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)
        {
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] coin = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Array.Sort(coin);
            int[] ret = new int[x[0] + 1]; ret[0] = 0;
            for (int i = 1; i <= x[0]; i++) ret[i] = int.MaxValue;
            for (int i = 1; i <= x[0]; i++)
            {
                for (int j = 0; j < x[1] && coin[j] <= i; j++)
                {
                    ret[i] = Math.Min(ret[i],ret[i - coin[j]] + 1);
                }
            }
            Console.WriteLine(ret[x[0]]);
        }
    }
}