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 Ex160424_1{
    public class Program{
        public static void Main(string[] args){
            var n = int.Parse(Console.ReadLine().Split(' ')[0]);
            var cm = Console.ReadLine().Split(' ').Select(int.Parse);
            var dp = new int[n + 1];

            foreach(var c in cm){
                if(c <= n) dp[c] = 1;
            }
            while(dp[n] == 0){
                foreach(var c in cm){
                    for(var i = 1; i <= n; i++){
                        if(i + c <= n && dp[i] != 0){
                            dp[i + c] = dp[i + c] == 0 ? dp[i] + 1 : Math.Min(dp[i + c], dp[i] + 1);
                        }
                    }
                }
            }
            Console.WriteLine(dp[n]);
        }
    }
}