A Star Unpredictable Errors - c++

My feeble attempt at an A* Algorithm is generating unpredictable errors.
My FindAdjacent() function is clearly a mess, and it actually doesn't work when I step through it. This is my first time trying a path finding algorithm, so this is all new to me.
When the application actually manages to find the goal nodes and path (or so I think), it can never set the path (called from within main by pressing enter). I do not know why it is unable to do this from looking at the SetPath() function.
Any help would be hugely appreciated, here's my code:
NODE CLASS
enum
{
NODE_TYPE_NONE = 0,
NODE_TYPE_NORMAL,
NODE_TYPE_SOLID,
NODE_TYPE_PATH,
NODE_TYPE_GOAL
};
class Node
{
public:
Node () : mTypeID(0), mNodeCost(0), mX(0), mY(0), mParent(0){};
public:
int mTypeID;
int mNodeCost;
int mX;
int mY;
Node* mParent;
};
PATH FINDING
/**
* finds the path between star and goal
*/
void AStarImpl::FindPath()
{
cout << "Finding Path." << endl;
GetGoals();
while (!mGoalFound)
GetF();
}
/**
* modifies linked list to find adjacent, walkable nodes
*/
void AStarImpl::FindAdjacent(Node* pNode)
{
for (int i = -1; i <= 1; i++)
{
for (int j = -1; j <= 1; j++)
if (i != 0 && j != 0)
if (Map::GetInstance()->mMap[pNode->mX+i][pNode->mY+j].mTypeID != NODE_TYPE_SOLID)
{
for (vector<Node*>::iterator iter = mClosedList.begin(); iter != mClosedList.end(); iter++)
{
if ((*iter)->mX != Map::GetInstance()->mMap[pNode->mX + i][pNode->mY + j].mX && (*iter)->mY != Map::GetInstance()->mMap[pNode->mX + i][pNode->mY + j].mY)
{
Map::GetInstance()->mMap[pNode->mX+i][pNode->mY+j].mParent = pNode;
mOpenList.push_back(&Map::GetInstance()->mMap[pNode->mX+i][pNode->mY+j]);
}
}
}
}
mClosedList.push_back(pNode);
}
/**
* colour the found path
*/
void AStarImpl::SetPath()
{
vector<Node*>::iterator tParent;
mGoalNode->mTypeID = NODE_TYPE_PATH;
Node *tNode = mGoalNode;
while (tNode->mParent)
{
tNode->mTypeID = NODE_TYPE_PATH;
tNode = tNode->mParent;
}
}
/**
* returns a random node
*/
Node* AStarImpl::GetRandomNode()
{
int tX = IO::GetInstance()->GetRand(0, MAP_WIDTH - 1);
int tY = IO::GetInstance()->GetRand(0, MAP_HEIGHT - 1);
Node* tNode = &Map::GetInstance()->mMap[tX][tY];
return tNode;
}
/**
* gets the starting and goal nodes, then checks te starting nodes adjacent nodes
*/
void AStarImpl::GetGoals()
{
// get the two nodes
mStartNode = GetRandomNode();
mGoalNode = GetRandomNode();
mStartNode->mTypeID = NODE_TYPE_GOAL;
mGoalNode->mTypeID = NODE_TYPE_GOAL;
// insert start node into the open list
mOpenList.push_back(mStartNode);
// find the starting nodes adjacent ndoes
FindAdjacent(*mOpenList.begin());
// remove starting node from open list
mOpenList.erase(mOpenList.begin());
}
/**
* finds the best f
*/
void AStarImpl::GetF()
{
int tF = 0;
int tBestF = 1000;
vector<Node*>::const_iterator tIter;
vector<Node*>::const_iterator tBestNode;
for (tIter = mOpenList.begin(); tIter != mOpenList.end(); ++tIter)
{
tF = GetH(*tIter);
tF += (*tIter)->mNodeCost;
if (tF < tBestF)
{
tBestF = tF;
tBestNode = tIter;
}
}
if ((*tBestNode) != mGoalNode)
{
Node tNode = **tBestNode;
mOpenList.erase(tBestNode);
FindAdjacent(&tNode);
}
else
{
mClosedList.push_back(mGoalNode);
mGoalFound = true;
}
}
/**
* returns the heuristic from the given node to goal
*/
int AStarImpl::GetH(Node *pNode)
{
int H = (int) fabs((float)pNode->mX - mGoalNode->mX);
H += (int) fabs((float)pNode->mY - mGoalNode->mY);
H *= 10;
return H;
}

A few suggestions:
ADJACENCY TEST
The test in FindAdjacent will only find diagonal neighbours at the moment
if (i != 0 && j != 0)
If you also want to find left/right/up/down neighbours you would want to use
if (i != 0 || j != 0)
ADJACENCY LOOP
I think your code looks suspicious in FindAdjacent at the line
for (vector<Node*>::iterator iter = mClosedList.begin(); iter != mClosedList.end(); iter++)
I don't really understand the intention here. I would have expected mClosedList to start empty, so this loop will never execute, and so nothing will ever get added to mOpenList.
