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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine().trim();
		String[] arr = line.split(" ");
		final int n = Integer.parseInt(arr[0]);
		final int m = Integer.parseInt(arr[1]);

		final int[] c = new int[m];
		line = br.readLine().trim();
		arr = line.split(" ");
		for (int i = 0; i < m; i++) {
			c[i] = Integer.parseInt(arr[i]);
		}
		br.close();

		final int[] dp = new int[n + 1];
		Arrays.fill(dp, 50000);
		dp[0] = 0;

		for (int i = 0; i < m; i++) {
			for (int j = c[i]; j <= n; j++) {
				dp[j] = Math.min(dp[j], dp[j - c[i]] + 1);
			}
		}

		System.out.println(dp[n]);
	}
}