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;


namespace ACTest
{
    class AOJDPLA
    {
        static void Main(string[] args)
        {
            // ??´??°?????\???
            // int a = int.Parse(Console.ReadLine());
            // ??????????????????????????´??°?????\???
            string[] input = Console.ReadLine().Split(' ');
            int pay = int.Parse(input[0]);
            int coin = int.Parse(input[1]);
            string[] input2 = Console.ReadLine().Split(' ');
            int[] numCoin = new int[input2.Length];
            for (int i = 0; i < input2.Length; i++)
            {
                numCoin[i] = int.Parse(input2[i]);
            }
            // ??????????????\???
            int[] T = new int[pay + 1];
            
            for (int i = 0; i < pay + 1; i++)
            {
                T[i] = pay;
            }
            T[0] = 0;
            ///DP
            for (int i = 0; i < coin; i++)
            {
                for (int j = numCoin[i]; j < pay + 1; j++)
                {
                    T[j] = Math.Min(T[j], T[j - numCoin[i]] + 1);
                }
            }

            Console.WriteLine(T[pay]);
            //while (true) ;
            //??????
            //Console.WriteLine((b + c) + " " + s);
        }
    }
}