My expectation at this part of the algorithm would be for you to test for each neighbour whether it should be added to the open list.
OPENLIST CHECK
If you look at the A* algorithm on wikipedia you will see that you are also missing the section starting
if neighbor not in openset or tentative_g_score < g_score[neighbor]
in which you should also check in FindAdjacent whether your new node is already in the OpenSet before adding it, and if it is then only add it if the score is better.

Related

Stuck/general help in developing A* on a 2D grid

I think I am close to finishing this implementation of A* but my mind is becoming fried and am looking for pointers on what I should be doing to complete it.
My current problem is that my function that runs through A* remains stuck on the same node, as in the current node never moves into any other of the open nodes.
Here is my main function, note that the heuristic(Node &n1, Node &n2) function is currently set to always to return 0, so it should currently be working more like a Dijkstra algorithm rather than A*. Also, movement is restricted to the NESW plane, no diagonal movement, so distance_between(Node &n1, Node &n2) always returns 1.
void astar(Node start_, Node end_) {
Node start = start_;
Node end = end_;
// compute f,g,h for the start node
start.g = 0;
start.h = heuristic(start, end);
start.f = start.g + start.h;
// insert start node into the open set
openNodes.insert(&start);
// while the set of open nodes is not empty
while (openNodes.size() > 0) {
// pick the most promising node to look at next
Node currentNode;
cout << "currentNode before: ";
currentNode.displaylocation();
// go through all the open nodes and find the one with the smallest 'f' value
Node* minf = (*openNodes.begin()); // set initial value for minimum f to be the first node in the set of open nodes
for (auto n : openNodes) {
if (n->f <= minf->f) {
minf = n;
}
}
currentNode = *minf; // set the current node to the node that holds the smallest 'f' value
cout << "currentNode after: ";
currentNode.displaylocation();
// if the current node is the end node, then we have found a path
if (currentNode.type == -3) {
break;
}
// remove the current node from the set of open nodes, and add it to the set of closed nodes
openNodes.erase(&currentNode);
closedNodes.insert(&currentNode);
// go through the currents node's neighbours
for (auto n : neighbours(currentNode)) {
cout << "neighbour local: " << n.location.x << "," << n.location.y << "\n";
if (closedNodes.count(&n) == 0 && n.type != -2) { // if this node is neither closed or a blocker
int new_g = currentNode.g + distance_between(currentNode, n);
if (openNodes.count(&n) != 0) { // if we have not seen this node before, add to the open set
openNodes.insert(&n);
}
else if (new_g >= n.g) { // else if we have seen this node before, and already found a shorter path to it from the starting node
}
n.g = new_g;
n.f = n.g + heuristic(n, end);
n.parent_ = &currentNode;
}
}
cout << "\n A* run success! \n";
//break;
}
}
Here is the deceleration of things like the Node struct and the global variables:
// The size of the grid
#define WIDTH 6
#define HEIGHT 6
// Holds values for x and y locations on the grid
struct Coord {
int x, y;
};
// holds data for each node required for A*
struct Node {
int type; // used for defining if this node is a blocker, empty, start or end
Coord location;
int g = 0;
int h = 0;
int f = g + h;
Node *parent_; // pointer to this node's parent
std::string debugmessage;
void displaylocation() {
std::cout << "I am the node at: " << location.x << "," << location.y << "\n";
}
};
// The 2D grid array for A*, requiring a Node struct to store the data of each cell
Node astarArray[WIDTH][HEIGHT];
// Sets for A*
std::set<Node *> openNodes; // contains the nodes that are yet to be considered (if this is empty, then there are no more paths to consider or there is no path)
std::set<Node *> closedNodes; // contains the nodes that have already been considered (if the end node is placed in here, a path has been found)
