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;

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