Coin Chain Problem — Total number of ways to get the denomination of coins.

By Recursion

private static int findMinWays(int[] coins, int amount, int currentcoin) {

  if (amount == 0) {
    return 1;
  }

  if (amount < 0) return 0;

  int ways = 0;
  for (int i = currentcoin; i < coins.length; i++) {
    ways += findMinWays(coins, amount - coins[i], i);
  }
  return ways;
}

Another Way recursion

static int minWaysAnotherWay(int coins[], int coinsLeng, int total, String way) {

  if (total == 0) return 1;

  if (total < 0) return 0;

  if (coinsLeng <= 0 && total >= 1) return 0;

  return minWaysAnotherWay(coins, coinsLeng - 1, total, "way1")
      + minWaysAnotherWay(coins, coinsLeng, total - coins[coinsLeng - 1], "way2");
}

Dynamic Programing

private static int minWayDP(int[] coins, int amount) {
  int m[] = new int[amount + 1];
  m[0] = 1;
  for (int i = 0; i < coins.length; i++) {
    for (int j = coins[i]; j <= amount; j++) {
      m[j] += m[j - coins[i]];
    }
  }
  return m[amount];
}