// stores the start and end values for A*
Node start_A, end_A;
void astar(Node start_, Node end_);
int distance_between(Node& n1, Node& n2);
int heuristic(Node& n1, Node& n2);
std::list<Node> neighbours(Node& n_);
// returns the distance between two nodes for A*
int distance_between(Node& n1, Node& n2) {
return 1; // always return 1 as we are working in a grid restricted to NSEW movement
}
int heuristic(Node& n1, Node& n2) {
return 0; // return 0 to work as a Dijkstra algorithm rather than A*
}
// finds a node's neighbours for A*
std::list<Node> neighbours(Node& n_) {
std::list<Node> neighbours_;
int x = n_.location.x;
int y = n_.location.y;
// start at the location belonging to 'n_'
//for (int y = n_.location.y; y < HEIGHT; y++) {
//for (int x = n_.location.x; x < WIDTH; x++) {
// east
if (x < WIDTH - 1) {
neighbours_.push_back(astarArray[x + 1][y]);
}
// west
if (x > 0) {
neighbours_.push_back(astarArray[x - 1][y]);
}
// south
if (y < HEIGHT - 1) {
neighbours_.push_back(astarArray[x][y + 1]);
}
// north
if (y > 0) {
neighbours_.push_back(astarArray[x][y -1]);
}
//}
//}
return neighbours_;
}
Thank you very much for reading and for any help you can give. I will provide more code if required.
The main problem you have is that you are using the pointers (mem address) to find out if a node is in your set or not.
currentNode = *minf; // set the current node to the node that holds the smallest 'f' value
Then you copy to currentNode the contents of minf.
currentNode will have a different address from the pointer to minf
openNodes.erase(&currentNode); will not remove minf because currentNode does not have the same address.
I would suggest you investigate more on how to implement A* as you are missing some steps. Look for priority queues.
Instead of the mem address of the node, use the position index for that node in the grid (pos.x * numCols) + pos.y

Problems implementing A star search C++

I am trying to implement an A star algorithm with C++ in a game that I am creating and it is not working, I don't really know if there's something I've missed about the code or the algorithm. I've used sets because they are sorted and the return value is a vector with the nodes I've got to visit. I've never used this algorithm before so probably I've got some kind of error.
struct node {
Pos pos;
int f; //the sum of the distance from the goal to succcessor
int g; // the sum of the cost of the current plus the one from the successor
int h; //distance from goal to successor
friend bool operator< (node right, node left) {
return (right.f < left.f);
} };
vector<node> search(Pos inicio,Pos desti){
set<node> opennodes;
vector<node> closednodes;
node inici;
node successor;
inici.pos = inicio;
inici.h = heuristic(inicio,desti);
inici.g = getcost(inicio);
inici.f = inici.g + inici.h;
opennodes.insert(inici);
closednodes.push_back(inici);
while(not opennodes.empty()){
node current = *(opennodes.begin());
opennodes.erase(opennodes.begin());
if(current.pos == desti) cerr<<"encontrao";
Dir direccio;
for(int i = 0; i < 4;++i){
if(i==0){
direccio = LEFT;
}
else if(i==1){
direccio = RIGHT;
}
else if(i==2){
direccio = TOP;
}
else {
direccio = BOTTOM;
}
successor.pos = current.pos + direccio;
if(successor.pos == desti) return closednodes;
if(pos_ok(successor.pos)){
successor.g = current.g + getcost(successor.pos);
successor.h = heuristic(successor.pos,desti);
successor.f = successor.g + successor.h;
node n1 = checkposition(successor.pos, opennodes); //I had to create two checkposition just to know if there's the node in the set or in the vector
node n2 = checkposition2(successor.pos, closednodes);
if (n1.f != -1 and n1.f < successor.f);
else if (n2.f != -1 and n2.f < successor.f);
else opennodes.insert(successor);
}
}
closednodes.push_back(current);
}
return closednodes;
}
So, first:
if(current.pos == desti) cerr<<"encontrao";
Shouldn't there be a break statement here? the cerr function doesn't break your loop, just throws and error message to your stdout.
