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;

namespace AOJDPL_1_A
{
    class Program
    {
        static void Main(string[] args)
        {
            var nm = ReadInt();
            int n = nm[0];
            int m = nm[1];

            var c = ReadInt().OrderBy(x => x).ToArray();

            int[,] dp = new int[m + 1, n + 1];
            for (int i = 0; i < m + 1; i++)
            {
                for (int j = 0; j < n + 1; j++)
                {
                    dp[i, j] = int.MaxValue / 2;
                }
            }
            dp[0, 0] = 0;

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

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

        static int[] ReadInt()
        {
            int[] ret = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return ret;
        }
        static long[] ReadLong()
        {
            long[] ret = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return ret;
        }
    }
}