JavaAlgorithms/DynamicProgramming/CoinChange.java

package 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 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();
  }
}