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 java.util.Scanner

object Main extends App { 
  val sc = new Scanner(System.in)
  val N, M = sc.nextInt()
  val coins = (for (i <- 1 to M) yield sc.nextInt).toList
  val inf = Int.MaxValue >> 1

  class DP(n:Int, coins:List[Int]) {
    val memo:Array[Int] = Array.fill(n+1)(inf)
    memo.update(0, 0)

    def solver():Int = {
      for (c <- coins; i <- 1 to n) {
        if (i < c) memo(i)
        else memo.update(i, (memo(i) min (memo(i-c)+1)))
      }
      memo(n)
    }
  }
  
  val dp = new DP(N, coins)

  println(dp.solver())

}