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 final int INF = Integer.MAX_VALUE / 4;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int M = scanner.nextInt();
        int[] c = new int[M];
        for (int i = 0; i < M; i++) {
            c[i] = scanner.nextInt();
        }
        int[] dp = new int[N + 1];
        Arrays.fill(dp, INF);
        dp[0] = 0;
        for (int i = 1; i <= N; i++) {
            for (int j = 0; j < M; j++) {
                if (c[j] <= i) {
                    dp[i] = Math.min(dp[i], dp[i - c[j]] + 1);
                }
            }
        }
        System.out.println(dp[N]);
    }
}