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.*;

class Main{
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] c = new int[m];
		for(int i = 0; i < m; i++){
			c[i] = sc.nextInt();
		}
		int[] DP = new int[n+1];
		Arrays.fill(DP,999999);
		DP[0] = 0;
		for(int i = 1; i <= n; i++){
			for(int j = 0; j < m; j++){
				if(i-c[j]>=0){
					DP[i] = Math.min(DP[i],DP[i-c[j]]+1);
				}
			}
		}
		System.out.println(DP[n]);
	}
}