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;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scanner=new Scanner(System.in);
		int n=scanner.nextInt();
		int m=scanner.nextInt();
		int[] v=new int[m+1];
		for(int i=1;i<=m;i++) v[i]=scanner.nextInt();
		int[] dp=new int[n+1];
		Arrays.fill(dp, Integer.MAX_VALUE/2);
		dp[0]=0;
		for(int i=0;i<=n;i++){
			if(dp[i]!=Integer.MAX_VALUE/2){
				for(int j=1;j<=m;j++){
					if(i+v[j]<=n)
						dp[i+v[j]]=Math.min(dp[i+v[j]], dp[i]+1);
				}
			}
		}
		System.out.println(dp[n]);
	}

}