How to determine the longest increasing subsequence using dynamic programming?

Question

I have a set of integers. I want to find the longest increasing subsequence of that set using dynamic programming.

Answer 1

Here is a Scala implementation of the O(n^2) algorithm:

object Solve {
  def longestIncrSubseq[T](xs: List[T])(implicit ord: Ordering[T]) = {
    xs.foldLeft(List[(Int, List[T])]()) {
      (sofar, x) =>
        if (sofar.isEmpty) List((1, List(x)))
        else {
          val resIfEndsAtCurr = (sofar, xs).zipped map {
            (tp, y) =>
              val len = tp._1
              val seq = tp._2
              if (ord.lteq(y, x)) {
                (len + 1, x :: seq) // reversely recorded to avoid O(n)
              } else {
                (1, List(x))
              }
          }
          sofar :+ resIfEndsAtCurr.maxBy(_._1)
        }
    }.maxBy(_._1)._2.reverse
  }

  def main(args: Array[String]) = {
    println(longestIncrSubseq(List(
      0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15)))
  }
}