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.Collections.Generic;
using System.IO;
using System.Linq;

namespace AizuOnline
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            var n = Console.ReadLine().Split(' ');
            var c = Console.ReadLine().Split(' ');

            var J = int.Parse(n[0]);
            var I = int.Parse(n[1]);
            var dp = new int[I + 1, J + 1];

            for (int i = 0; i <= I; i++)
            {
                for (int j = 0; j <= J; j++)
                {
                    if (i == 0 || j == 0)
                    {
                        dp[i, j] = 0;
                    }
                    else
                    {
                        dp[i, j] = int.MaxValue;
                    }
                    if (i == 1)
                    {
                        dp[i, j] = j;
                    }
                }
            }

            for (int i = 1; i < I; i++)
            {
                for (int j = 0; j < J + 1; j++)
                {
                    if (j - int.Parse(c[i]) >= 0)
                    {
                        dp[i + 1, j]
                            = Math.Min(
                                dp[i, j],
                                dp[i + 1, j - int.Parse(c[i])] + 1);
                    }
                    else
                    {
                        dp[i + 1, j] = dp[i, j];
                    }
                }
            }
            var min = int.MaxValue;
            for (int i = 1; i < I+1; i++)
            {
                min = Math.Min(min, dp[i, J]);
            }
            Console.WriteLine(min);
            Console.ReadLine();
        }
    }
}