Recursively Generate Pascals Triangle

PascalsTriangle.scala

import scala.annotation.tailrec

object PascalsTriangle {

  type Triangle = Map[(Int, Int), Int]
  type TriangleResult = (Triangle, Int, Int) => Triangle

  def generateTriangle(colMax: Int, rowMax: Int, generateResult: TriangleResult): Triangle = {
    @tailrec
    def recLoop(triangle: Triangle, colIt: Int, rowIt: Int): Triangle =
      if (rowIt > rowMax + 1)
        triangle
      else if (colIt < rowIt)
        recLoop(generateResult(triangle, colIt, rowIt), colIt + 1, rowIt)
      else
        recLoop(generateResult(triangle, colIt, rowIt), 0, rowIt + 1)

    recLoop(TreeMap[(Int, Int), Int](), 0, 0)
  }

  private def calcPascalsTriangleCell(tri: Triangle, col: Int, row: Int): Triangle =
    if (col == 0 || col == row)
      tri ++ TreeMap((col, row) -> 1)
    else
      tri ++ TreeMap((col, row) -> (tri(col - 1, row - 1) + tri(col, row - 1)))

  def pascalsTriangle(col: Int, row: Int): Int =
    generateTriangle(col, row, calcPascalsTriangleCell)((col, row))
  
}