This is Coin Change Implementation in Java using Recursion and Dynamic Programming

CoinProblem.java

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

public class CoinProblem {
    public static void main(String[] args) {
        System.out.println(countMakeChangeCombinations(new int[]{1, 2, 5}, 7));
        System.out.println(countMinimumChangeCoins(new int[]{1, 2, 5}, 7));
    }

    public static int countMakeChangeCombinations(int[] coins, int money) {
        return countMakeChangeCombinations(coins, money, 0, new HashMap<>());
    }

    public static int countMakeChangeCombinations(int[] coins, int money, int index, Map<String, Integer> memo) {
        if(money == 0)
            return 1;
        if(index >= coins.length)
            return 0;

        String key = money + "-" + index;
        if(memo.containsKey(key))
            return memo.get(key);

        int amountWithCoins = 0;
        int ways = 0;
        while(amountWithCoins <= money) {
            int remaining = money - amountWithCoins;
            ways += countMakeChangeCombinations(coins, remaining, index+1, memo);
            amountWithCoins += coins[index];
        }
        memo.put(key, ways);
        return ways;
    }

    public static int countMinimumChangeCoins(int coins[], int money) {
        Arrays.sort(coins);
        int count = 0;
        int remaining = money;
        int index = coins.length - 1;

        while(index >= 0) {
            if(remaining >= coins[index]) {
                remaining -= coins[index];
                count++;
            }
            else
                index--;
        }

        if(remaining == 0)
            return count;
        else
            return 0;
    }
}