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;
class Program
    {
        static int n;
        static int m;
        static int[] c;
        static int[] t;
        static void Main(string[] args){
            String[] str_1 = Console.ReadLine().Split(' ');
            String[] str_2 = Console.ReadLine().Split(' ');
            n = int.Parse(str_1[0]);
            m = int.Parse(str_1[1]);
            c = new int[m];
            t = new int[n+1];
            for (int i=0; i < m; i++){
                c[i] = int.Parse(str_2[i]);
            }
            Console.WriteLine(coin());
        }
        static int coin()
        {
            for (int j = 0; j < n+1; j++)
            {
                t[j] = 10000000;
            }
            t[0] = 0;
            for (int i = 0; i < m; i++) {
                for (int j = c[i]; j < n + 1; j++) {
                    t[j] = Math.Min(t[j],t[j-c[i]]+1);
                }
            }
            return t[n];
        }
    }