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 Aizu {
    public class OnlineJudge {
        static void Main() {
            var n = Console.ReadLine().Split().Select(int.Parse).First();
            var dp = Enumerable.Repeat(int.MaxValue, n + 1).ToArray();
            var coins = Console.ReadLine().Split().Select(int.Parse).OrderBy(q => q).ToArray();

            dp[0] = 0;

            for (var i = 0; i < dp.Length; ++i) {
                for (var j = 0; j < coins.Length; ++j) {
                    if (i < coins[j]) {
                        break;
                    }
                    dp[i] = Math.Min(dp[i - coins[j]] + 1, dp[i]);
                }
            }

            Console.WriteLine(dp[n]);
        }
    }
}