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: Wrong Answer)

import java.util.Scanner;
public class Main{
    public static int min_num(int coins[], int n, int start, int sum, int count){
        if(start == coins.length)
            return n;
        else if(sum > n)
            return n;
        else if(sum == n)
            return 0;
        else
            return Math.min(count + min_num(coins,n,start+1,sum-coins[start],count), count + 1 + min_num(coins,n,start+1,sum,count));
    }
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int coins[] = new int[m];
        for(int i = 0 ; i < m ; i++)
            coins[i] = sc.nextInt();
        System.out.println(min_num(coins,n,0,0,0));
    }
}