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.Web;

namespace Competitive
{

    internal class Solution
    {
        public int N, M;
        public int[] C;

        public void Run()
        {
            var line1 = Input.ReadIntArray();
            N = line1[0];
            M = line1[1];
            C = Input.ReadIntArray();

            int[,] dp = new int[N + 1, M + 1];
            for(int i = 0; i <= N; i++)
            for (int j = 0; j <= M; j++)
                dp[i, j] = int.MaxValue;

            for (int i = 0; i <= N; i++)
            {
                for (int j = 0; j <= M; j++)
                {
                    if (j == 0)
                    {
                        if (i == 0)
                            dp[i, j] = 0;
                        else
                            dp[i, j] = int.MaxValue;
                    }
                    else
                    {
                        int c = C[j - 1];
                        if (i < c || dp[i - c, j] == int.MaxValue)
                            dp[i, j] = dp[i, j - 1];
                        else
                            dp[i, j] = Math.Min(dp[i,j - 1], dp[i - c, j] + 1);
                    }
                   
                }
            }

            Console.WriteLine(dp[N, M]);
        }

       
    }

    
    internal static class Input
    {
        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}