And the for statement inside your while is always running up to 4, so direccio is always set to BOTTOM.
Other than that, I think the heuristic is fine, the problem is within the code structure, I'd suggest debugging it and posting here your results.

A* Performance at large maps

i would like some help for my AStar algorithm search, which takes from my point of view far to long. Even though my map is with 500 * 400 coordinates(objectively is my tile graph a bit smaller since I don't took the walls into the TileGraph.) large, I would like to expect the result after a few seconds. The world looks like this, despite the task not being mine
I want to search from marked coordinates "Start"(120|180) to "Ziel"(320|220), which currently takes 48 minutes. And sorry for all, who don't speak german, but the text at the picture isn't important.
At first I want to show you, what I've programmed for A*. In General adapted myself to the pseudocode at https://en.wikipedia.org/wiki/A*_search_algorithm .
bool AStarPath::Processing(Node* Start, Node* End)
m_Start = Start;
m_End = End;
for (Node* n : m_SearchRoom->GetAllNodes())
{
DistanceToStart[n] = std::numeric_limits<float>::infinity();
CameFrom[n] = nullptr;
}
DistanceToStart[m_Start] = 0;
NotEvaluatedNodes.AddElement(0, m_Start);
while (NotEvaluatedNodes.IsEmpty() == false)
{
Node* currentNode = NotEvaluatedNodes.GetElement();
NotEvaluatedNodes.DeleteElement();
if (currentNode == m_End)
{
ReconstructPath();
return true;
}
EvaluatedNodes.insert(currentNode);
ExamineNeighbours(currentNode);
}
return false;
//End Processing
void AStarPath::ExamineNeighbours(Node* current)
for (Node* neighbour : m_SearchRoom->GetNeighbours(current))
{
if (std::find(EvaluatedNodes.begin(), EvaluatedNodes.end(), neighbour) != EvaluatedNodes.end())
{
continue;
}
bool InOpenSet = NotEvaluatedNodes.ContainsElement(neighbour);
float tentative_g_score = DistanceToStart[current] + DistanceBetween(current, neighbour);
if (InOpenSet == true && tentative_g_score >= DistanceToStart[neighbour])
{
continue;
}
CameFrom[neighbour] = current;
DistanceToStart[neighbour] = tentative_g_score;
float Valuation = tentative_g_score + DistanceBetween(neighbour, m_End);
if (InOpenSet == false)
{
NotEvaluatedNodes.AddElement(Valuation, neighbour);
}
else
{
NotEvaluatedNodes.UpdatePriority(neighbour, Valuation);
}
}
//END ExamineNeighbours
double AStarPath::DistanceBetween(Node* a, Node* b)
return sqrt(pow(m_SearchRoom->GetNodeX(a) - m_SearchRoom->GetNodeX(b), 2)
+ pow(m_SearchRoom->GetNodeY(a) - m_SearchRoom->GetNodeY(b), 2));
//END DistanceBetween
I'm sorry for the bad formatting, but I don't really know how to work with the code blocks here.
class AStarPath
private:
std::unordered_set<Node*> EvaluatedNodes;
Binary_Heap NotEvaluatedNodes;
std::unordered_map<Node*, float> DistanceToStart;
std::unordered_map<Node*, Node*> CameFrom;
std::vector<Node*> m_path;
TileGraph* m_SearchRoom;
//END Class AStarPath
Anyway, i have thought myself over my problem already and changed some things.
