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;

class Program
{
    // 最小値保持
    private static int [] a = new int[50001];

    static void Main()
    {
        string[] s = Console.ReadLine().Split(' ');
        int n = int.Parse(s[0]);
        int m = int.Parse(s[1]);

        s = Console.ReadLine().Split(' ');
        int[] g = new int[m];
        
        for (int i = 0; i < m; i++) g[i] = int.Parse(s[i]);

        Console.WriteLine(Coin(n, g, m));
    }

    static int Coin(int n, int[] g, int m)
    {
        int g_min = 10000; //額面最大値

        if (a[n] != 0) return a[n];
        if (n == 0)    return 0;

        for (int i = 0; i < m; i++)
        {
            if (n - g[i] >= 0)
            {
                int r = Coin(n - g[i], g, m) + 1;
                if (g_min > r) g_min = r;
            }
        }

        a[n] = g_min;
        return a[n];
    }
}