TopCoder SRM 508 Division 2 - 250 point problem

CandyShop.java

import java.util.HashSet;
import java.util.Set;

public class CandyShop {

    public int countProbablePlaces(int[] X, int[] Y, int[] R) {
        Set<Position> pos = new HashSet<Position>();
        pos.add(new Position(X[0], Y[0]));
        pos = locationsFor(R[0], pos);
        for (int i = 1; i < X.length; i++) {
            Set<Position> newPos = new HashSet<Position>();
            newPos.add(new Position(X[i], Y[i]));
            newPos = locationsFor(R[i], newPos);
            Set<Position> intersection = new HashSet<Position>();
            for (Position p : pos) {
                if (newPos.contains(p)) {
                    intersection.add(p);
                }
            }
            pos = intersection;
        }
        return pos.size();
    }

    private Set<Position> locationsFor(int r, Set<Position> pos) {
        if (r == 0) return pos;
        Set<Position> newPos = new HashSet<Position>();
        for (Position p : pos) {
            for (int i = -1; i <= 1; i++) {
                for (int j = -1; j <= 1; j++) {
                    if (Math.abs(i) + Math.abs(j) == 1) {
                        newPos.add(new Position(p.x + i, p.y + j));
                    }
                }
            }
        }
        pos.addAll(newPos);
        return locationsFor(r - 1, pos);
    }

    private static class Position {
        private int x;
        private int y;

        private Position(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + x;
            result = prime * result + y;
            return result;
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj) return true;
            if (obj == null) return false;
            if (getClass() != obj.getClass()) return false;
            Position other = (Position) obj;
            if (x != other.x) return false;
            if (y != other.y) return false;
            return true;
        }

        @Override
        public String toString() {
            return "Position [x=" + x + ", y=" + y + "]";
        }

    }
}