Firstly, I implemented a binary heap instead of the std::priority_queue. I used a page at policyalmanac for it, but I'm not permitted to add another link, so I can't really give you the address. It improved the performance, but it still takes quite long as I told at the beginning.
Secondly, I used unordered containers (if there are two options), so that the containers don't have to be sorted after the changes. For my EvaluatedNodes I took the std::unordered_set, since from my knowledge it's fastest for std::find, which I use for containment checks.
The usage of std::unordered_map is caused by the need of having seperate keys and values.
Thirdly, I thought about splitting my map into nodes, which represent multiple coordinates(instead of now where one node represents one coordinate) , but I'm not really sure how to choose them. I thought about setting points at position, that the algorithm decises based on the length and width of the map and add neighbouring coordinates, if there aren't a specific distance or more away from the base node/coordinate and I can reach them only from previous added coordinates. To Check whether there is a ability to walk, I would have used the regular A*, with only the coordinates(converted to A* nodes), which are in these big nodes. Despite this I'm unsure which coordinates I should take for the start and end of this pathfinding. This would probably reduce the number of nodes/coordinates, which are checked, if I only use the coordinates/nodes, which were part of the big nodes.(So that only nodes are used, which where part of the bigger nodes at an upper level)
I'm sorry for my english, but hope that all will be understandable. I'm looking forward to your answers and learning new techniques and ways to handle problems and as well learn about all the hundreds of stupids mistakes I produced.
If any important aspect is unclear or if I should add more code/information, feel free to ask.
EDIT: Binary_Heap
class Binary_Heap
private:
std::vector<int> Index;
std::vector<int> m_Valuation;
std::vector<Node*> elements;
int NodesChecked;
int m_NumberOfHeapItems;
void TryToMoveElementUp(int i_pos);
void TryToMoveElementDown(int i_pos);
public:
Binary_Heap(int i_numberOfElements);
void AddElement(int Valuation, Node* element);
void DeleteElement();
Node* GetElement();
bool IsEmpty();
bool ContainsElement(Node* i_node);
void UpdatePriority(Node* i_node, float newValuation);
Binary_Heap::Binary_Heap(int i_numberOfElements)
Index.resize(i_numberOfElements);
elements.resize(i_numberOfElements);
m_Valuation.resize(i_numberOfElements);
NodesChecked = 0;
m_NumberOfHeapItems = 0;
void Binary_Heap::AddElement(int valuation, Node* element)
++NodesChecked;
++m_NumberOfHeapItems;
Index[m_NumberOfHeapItems] = NodesChecked;
m_Valuation[NodesChecked] = valuation;
elements[NodesChecked] = element;
TryToMoveElementUp(m_NumberOfHeapItems);
void Binary_Heap::DeleteElement()
elements[Index[1]] = nullptr;
m_Valuation[Index[1]] = 0;
Index[1] = Index[m_NumberOfHeapItems];
--m_NumberOfHeapItems;
TryToMoveElementDown(1);
bool Binary_Heap::IsEmpty()
return m_NumberOfHeapItems == 0;
Node* Binary_Heap::GetElement()
return elements[Index[1]];
bool Binary_Heap::ContainsElement(Node* i_element)
return std::find(elements.begin(), elements.end(), i_element) != elements.end();
void Binary_Heap::UpdatePriority(Node* i_node, float newValuation)
if (ContainsElement(i_node) == false)
{
AddElement(newValuation, i_node);
}
else
{
int treePosition;
for (int i = 1; i < Index.size(); i++)
{
if (elements[Index[i]] == i_node)
{
treePosition = i;
break;
}
}
//Won't influence each other, since only one of them will change the position
TryToMoveElementUp(treePosition);
TryToMoveElementDown(treePosition);
}
void Binary_Heap::TryToMoveElementDown(int i_pos)
int nextPosition = i_pos;
while (true)
{
int currentPosition = nextPosition;
if (2 * currentPosition + 1 <= m_NumberOfHeapItems)
{
if (m_Valuation[Index[currentPosition]] >= m_Valuation[Index[2 * currentPosition]])
{
nextPosition = 2 * currentPosition;
}
if (m_Valuation[Index[currentPosition]] >= m_Valuation[Index[2 * currentPosition + 1]])
{
nextPosition = 2 * currentPosition + 1;
}
}
else
{
if (2 * currentPosition <= m_NumberOfHeapItems)
{
if (m_Valuation[Index[currentPosition]] >= m_Valuation[Index[2 * currentPosition]])
{
nextPosition = 2 * currentPosition;
}
}
}
if (currentPosition != nextPosition)
{
int tmp = Index[currentPosition];
Index[currentPosition] = Index[nextPosition];
Index[nextPosition] = tmp;
}
else
{
break;
}
}
void Binary_Heap::TryToMoveElementUp(int i_pos)
int treePosition = i_pos;
while (treePosition != 1)
{
if (m_Valuation[Index[treePosition]] <= m_Valuation[Index[treePosition / 2]])
{
int tmp = Index[treePosition / 2];
Index[treePosition / 2] = Index[treePosition];
Index[treePosition] = tmp;
treePosition = treePosition / 2;
}
else
{
break;
}
}
This line introduces major inefficiency, as it needs to iterate over all the nodes in the queue, in each iteration.
