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.*;

public 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+1];
        for (int i = 1; i <= m; i++) {
            c[i] = sc.nextInt();
        }
        int[][] dp = new int[m+1][n+1];
        for (int i = 0; i < m+1; i++) {
            Arrays.fill(dp[i], n);
        }
        dp[0][0] = 0;
        for (int i = 1; i <= m; i++) {
            for (int j = 0; j <= n; j++) {
                dp[i][j] = dp[i-1][j];
                if(j < c[i])continue;
                if(dp[i][j] > dp[i-1][j-c[i]] + 1) dp[i][j] = dp[i-1][j-c[i]] + 1;
                if(dp[i][j] > dp[i][j-c[i]] + 1) dp[i][j] = dp[i][j-c[i]] + 1;
            }
        }
        System.out.println(dp[m][n]);
        sc.close();

    }

}