Problem:
Coin Changing Problem

Find the minimum number of coins to make change for n cents using coins of denominations d1, d2,.., dm. The coins can be used any number of times.

Input

n m
d1 d2 ... dm

Two integers n and m are given in the first line. The available denominations are given in the second line.

Output

Print the minimum number of coins in a line.

Constraints

1 ≤ n ≤ 50000

1 ≤ m ≤ 20

1 ≤ denomination ≤ 10000

The denominations are all different and contain 1.

Sample Input 1

55 4
1 5 10 50

Sample Output 1

2

Sample Input 2

15 6
1 2 7 8 12 50

Sample Output 2

2

Sample Input 3

65 6
1 2 7 8 12 50

Sample Output 3

3

Solution in Scala (judge verdict: Accepted)

import scala.io.StdIn
import scala.collection.mutable.{ Map => MMap }

object Main {
  def main(args: Array[String]) = {
    val Seq(n, m, _*) = StdIn.readLine.split(" ").map(_.toInt).toSeq
    val coins = StdIn.readLine.split(" ").map(_.toInt)
    val dp = MMap[Int, Int]()
    val result = coin(n, dp, coins)
    println(result)
  }

  def coin(n: Int, dp: MMap[Int, Int], coins: Seq[Int]): Int = {
    if (coins contains n) {
      dp(n) = 1
      return 1
    }
    if (dp contains n) {
      return dp(n)
    }
    val res = coins.map(n - _).filter(_ > 0).map(coin(_, dp, coins)).min + 1
    dp(n) = res
    res
  }
}