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;
using System.Text;
using System.Text.RegularExpressions;

namespace CsharpSpiral {
    partial class Program {
        static void Main(string[] args) {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            new Program().Solve(new ConsoleInput(Console.In, ' '));
            Console.Out.Flush();
        }
        public void Solve(ConsoleInput cin) {
            var n = cin.ReadInt;
            var m = cin.ReadInt;
            var C = cin.ReadIntArray(m);
            var dp = Enumerable.Repeat(-1, n + 1).ToArray();
            dp[0] = 0;
            for(int i = 1; i <= n; i++) {
                dp[i] = C.Min(c => i < c ? int.MaxValue : dp[i - c] + 1);
            }
            Console.WriteLine(dp[n]);
        }
        class ResidueField {
            public readonly long modulo;
            public ResidueField(int mModulo) {
                modulo = mModulo;
            }
            private long[] factorialTable = { 1 };
            private int factorialTableLastIndex { get { return factorialTable.Length - 1; } }
            public long mod(long x) => x < 0 ? x % modulo + modulo : x % modulo;
            public long Add(long a, long b) => mod(a + b);
            public long Sub(long a, long b) => mod(a - b);
            public long Mul(long a, long b) => mod(a * b);
            public long Pow(long a, long n) {
                if(n == 0) return 1;
                var R = 1L;
                n = n < 0 ? n % (modulo - 1) + (modulo - 1) : n % (modulo - 1);
                for(; n > 0; a = Mul(a, a), n >>= 1) {
                    if((n & 1) != 0) R = Mul(R, a);
                }
                return R;
            }
            private static long extgcd(long a, long b, ref long x, ref long y) {
                if(b == 0) {
                    x = 1; y = 0; return a;
                }
                var q = a / b;
                var g = extgcd(b, a - q * b, ref x, ref y);
                var z = x - q * y;
                x = y; y = z;
                return g;
            }
            public long Inv(long a) {
                if(a == 0) throw new DivideByZeroException();
                long x = 0, y = 0;
                extgcd(a, modulo, ref x, ref y);
                return mod(x);
            }
            public long Div(long a, long b) => Mul(a, Inv(b));
            public void ExpandFactorialTable(int N) {
                var k = factorialTableLastIndex;
                Array.Resize(ref factorialTable, N + 1);
                for(int i = k + 1; i <= N; i++) {
                    if(i == 0) { factorialTable[i] = 1; continue; }
                    factorialTable[i] = Mul(factorialTable[i - 1], i);
                }
            }
            public long Factorial(int n) {
                if(n > factorialTableLastIndex)
                    ExpandFactorialTable(n);
                return factorialTable[n];
            }
            public long Permutation(int n, int k) {
                if(k < 0 || k > n) return 0;
                return Div(Factorial(n), Factorial(n - k));
            }
            public long Combination(int n, int k) {
                if(k < 0 || k > n) return 0;
                return Div(Factorial(n), Mul(Factorial(k), Factorial(n - k)));
            }
            
        }
    }

    static class ExtendClass {
        public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
    }

    class ConsoleInput {
        private readonly TextReader _stream;
        private readonly char _separator = ' ';
        private readonly Queue<string> inputStream;
        public ConsoleInput(TextReader stream, char separator = ' ') {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read {
            get {
                if(inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for(int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) {
            var ret = new string[N];
            for(long i = 0; i < N; ++i)
                ret[i] = Read;
            return ret;
        }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i < N; ++i) ret[i] = ReadDouble; return ret; }
    }

}