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 C# (judge verdict: Accepted)

using System;
using System.Linq;

namespace DPL1_A
{
    class Program
    {
        static void Main(string[] args)
        {
            var a = scan;
            var n = a[0];
            var dp = Enumerable.Repeat(int.MaxValue, n + 1).ToArray();
            dp[0] = 0;
            var c = scan;

            foreach (var t in c)
            {
                for (int i = t; i <= n; i++)
                {
                    dp[i] = Math.Min(dp[i], dp[i - t] + 1);
                }
            }

            Console.WriteLine(dp[n]);
            
        }

        static int[] scan
        {
            get { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
        }
    }
}