0518-coin-change-ii.java

// Dynammic Programming - Tabulation
// Time Complexity (n * amount) | Space Complexity (amount) where n is the length of coins
class Solution {

    public int change(int amount, int[] coins) {
        int n = coins.length;
        int[] dp = new int[amount + 1];
        Arrays.fill(dp, 0);

        // if amount is 0, there is only 1 way of making change (no money)
        dp[0] = 1;

        for (int coin : coins) {
            for (int i = 1; i <= amount; i++) {
                if (coin <= i) {
                    dp[i] = dp[i] + dp[i - coin];
                }
            }
        }

        return dp[amount];
    }
}