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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CoinProblem {
	class Program {
		private const int MMAX = 20;
		private const int NMAX = 50000;
		private const int INFTY = (1 << 29);

		static void Main(string[] args) {
			int n, m;
			int[] C = new int[21];
			int[] T = new int[NMAX + 1];

			var line = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
			n = line[0]; m = line[1];

			foreach (var item in Console.ReadLine().Split(' ').Select((v, ix) => new { v, ix }))
				C[item.ix + 1] = int.Parse(item.v);

			for (int i = 0; i <= NMAX; i++) T[i] = INFTY;
			T[0] = 0;
			for( int i = 1; i <= m; i++) {
				for( int j = 0; j + C[i] <= n; j++) {
					T[j + C[i]] = Math.Min(T[j + C[i]], T[j] + 1);
				}
			}

			Console.WriteLine(T[n]);
		}
	}
}