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 JAVA (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    private static final int MOD = 1_000_000_007;

    public static void main(String[] args) {
        try (CustomReader in = new CustomReader()) {
            new Main().execute(in);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    public void execute(CustomReader in) throws IOException {
        int[] nm = in.readLineAsIntArray();
        final int n = nm[0];
        final int m = nm[1];

        int[] coins = in.readLineAsIntArray();

        int[] dp = new int[n + 1];
        Arrays.fill(dp, Integer.MAX_VALUE);

        for (int c : coins) {
            if(c<=n) {
                dp[c] = 1;
            }
        }

        for (int i = 1; i <= n; i++) {
            for (int c : coins) {
                if(i + c <=n) {
                    dp[i + c] = Math.min(dp[i + c], dp[i] + 1);
                }
            }
        }
        System.out.println(dp[n]);
    }


    static class CustomReader extends BufferedReader {

        private static final int DEFAULT_BUF_SIZE = 2048;
        // private static final int DEFAULT_BUF_SIZE = 4096;
        // private static final int DEFAULT_BUF_SIZE = 8192;
        //private static final int DEFAULT_BUF_SIZE = 16384;
        // private static final int DEFAULT_BUF_SIZE = 1048576;

        public CustomReader() throws IOException {
            super(new InputStreamReader(System.in), DEFAULT_BUF_SIZE);
        }

        public int[] readLineAsIntArray() throws IOException {
            String[] strArray = this.readLine().split(" ");
            int[] intArray = new int[strArray.length];
            for (int i = 0, n = strArray.length; i < n; i++) {
                intArray[i] = Integer.parseInt(strArray[i]);
            }
            return intArray;
        }

        public int[][] readAsIntMatrix(int rows, int columns) throws IOException {
            int[][] matrix = new int[rows][columns];
            for (int i = 0; i < rows; i++) {
                String[] r = this.readLine().split(" ");
                for (int j = 0; j < columns; j++) {
                    matrix[i][j] = Integer.parseInt(r[j]);
                }
            }
            return matrix;
        }
    }
}