bool InOpenSet = NotEvaluatedNodes.ContainsElement(neighbour);
Try using a more efficient data structure, e.g. the unordered_set you use for EvaluatedNodes. Whenever you push or pop a node from the heap, modify the set accordingly to always contain only the nodes in the heap.

Finding cycle in Aho-Corasick automaton

I'am facing a problem which should be solved using Aho-Corasick automaton. I'am given a set of words (composed with '0' or '1') - patterns and I must decide if it is possible to create infinite text, which wouldn't contain any of given patterns. I think, the solution is to create Aho-Corasick automaton and search for a cycle without matching states, but I'm not able to propose a good way to do that. I thought of searching the states graph using DFS, but I'm not sure if it will work and I have an implementation problem - let's assume, that we are in a state, which has an '1' edge - but state pointed by that edge is marked as matching - so we cannot use that edge, we can try fail link (current state doesn't have '0' edge) - but we must also remember, that we could not go with '1' edge from state pointed by fail link of the current one.
Could anyone correct me and show me how to do that? I've written Aho-Corasick in C++ and I'am sure it works - I also understand the entire algorithm.
Here is the base code:
class AhoCorasick
{
static const int ALPHABET_SIZE = 2;
struct State
{
State* edge[ALPHABET_SIZE];
State* fail;
State* longestMatchingSuffix;
//Vector used to remember which pattern matches in this state.
vector< int > matching;
short color;
State()
{
for(int i = 0; i < ALPHABET_SIZE; ++i)
edge[i] = 0;
color = 0;
}
~State()
{
for(int i = 0; i < ALPHABET_SIZE; ++i)
{
delete edge[i];
}
}
};
private:
State root;
vector< int > lenOfPattern;
bool isFailComputed;
//Helper function used to traverse state graph.
State* move(State* curr, char letter)
{
while(curr != &root && curr->edge[letter] == 0)
{
curr = curr->fail;
}
if(curr->edge[letter] != 0)
curr = curr->edge[letter];
return curr;
}
//Function which computes fail links and longestMatchingSuffix.
void computeFailLink()
{
queue< State* > Q;
root.fail = root.longestMatchingSuffix = 0;
for(int i = 0; i < ALPHABET_SIZE; ++i)
{
if(root.edge[i] != 0)
{
Q.push(root.edge[i]);
root.edge[i]->fail = &root;
}
}
while(!Q.empty())
{
State* curr = Q.front();
Q.pop();
if(!curr->fail->matching.empty())
{
curr->longestMatchingSuffix = curr->fail;
}
else
{
curr->longestMatchingSuffix = curr->fail->longestMatchingSuffix;
}
for(int i = 0; i < ALPHABET_SIZE; ++i)
{
if(curr->edge[i] != 0)
{
Q.push(curr->edge[i]);
State* state = curr->fail;
state = move(state, i);
curr->edge[i]->fail = state;
}
}
}
isFailComputed = true;
}
public:
AhoCorasick()
{
isFailComputed = false;
}
//Add pattern to automaton.
