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 Aizu
{
    class Program
    {
        static void Main(string[] args)
        {
            var firstLine = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToArray();
            var n = firstLine[0];
            var m = firstLine[1];
            var coins = Console.ReadLine().Split(' ').Select(value => int.Parse(value)).ToArray();

            var numbers = new int[m + 1, n + 1];

            for (var i = 0; i <= m; i++)
            {
                for(var j = 0; j <= n; j++)
                {
                    if (j == 0)
                    {
                        numbers[i, j] = 0;
                    }
                    else
                    {
                        numbers[i, j] = int.MaxValue - 2;
                    }
                }
            }

            for (var i = 1; i <= m; i++)
            {
                for (var j = 1; j <= n; j++)
                {
                    if (j  >= coins[i - 1])
                    {
                        numbers[i, j] = Math.Min(numbers[i - 1, j], numbers[i, j - coins[i - 1]] + 1);
                    }
                    else
                    {
                        numbers[i, j] = numbers[i - 1, j];
                    }
                }
            }

            Console.WriteLine(numbers[m, n]);
        }
    }
}