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_Coin_Changing_Problem
{
	class Program
	{
		static void Main ( string[] args )
		{
			//input
			int[] input = Array.ConvertAll (Console.ReadLine ().Split (' '), int.Parse);
			int price = input[0];

			int[] coinArray = Array.ConvertAll (Console.ReadLine ().Split (' '), int.Parse);

			//process
			int[] priceArray = Enumerable.Repeat (int.MaxValue, price + 1).ToArray ();
			priceArray[0] = 0;

			foreach (var coin in coinArray)
			{
				for (int index = 0; index + coin <= price; index++)
				{
					priceArray[index + coin] = Math.Min (priceArray[index + coin], priceArray[index] + 1);
				}
			}

			Console.WriteLine (priceArray[price]);
		}
	}
}