//pattern - pointer to pattern, which will be added
//fun - function which will be used to transform character to 0-based index.
void addPattern(const char* const pattern, int (*fun) (const char *))
{
isFailComputed = false;
int len = strlen(pattern);
State* curr = &root;
const char* pat = pattern;
for(; *pat; ++pat)
{
char tmpPat = fun(pat);
if(curr->edge[tmpPat] == 0)
{
curr = curr->edge[tmpPat] = new State;
}
else
{
curr = curr->edge[tmpPat];
}
}
lenOfPattern.push_back(len);
curr->matching.push_back(lenOfPattern.size() - 1);
}
};
int alphabet01(const char * c)
{
return *c - '0';
}
I didn't look through your code, but I know very simple and efficient implementation.
First of all, lets add Dictionary Suffix Links to the tree (their description you can find in Wikipedia). Then you have to look through all your tree and somehow mark matching nodes and nodes that have Dict Suffix Links as bad nodes. The explanation of these actions is obvious: you don't need all the matching nodes, or nodes that have a matching suffix in them.
Now you have an Aho-Corasick tree without any matching nodes. If you just run DFS algo on the resulting tree, you will get what you want.

Algorithm for finding the maximum difference in an array of numbers

I have an array of a few million numbers.
double* const data = new double (3600000);
I need to iterate through the array and find the range (the largest value in the array minus the smallest value). However, there is a catch. I only want to find the range where the smallest and largest values are within 1,000 samples of each other.
So I need to find the maximum of: range(data + 0, data + 1000), range(data + 1, data + 1001), range(data + 2, data + 1002), ...., range(data + 3599000, data + 3600000).
I hope that makes sense. Basically I could do it like above, but I'm looking for a more efficient algorithm if one exists. I think the above algorithm is O(n), but I feel that it's possible to optimize. An idea I'm playing with is to keep track of the most recent maximum and minimum and how far back they are, then only backtrack when necessary.
I'll be coding this in C++, but a nice algorithm in pseudo code would be just fine. Also, if this number I'm trying to find has a name, I'd love to know what it is.
Thanks.
This type of question belongs to a branch of algorithms called streaming algorithms. It is the study of problems which require not only an O(n) solution but also need to work in a single pass over the data. the data is inputted as a stream to the algorithm, the algorithm can't save all of the data and then and then it is lost forever. the algorithm needs to get some answer about the data, such as for instance the minimum or the median.
Specifically you are looking for a maximum (or more commonly in literature - minimum) in a window over a stream.
Here's a presentation on an article that mentions this problem as a sub problem of what they are trying to get at. it might give you some ideas.
I think the outline of the solution is something like that - maintain the window over the stream where in each step one element is inserted to the window and one is removed from the other side (a sliding window). The items you actually keep in memory aren't all of the 1000 items in the window but a selected representatives which are going to be good candidates for being the minimum (or maximum).
read the article. it's abit complex but after 2-3 reads you can get the hang of it.
The algorithm you describe is really O(N), but i think the constant is too high. Another solution which looks reasonable is to use O(N*log(N)) algorithm the following way:
* create sorted container (std::multiset) of first 1000 numbers
* in loop (j=1, j<(3600000-1000); ++j)
- calculate range
- remove from the set number which is now irrelevant (i.e. in index *j - 1* of the array)
- add to set new relevant number (i.e. in index *j+1000-1* of the array)
I believe it should be faster, because the constant is much lower.
This is a good application of a min-queue - a queue (First-In, First-Out = FIFO) which can simultaneously keep track of the minimum element it contains, with amortized constant-time updates. Of course, a max-queue is basically the same thing.
Once you have this data structure in place, you can consider CurrentMax (of the past 1000 elements) minus CurrentMin, store that as the BestSoFar, and then push a new value and pop the old value, and check again. In this way, keep updating BestSoFar until the final value is the solution to your question. Each single step takes amortized constant time, so the whole thing is linear, and the implementation I know of has a good scalar constant (it's fast).
