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def makePalindrome(str: String): String = {
def paretoMin(points: Iterable[(Int, Int)]): List[(Int, Int)] = {
val sorted = points.toSeq.sortBy(identity)
(List.empty[(Int, Int)] /: sorted) { (result, e) =>
if (result.isEmpty  e._2 <= result.head._2)
e :: result
else
result
}
}
/** Find all pairs directly nested within a given pair.
* For performance reasons tries to not include suboptimal pairs (pairs nested in any of the pairs also in the result)
* although it wouldn't break anything as prune takes care of this. */
def pairs(left: Int, right: Int): Iterable[(Int, Int)] = {
val builder = List.newBuilder[(Int, Int)]
var rightMax = str.length
for (i < left until (str.length  right)) {
rightMax = math.min(str.length  left, rightMax)
val subPairs =
for (j < right until rightMax if str(i) == str(str.length  j  1)) yield (i, j)
subPairs.headOption match {
case Some((a, b)) => rightMax = b; builder += ((a, b))
case None =>
}
}
builder.result()
}
/** Builds sequences of size n+1 from sequence of size n */
def extend(path: List[(Int, Int)]): Iterable[List[(Int, Int)]] =
for (p < pairs(path.head._1 + 1, path.head._2 + 1)) yield p :: path
/** Whether full or degenerated. Fullpairs save us 2 characters, degenerated save us only 1. */
def isFullPair(pair: (Int, Int)) =
pair._1 + pair._2 < str.length  1
/** Removes paretosuboptimal sequences */
def prune(sequences: List[List[(Int, Int)]]): List[List[(Int, Int)]] = {
val allowedHeads = paretoMin(sequences.map(_.head)).toSet
val containsFullPair = allowedHeads.exists(isFullPair)
sequences.filter(s => allowedHeads.contains(s.head) && (isFullPair(s.head)  !containsFullPair))
}
/** DynamicProgramming step */
@tailrec
def search(sequences: List[List[(Int, Int)]]): List[List[(Int, Int)]] = {
val nextStage = prune(sequences.flatMap(extend))
nextStage match {
case List() => sequences
case x => search(nextStage)
}
}
/** Converts a sequence of nested pairs to a palindrome */
def sequenceToString(sequence: List[(Int, Int)]): String = {
val lStr = str
val rStr = str.reverse
val half =
(for (List(start, end) < sequence.reverse.sliding(2)) yield
lStr.substring(start._1 + 1, end._1) + rStr.substring(start._2 + 1, end._2) + lStr(end._1)).mkString
if (isFullPair(sequence.head))
half + half.reverse
else
half + half.reverse.substring(1)
}
sequenceToString(search(List(List((1, 1)))).head)
}
