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N-Queens Problem

BacktrackingHard1:30

The N-Queens problem asks you to place N queens on an N x N chessboard so that no two queens threaten each other. Queens attack along rows, columns, and both diagonals.

For example, one valid solution for N = 4 places queens at positions (0,1), (1,3), (2,0), (3,2).

Explain your approach to solving this problem. How do you efficiently check whether placing a queen is safe? What is the time complexity?

How to approach it

  • Hint 1

    Place queens one row at a time -- since each row must have exactly one queen, you only need to decide the column for each row.

  • Hint 2

    To check safety efficiently, maintain sets for occupied columns, occupied main diagonals (row - col), and occupied anti-diagonals (row + col).

  • Hint 3

    When a placement fails, backtrack: remove the queen and try the next column in the same row.

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