/**

* Finds and return a solution to the problem, consisting of a list of

* states.

*

* The list should start with the initial state of the underlying problem.

* Then, it should have one or more additional states. Each state should be

* a successor of its predecessor. The last state should be a goal state of

* the underlying problem.

*

* If there is no solution, then this method should return an empty list.

*

* @return a solution to the problem (or an empty list)

*/

public List findSolution() {

Queue frontier = new LinkedList<>();

frontier.add((T) searchProblem);

Map successor = new HashMap<>();

successor.put((T) searchProblem, null);

List path = new ArrayList<>();

while (!frontier.isEmpty()) {

T current = frontier.remove();

for (T next : BaseGraph.getNeighbors(current)) {

if (!successor.containsKey(next)) {

frontier.add(next);

successor.put(next, current);

}

}

if (current.equals(searchProblem)) {

path.add(current);

T previous = successor.get(current);

while (previous != null) {

path.add(0, previous);

previous = successor.get(previous);

}

break;

}

}

return path;

}

/**

* Checks that a solution is valid.

*

* A valid solution consists of a list of states. The list should start with

* the initial state of the underlying problem. Then, it should have one or

* more additional states. Each state should be a successor of its

* predecessor. The last state should be a goal state of the underlying

* problem.

*

* @param solution

* @return true iff this solution is a valid solution

* @throws NullPointerException

* if solution is null

*/

public final boolean isValidSolution(List solution) throws NullPointerException {

int inversions = 0;

for (T i : solution) {

if (solution.get(i) == 0) {

continue;

}

}

for (int i = 0; i < solution.size(); i++) {

if (solution.get(i) == 0) {

continue;

}

for (int j = i; j < solution.size(); j++) {

if (solution.get(j) == 0) {

continue;

}

if (solution.get(j) < solution.get(i)) {

inversions++;

}

}

}

return (inversions & 1) == 0;

}

The bolded part is my work, but I want to know the correct way to do it. Please help, this is for a 8-puzzle game and the method checks if the solution is valid or not, and the other finds the solution.