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.io.*;
import java.util.*;

class Main{
	public static void main(String[] args){
		solve();
	}
	public static void solve(){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] c = new int[m];
		int[] dp = new int[n+1];
		Arrays.fill(dp, 50000);
		for(int i=0;i<m;i++){
			c[i] = sc.nextInt();
		}

		for(int i=0;i<m;i++){
			if(n<c[i]){
				continue;
			}
			dp[c[i]] = 1;
			for(int j=0;j<n;j++){
				if(j+c[i]>n){
					break;
				}
				if(dp[j]!=0){
					dp[c[i]+j] = Math.min(dp[c[i]+j], dp[j]+1);
				}
			}
		}

		System.out.println(dp[n]);

	}
}