LeetCode-in-All
51. N-Queens
Hard
The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.
Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens’ placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
Example 1:
Input: n = 4
Output: [[“.Q..”,”…Q”,”Q…”,”..Q.”],[”..Q.”,”Q…”,”…Q”,”.Q..”]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
Example 2:
Input: n = 1
Output: [[“Q”]]
Constraints:
1 <= n <= 9
Solution
defmodule Solution do
@spec solve_n_queens(n :: integer) :: [[String.t]]
def solve_n_queens(n) do
solve([], n, {0, 0}, []) |> Enum.map(&normalize(&1, n))
end
# A board is just a bunch of coordinates where a queen resides.
defp solve(board, n, {n, 0}, acc), do: [board | acc]
defp solve(_board, n, {_, n}, acc), do: acc
defp solve(board, n, {i, j}, acc) do
acc =
if attacked?(board, {i, j}) do
acc
else
solve([{i, j} | board], n, {i + 1, 0}, acc)
end
solve(board, n, {i, j + 1}, acc)
end
defp attacked?(board, {i, j}) do
Enum.any?(board, fn {ii, jj} ->
jj == j or
ii - jj == i - j or
ii + jj == i + j
end)
end
defp normalize(board, n) do
for { {x, y}, i} <- Enum.with_index(board) do
0..n-1
|> Enum.map(fn j ->
if {n - i - 1, j} == {x, y}, do: "Q", else: "."
end)
|> IO.iodata_to_binary()
end
end
end