Writing an algorithm to decide whether a target number can be reached with a set of other numbers and specific operators?

Question

I\'m trying to learn more about algorithm design, and I\'ve set myself the challenge of creating a simple game that presents users with an array of numbers, a target number,

Answer 1

Here is a Java solution from programcreek.

public static boolean isReachable(ArrayList list, int target) {
    if (list == null || list.size() == 0)
        return false;

    int i = 0;
    int j = list.size() - 1;

    ArrayList results = getResults(list, i, j, target);

    for (int num : results) {
        if (num == target) {
            return true;
        }
    }

    return false;
}

public static ArrayList getResults(ArrayList list,
        int left, int right, int target) {
    ArrayList result = new ArrayList();

    if (left > right) {
        return result;
    } else if (left == right) {
        result.add(list.get(left));
        return result;
    }

    for (int i = left; i < right; i++) {

        ArrayList result1 = getResults(list, left, i, target);
        ArrayList result2 = getResults(list, i + 1, right, target);

        for (int x : result1) {
            for (int y : result2) {
                result.add(x + y);
                result.add(x - y);
                result.add(x * y);
                if (y != 0)
                    result.add(x / y);
            }
        }
    }

    return result;
}