Dynamic Programming Coin Change Problems

Question

I am having issues with understanding dynamic programming solutions to various problems, specifically the coin change problem:

\"Given a value N, if we want to make

Answer 1

This is a very good explanation of the coin change problem using Dynamic Programming.

The code is as follows:

public static int change(int amount, int[] coins){
    int[] combinations = new int[amount + 1];

    combinations[0] = 1;

    for(int coin : coins){
        for(int i = 1; i < combinations.length; i++){
            if(i >= coin){
                combinations[i] += combinations[i - coin];
                //printAmount(combinations);
            }
        }
        //System.out.println();
    }

    return combinations[amount];
}