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;

public class hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var m = int.Parse(line[1]);
        string[] line2 = Console.ReadLine().Trim().Split(' ');
        var a = Array.ConvertAll(line2, int.Parse);
        Array.Sort(a);
        var dp = new int[n + a[a.Length-1]  +1];
        for (int i = 0; i < dp.Length; i++) dp[i] = 99999999;
        for (int i = 0; i < m; i++) dp[a[i]] = 1;
        for (int i = 1; i < n; i++)
        {
            if (dp[i] != 99999999)
                for (int j = 0; j < m; j++)
                    dp[i + a[j]] = Math.Min(dp[i + a[j]], dp[i] + 1);
        }
        Console.WriteLine(dp[n]);
    }
}