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.*;

public class Main {
    static int[][] dp;
    static int[] coins;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        coins = new int[m];
        for (int i = 0; i < m; i++) {
            coins[i] = sc.nextInt();
        }
        Arrays.sort(coins);
        dp = new int[m][n + 1];
        System.out.println(dfw(m - 1, n));
    }
    
    static int dfw(int idx, int amount) {
        if (amount == 0) {
            return 0;
        }
        if (idx < 0) {
            return Integer.MAX_VALUE / 10;
        }
        if (dp[idx][amount] != 0) {
            return dp[idx][amount];
        }
        if (amount % coins[idx] == 0) {
            return dp[idx][amount] = amount / coins[idx];
        }
        int min = Integer.MAX_VALUE;
        for (int i = 0; i * coins[idx] <= amount; i++) {
            min = Math.min(min, dfw(idx - 1, amount - coins[idx] * i) + i);
        }
        return dp[idx][amount] = min;
    }
}