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.util.Arrays;
import java.util.Scanner;

class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int m = sc.nextInt(), n = sc.nextInt(), c[] = new int[n], a[] = new int[m + 1];
        for (int i = 0; i < n; i++) {
            c[i] = sc.nextInt();
        }
        Arrays.fill(a, Integer.MAX_VALUE);
        a[0] = 0;
                for (int i = 0; i < n; i++)
                    for (int j = c[i]; j <= m; j++) {
                        a[j] = Math.min(a[j], a[j - c[i]] + 1);
                    }
        System.out.println(a[m]);
    }
}