Some scala functions

codes.scala

def permutations(nums: Seq[Int]): Seq[Seq[Int]] = {
  if (nums.isEmpty)
    Array(Seq())
  else {
    for (
      n <- nums;
      perms <- permutations(nums.filter(_ != n))
    ) yield n +: perms
  }
}

permutations(Array(1, 2, 3))

def combinations(nums: Seq[Int]): Seq[Seq[Int]] = {
  if (nums.isEmpty)
    Seq(nums)
  else if (nums.length == 1)
    Seq(nums)
  else {
    val combs = combinations(nums.tail)
    val combs1 = Seq(nums.head) +: combs
    val combs2 = combs.map(x => nums.head +: x)
    combs1 ++ combs2
  }
}

combinations(Vector(1, 2, 3, 4))

def nQueens(n: Int): List[List[(Int, Int)]] = {

  def isSafe(queen: (Int, Int), queens: List[(Int, Int)]): Boolean =
    queens.forall(aQueen =>
      aQueen._1 != queen._1 &&
        aQueen._2 != queen._2 &&
        Math.abs(aQueen._1 - queen._1) != Math.abs(aQueen._2 - queen._2)
    )

  def placeQueen(k: Int): List[List[(Int, Int)]] = {
    if (k < 0) {
      List(List())
    }
    else {
      for (
        queens <- placeQueen(k - 1);
        column <- 0 until n;
        queen = (k, column)
        if isSafe(queen, queens)
      ) yield queen :: queens
    }
  }

  placeQueen(n - 1)
}

val solutions = nQueens(8)