Question

I know that A* algorithm implementation problems are relatively common on stackoverflow (I’ve been through a lot of other postings). I have been trying for the past couple of days to implement a simple C++ A* system. I am only allowing movement in four directions (no diagonal checking), so this should be an especially simple task (this is also why I only have a heuristic as my cost). Also, I have stepped through the code and, for all starting positions, an object is able to successfully find a valid path to the target. The issue, however, is that I am unable to step back through the parent pointers and store the path / movement sequence. I am using references, so I am not quite sure why there is an issue with the pointer assignments. I ran through what I “think” the code is doing on paper for a few, short example paths and I do not understand what I am doing incorrectly. Looping through the parent pointers, which should eventually get to NULL infinitely prints the posY of the target.

Here is my header file:

    //to access a priority queue's underlying container, you must extend functionality
    template <class T, class S, class C>
        S& Container(std::priority_queue<T, S, C>& q) {
            struct HackedQueue : private std::priority_queue<T, S, C> {
                static S& Container(std::priority_queue<T, S, C>& q) {
                    return q.*&HackedQueue::c;
                }
            };
        return HackedQueue::Container(q);
    }
    //different enough from a "Grid" to be a new object
    typedef struct Node{
        int cost, posX, posY;
        Node* parent;
        Node(int cost = 0, int posX = 0, int posY = 0, Node* parent = 0) : cost(cost), posX(posX), posY(posY), parent(parent) {}
        //overloading operators will make the cpp file easier to read
        bool operator==(const Node& rhs){
            return (posX == rhs.posX && posY == rhs.posY);
        }
        bool operator<(const Node& rhs){
            return (posX == rhs.posX && posY == rhs.posY && cost < rhs.cost);
        }
    } Node;
    typedef struct NodeCompare{
        //compare n1 against a node n2
        bool operator()(const Node& n1, const Node& n2){
            //if n2 has a lower cost, it has a higher priority
            return n2.cost < n1.cost;
        }
    } NodeCompare;
    //a list is essentially a linked list, a vector is a robust array; if you do not need random access, lists are faster than vectors
    //we need random access for the priority queue, because it will constantly be resorted
    bool PathSearch(std::list<Node>& path, const World& World, const WorldObj& obj, const Node& target); //path is our output list
    void NodeSuccessors(std::priority_queue<Node, std::vector<Node>, NodeCompare>& open, std::list<Node>& closed, Node& parentNode, const World& World, const Node& target);
    int Heuristic(int posX, int posY, const Node& target);
}

And, here’s my implementation:

bool PathSearch(std::list<Node>& path, const World& World, const WorldObj& obj, const Node& target){
    std::priority_queue<Node, std::vector<Node>, NodeCompare> open;
    std::list<Node> closed;
    //put our starting position into our queue of nodes to inspect
    Node start(Heuristic(obj.GetposX(), obj.GetposY(), target), obj.GetposX(), obj.GetposY());
    open.push(start);
    while(!open.empty()){
        Node bestNode = open.top(); //has the lowest score by definition
        open.pop();
        if(bestNode == target){ //made it to the target
            Node* ptrNode = &bestNode;
            while(ptrNode){ //this is where we would reconstruct the path
                std::cout<<ptrNode->posY<<std::endl;
                ptrNode = ptrNode->parent;
            }
            return 1;
        }
        NodeSuccessors(open, closed, bestNode, World, target); //look at the Node's neighbors
        closed.push_back(bestNode);
    }
    return 0; //no path found
}
//check for towers and check for boundaries; if they exist, skip the creation of that node
//pathfinding works for up, down, left, right, but not diagonal movement
void NodeSuccessors(std::priority_queue<Node, std::vector<Node>, NodeCompare>& open, std::list<Node>& closed, Node& parentNode, const World& World, const Node& target){
    std::vector<Node>& openVec = Container(open);
    int offsetX, offsetY;
    bool skip;
    for(int i = 0; i < 4; ++i){
        offsetX = 0; offsetY = 0;
        skip = 0;
        if(i == 0) offsetY = -30; //up
        else if(i == 1) offsetY = 30; //down
        else if(i == 2) offsetX = -30; //left
        else if(i == 3) offsetX = 30; //right
        //add check for out of boundaries or in an occupied space
        Node newNode(parentNode.cost + Heuristic((parentNode.posX + offsetX), (parentNode.posY + offsetY), target), parentNode.posX + offsetX, parentNode.posY + offsetY, &parentNode);
        //if the Node already exists on open or closed with a lower score, we can skip to the next neighbor
        //if the Node already exists on open or closed with a higher score, then we need to remove it
        //the erasing is somewhat expensive, but simplifies the implementation
        for(std::list<Node>::iterator itr = closed.begin(); itr != closed.end(); ++itr){
            if(*itr < newNode){
                skip = 1;
                break;
            }
            else if(*itr == newNode){
                closed.erase(itr);
                break;
            }
        }
        if(skip) continue;
        for(std::vector<Node>::iterator itr = openVec.begin(); itr != openVec.end(); ++itr){
            if(*itr < newNode){
                skip = 1;
                break;
            }
            else if(*itr == newNode){
                openVec.erase(itr);
                break;
            }
        }
        if(skip) continue;
        open.push(newNode);
    }
}
int Heuristic(int posX, int posY, const Node& target){
    return abs(posX - target.posX) + abs(posY - target.posY);
}

By inspection, closed and open contain the correct results. So, I’m sure that I am doing something really silly with my pointers. Any help would be very much appreciated. 🙂

Answer 1

The problem is that you created an instance on the stack in PathSearch() and passed its address to NodeSuccessors().

It’s not about your question exactly, but your algorithm has a performance issue. Priority queue is an excellent choice since a priority queue has O(1) in finding the node with the lowest score and O(log(n)) in inserting a node. However, your algorithm has O(n) in finding a node in open and closed. The performance will be much better if you also maintain the order of nodes so that you can find a node in O(log(n)).

---

I don’t remember exactly but this is a brief structure I used.

struct status {}; // represents the position, less-than comparable

struct node {
    status s;
    cost g;
    cost h;
    status parent;

    cost score() const { return g + h; }
};

struct node_comparator {
    bool operator(const node& x, const node& y) const { return x.score() < y.score(); }
};

typedef std::multiset<node, node_comparator> open_set;
// should be multiset since two or more nodes can have the same score

typedef std::map<Status, typename open_set::iterator> open_map;

• Insertion : O(log(n))
  • Insert a node to open_set
  • Insert the returned iterator to open_map
• Finding the lowest score node : O(log(n))
  • Pop the first node from open_set
  • Pop the corresponding status from open_map
• Updating – If the neighbor is in open_map, : O(log(n))
  • Pop the node from open_set using the iterator in open_map
  • Update the cost
  • Insert to open_set
  • Update the open_map to point the reinserted iterator

A huge amount of elements are dynamically allocated when you insert or delete. Adopting a pool allocator for containers might help.