I have to recursively solve the following problem, using a brute force approach:Suppose two people, A and B, have an even number of ordered boxes, each with a given value. For example, boxes = {5, 3, 7, 10}. They need to split the boxes between them, in this way: person A chooses either the first or the last box in the set, then person B does the same, and so on until there are no boxes left. Person A wants to know, what's the maximum value he can get, in total, bearing in mind that at each turn person B can make two choices as well. In other words, the problem is to come up with an algorithm that simulates all the choices of both people, considering they're all aiming to have the maximum value in the long term.So, for now I have this:public static int maxValue(ArrayList <Integer> boxes, int choice, int person){    int value;    //Stop condition - if there are no more boxes, return 0    if (boxes.isEmpty())        return 0;    if (choice == 0) //Person chose the first box in the sequence        value = boxes.remove(0);    else //Person chose the last box in the sequence        value = boxes.remove(boxes.size() - 1);    //Person A makes a choice, checking which one works best in the long run    if (person == 1)        return (value + max(maxValue(boxes, 0, 2), maxValue(boxes, 1, 2)));    //Person B makes a choice, checking which one works best in the long run    else        return (value + max(maxValue(boxes, 0, 1), maxValue(boxes, 1, 1)));}For an input of boxes = {5, 3, 7, 10}, the code is supposed to produce 15, yet the one I wrote above gives me 25. After placing some debugging prints, I saw it goes:Person A chooses '10'Person B chooses '7'Person A chooses '3'Person B chooses '5'And then just adds all the values. I'm figuring it's because of the way the function is called by person A with reference to person B (in max(maxValue(boxes, 0, 2), maxValue(boxes, 1, 2))), and vice-versa, and also because of that stop condition (if I change it slightly the value returned is different).
Recursive Brute-Force
java;recursion