board is printed.
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"""
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solution.append(board)
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printboard(board)
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print()
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return True
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for i in range(len(board)):
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"""
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For every row it iterates through each column to check if it is feasible to
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place a queen there.
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If all the combinations for that particular branch are successful the board is
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reinitialized for the next possible combination.
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"""
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if isSafe(board, row, i):
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board[row][i] = 1
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solve(board, row + 1)
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board[row][i] = 0
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return False
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def printboard(board: list[list[int]]) -> None:
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"""
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Prints the boards that have a successful combination.
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"""
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for i in range(len(board)):
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for j in range(len(board)):
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if board[i][j] == 1:
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print("Q", end=" ")
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else:
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print(".", end=" ")
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print()
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# n=int(input("The no. of queens"))
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n = 8
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board = [[0 for i in range(n)] for j in range(n)]
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solve(board, 0)
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print("The total no. of solutions are :", len(solution))
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