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;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            const int INFTY = int.MaxValue;

            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int m = int.Parse(input[1]);

            int[] C = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);

            int[] dp = Enumerable.Repeat(INFTY, n + 1).ToArray();
            dp[0] = 0;

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

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