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.Scanner;

class Main {
	public static void main(String args[]) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(); //yen
		int m = in.nextInt();
		int[] c = new int[m];
		for (int i = 0; i < m; i++) {
			c[i] = in.nextInt();
		}

		int[] t = new int[n + 1];
		for (int i = 0; i <= n; i++) {
			t[i] = 50000;
		}
		t[0] = 0;

		for (int i = 0; i < m; i++) {

			for (int j = c[i]; j <= n; j++) {

				t[j] = Math.min(t[j], t[j - c[i]] + 1);

			}
		}

		System.out.println(t[n]);
		in.close();
	}
}