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

class Program
{
	static void Main(string[] args)
	{
		string[] first = Console.ReadLine().Split();

		int n = int.Parse(first[0]);
		int m = int.Parse(first[1]);

		int[] cs = Console.ReadLine().Split().Select(str => int.Parse(str)).ToArray();

		int[] minCounts = new int[50001];

		for (int i = 1; i <= n; i++)
		{
			// コイン持っているかどうか
			for (int ci = 0; ci < m; ci++)
			{
				if (cs[ci] == i)
				{
					minCounts[i] = 1;
					break;
				}
			}

			if (minCounts[i] > 0)
			{
				continue;
			}

			int min = n;
			for (int j = 1; j < i; j++)
			{
				int current = minCounts[i - j] + minCounts[j];
				if (current < min)
				{
					min = current;
				}
				if (i - j < j)
				{
					break;
				}
			}
			minCounts[i] = min;
		}

		System.Console.WriteLine(minCounts[n]);
	}
}