[COURSERA-1][RECURSION] pascal triangle, count '(', count change money

coursera week 1

/**
   * Exercise 1
   */
  def pascal(c: Int, r: Int): Int = {
    if (c == 0 || c == r) 1 // si r == c alors la décomposition en dessous tombe forcement sur pascal(c>r) et c'est impossible
    else pascal(c - 1, r - 1) + pascal(c, r - 1)
  }

  /**
   * Exercise 2
   */
  def balance(chars: List[Char]): Boolean = count( chars, 0 ) == 0

  /**
   * Exercise 3
   */
  def countChange(money: Int, coins: List[Int]): Int = {
    val sortedCoins: List[Int] = coins.sortWith( (x,y) => x < y )
    rideTree(money, sortedCoins, List(0))
  }
  
  private def rideTree(money: Int, coins: List[Int], branch: List[Int]): Int = {
    coins.map {
      coin =>
        if(coin >= branch.last )
          if((branch.sum + coin) < money)
            rideTree(money, coins, branch :+ coin )
          else if((branch.sum + coin) == money) 1
          else 0

        else 0
    }.sum
  }

  // !!! ceci va entrainer un stack overflow - voir https://class.coursera.org/progfun-2012-001/lecture/33 pour explication
  /*private def fact(n: Int): Int = {
    if (n == 0) 1
    else n * fact(n - 1)
  }*/

  private def count(chars: List[Char], state: Int): Int = {
    if(chars.isEmpty) state
    else if(state < 0) state
    else
      if(chars.head == '(') count(chars.tail, state + 1)
      else if(chars.head == ')') count(chars.tail,  state - 1)
      else count(chars.tail,  state)
  }