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.*;
import java.util.function.*;
import java.math.*;
public class Main {
    public static void main(String[] args){
	Scanner s = new Scanner(System.in);
		int N = s.nextInt();
		int M = s.nextInt();
		int[] c = new int[M];
		for(int i = 0; i < M; i++) {
			c[i] = s.nextInt();
		}
		
		int[] dp = new int[N+1];
		for(int i = 0; i < N + 1; i++) {
			dp[i] = 1000000;
		}
		dp[0] = 0;
		
		for(int i = 0; i < M; i++) {
			for(int j = c[i]; j < N + 1; j++ ) {
				dp[j] = Math.min(dp[j], dp[j-c[i]] + 1);
			}
		}
		
		System.out.println(dp[N]);	
    }
}