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)

/**
 * Combinatorial - Coin Changing Problem
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.String;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line;

		while ((line = br.readLine()) != null && !line.isEmpty()) {
			int n = parseInt(line.substring(0, line.indexOf(' ')));
			int m = parseInt(line.substring(line.indexOf(' ') + 1));

			int[] ns = new int[n + 1];
			int[] cs = new int[m];

			for (int i = 1; i < ns.length; i++) ns[i] = Integer.MAX_VALUE;

			StringTokenizer st = new StringTokenizer(br.readLine());
			for (int i = 0; i < m; i++) cs[i] = parseInt(st.nextToken());

			//solve
			for (int i = 0; i < cs.length; i++) {
				for (int j = cs[i]; j < ns.length; j++) {
					ns[j] = Math.min(ns[j], ns[j - cs[i]] + 1);
				}
			}
			System.out.println(ns[n]);
		}//end while
	}//end main
}