PPM Minimum Distance Point

package com.logikujo
package pebeeme

import scalaz._
import Scalaz._
import java.io.File
import scala.collection.Map

/**
 *
 * pebeeme / LogiDev - [Fun Functional] / Logikujo.com
 *
 * com.logikujo 5/01/14 :: 11:50 :: eof
 *
 */

case class PPM(pixels: List[Pixel]) extends PBM

object PPM {
  type D = List[List[((Int,Int), Double)]]

  def pointDistances(l: List[Pixel], res: D, n:Int): D = (l.length <= 1)? res | {
    val listOfHeads = List.tabulate(l.length -1)(_ => l.head)
    val lSums = listOfHeads.zip(l.tail).map {
      case (p1,p2) => p1.distance(p2)
    }.zipWithIndex.map {
      case (s,i) => (n, i+1+n) -> s
    }
    pointDistances(l.tail, lSums :: res, n+1)
  }
  def getIndex(m:Map[(Int,Int),Double], idx:(Int,Int)) = idx match {
    case (i,j) => m.get(i->j).orElse(m.get(j->i))
  }

  /* DANGER: Double doesnt conform a Monoid. Addition is not associative! */
  implicit val doubleInstance: Monoid[Double] = new Monoid[Double] {
    def append(d1: Double, d2: => Double): Double = d1 + d2
    def zero: Double = 0
  }

  def minimumDistancePoint(ppm: PPM) = {
    val len = ppm.pixels.length
    val distances = pointDistances(ppm.pixels, List(), 1).flatten.toMap
    (for {
      i <- 1 to len
    } yield for {
        j <- 1 to len
      } yield getIndex(distances, i -> j)).map { l =>
      l.reduce(_ |+| _)
    }.toList.min
  }