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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
# @param {Integer} n
# @return {String[][]}
def solve_n_queens(n)
pos = Array.new(2 * n - 1 + 2 * n - 1, false)
pos2 = Array.new(n, 0)
ans = []
helper_queens(n, 0, pos, pos2, ans)
ans
end
private
def helper_queens(n, row, pos, pos2, ans)
return construct(n, pos2, ans) if row == n
(0...n).each do |i|
index = n + 2 * n - 1 + n - 1 + i - row
next if pos[i] || pos[n + i + row] || pos[index]
pos[i] = true
pos[n + i + row] = true
pos[index] = true
pos2[row] = i
helper_queens(n, row + 1, pos, pos2, ans)
pos[i] = false
pos[n + i + row] = false
pos[index] = false
end
end
def construct(n, pos, ans)
sol = []
(0...n).each do |r|
queen_row = Array.new(n, '.')
queen_row[pos[r]] = 'Q'
sol << queen_row.join
end
ans << sol
end