Java/src/main/java/com/thealgorithms/dynamicprogramming/CoinChange.java

package com.thealgorithms.dynamicprogramming;

/**
 * @author Varun Upadhyay (https://github.com/varunu28)
 */
public class CoinChange {

    // Driver Program
    public static void main(String[] args) {
        int amount = 12;
        int[] coins = { 2, 4, 5 };

        System.out.println(
            "Number of combinations of getting change for " +
            amount +
            " is: " +
            change(coins, amount)
        );
        System.out.println(
            "Minimum number of coins required for amount :" +
            amount +
            " is: " +
            minimumCoins(coins, amount)
        );
    }

    /**
     * This method finds the number of combinations of getting change for a
     * given amount and change coins
     *
     * @param coins The list of coins
     * @param amount The amount for which we need to find the change Finds the
     * number of combinations of change
     */
    public static int change(int[] coins, int amount) {
        int[] combinations = new int[amount + 1];
        combinations[0] = 1;

        for (int coin : coins) {
            for (int i = coin; i < amount + 1; i++) {
                combinations[i] += combinations[i - coin];
            }
            // Uncomment the below line to see the state of combinations for each coin
            // printAmount(combinations);
        }

        return combinations[amount];
    }

    /**
     * This method finds the minimum number of coins needed for a given amount.
     *
     * @param coins The list of coins
     * @param amount The amount for which we need to find the minimum number of
     * coins. Finds the minimum number of coins that make a given value.
     */
    public static int minimumCoins(int[] coins, int amount) {
        // minimumCoins[i] will store the minimum coins needed for amount i
        int[] minimumCoins = new int[amount + 1];

        minimumCoins[0] = 0;

        for (int i = 1; i <= amount; i++) {
            minimumCoins[i] = Integer.MAX_VALUE;
        }
        for (int i = 1; i <= amount; i++) {
            for (int coin : coins) {
                if (coin <= i) {
                    int sub_res = minimumCoins[i - coin];
                    if (
                        sub_res != Integer.MAX_VALUE &&
                        sub_res + 1 < minimumCoins[i]
                    ) {
                        minimumCoins[i] = sub_res + 1;
                    }
                }
            }
        }
        // Uncomment the below line to see the state of combinations for each coin
        // printAmount(minimumCoins);
        return minimumCoins[amount];
    }

    // A basic print method which prints all the contents of the array
    public static void printAmount(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }
}