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.Linq;
namespace DPL_1_A
{
    class Program
    {
        static void Main(string[] args)
        {
            string [] first = Console.ReadLine().Trim().Split(' ');
            var n = int.Parse(first[0]);
            var m = int.Parse(first[1]);
            int [] coinCnt = new int [n+1];

            string [] types = Console.ReadLine().Trim().Split(' ');
            for (int j = 0; j < types.Length; j++)
            {
                var money = int.Parse(types[j]);
                for (int i = 0; i < n+1; i++)
                {
                    if(i - money >= 0){
                        if(coinCnt[i] == 0){
                            coinCnt[i] = coinCnt[i - money] + 1;
                        }else{
                            coinCnt[i] = coinCnt[i-money] + 1 < coinCnt[i] ? 
                                coinCnt[i-money] + 1 : coinCnt[i];
                        }
                    }
                }
            }
            Console.WriteLine(coinCnt[n]);
        }
    }
}