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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
object Solution {
def solveNQueens(n: Int): List[List[String]] = {
val rst = scala.collection.mutable.ListBuffer[List[String]]()
dfs(n, List[Int](), rst)
rst.toList
}
@SuppressWarnings(Array("scala:S3776"))
private def dfs(n: Int, oneSol: List[Int], rst: scala.collection.mutable.ListBuffer[List[String]]): Unit = {
if (oneSol.length == n) {
val line = for (idx <- oneSol) yield ("." * idx + "Q" + "." * (n - idx - 1))
rst += line
return
}
for (col <- 0 until n) {
if (!oneSol.contains(col)) {
var i = oneSol.length - 1
var j = col - 1
var k = col + 1
var continue = true
while (continue && i >= 0 && (j >= 0 || k < n)) {
if (oneSol(i) == j || oneSol(i) == k) {
continue = false
}
i -= 1
j -= 1
k += 1
}
if (continue) {
dfs(n, oneSol :+ col, rst)
}
}
}
}
}