I don't know of any documentation on min-queue's - this is a data structure I came up with in collaboration with a coworker. You can implement it by internally tracking a binary tree of the least elements within each contiguous sub-sequence of your data. It simplifies the problem that you'll only pop data from one end of the structure.
If you're interested in more details, I can try to provide them. I was thinking of writing this data structure up as a paper for arxiv. Also note that Tarjan and others previously arrived at a more powerful min-deque structure that would work here, but the implementation is much more complex. You can google for "mindeque" to read about Tarjan et al.'s work.
std::multiset<double> range;
double currentmax = 0.0;
for (int i = 0; i < 3600000; ++i)
{
if (i >= 1000)
range.erase(range.find(data[i-1000]));
range.insert(data[i]);
if (i >= 999)
currentmax = max(currentmax, *range.rbegin());
}
Note untested code.
Edit: fixed off-by-one error.
read in the first 1000 numbers.
create a 1000 element linked list which tracks the current 1000 number.
create a 1000 element array of pointers to linked list nodes, 1-1 mapping.
sort the pointer array based on linked list node's values. This will rearrange the array but keep the linked list intact.
you can now calculate the range for the first 1000 numbers by examining the first and last element of the pointer array.
remove the first inserted element, which is either the head or the tail depending on how you made your linked list. Using the node's value perform a binary search on the pointer array to find the to-be-removed node's pointer, and shift the array one over to remove it.
add the 1001th element to the linked list, and insert a pointer to it in the correct position in the array, by performing one step of an insertion sort. This will keep the array sorted.
now you have the min. and max. value of the numbers between 1 and 1001, and can calculate the range using the first and last element of the pointer array.
it should now be obvious what you need to do for the rest of the array.
The algorithm should be O(n) since the delete and insertion is bounded by log(1e3) and everything else takes constant time.
I decided to see what the most efficient algorithm I could think of to solve this problem was using actual code and actual timings. I first created a simple solution, one that tracks the min/max for the previous n entries using a circular buffer, and a test harness to measure the speed. In the simple solution, each data value is compared against the set of min/max values, so that's about window_size * count tests (where window size in the original question is 1000 and count is 3600000).
I then thought about how to make it faster. First off, I created a solution that used a fifo queue to store window_size values and a linked list to store the values in ascending order where each node in the linked list was also a node in the queue. To process a data value, the item at the end of the fifo was removed from the linked list and the queue. The new value was added to the start of the queue and a linear search was used to find the position in the linked list. The min and max values could then be read from the start and end of the linked list. This was quick, but wouldn't scale well with increasing window_size (i.e. linearly).
So I decided to add a binary tree to the system to try to speed up the search part of the algorithm. The final timings for window_size = 1000 and count = 3600000 were:
Simple: 106875
Quite Complex: 1218
Complex: 1219
which was both expected and unexpected. Expected in that using a sorted linked list helped, unexpected in that the overhead of having a self balancing tree didn't offset the advantage of a quicker search. I tried the latter two with an increased window size and found that the were always nearly identical up to a window_size of 100000.
Which all goes to show that theorising about algorithms is one thing, implementing them is something else.
Anyway, for those that are interested, here's the code I wrote (there's quite a bit!):
Range.h:
#include <algorithm>
#include <iostream>
#include <ctime>
using namespace std;
// Callback types.
typedef void (*OutputCallback) (int min, int max);
typedef int (*GeneratorCallback) ();
// Declarations of the test functions.
clock_t Simple (int, int, GeneratorCallback, OutputCallback);
clock_t QuiteComplex (int, int, GeneratorCallback, OutputCallback);
clock_t Complex (int, int, GeneratorCallback, OutputCallback);
main.cpp:
#include "Range.h"
int
checksum;
// This callback is used to get data.
int CreateData ()
{
return rand ();
}
// This callback is used to output the results.
void OutputResults (int min, int max)
{
//cout << min << " - " << max << endl;
checksum += max - min;
}
// The program entry point.
void main ()
{
int
count = 3600000,
window = 1000;
srand (0);
checksum = 0;
std::cout << "Simple: Ticks = " << Simple (count, window, CreateData, OutputResults) << ", checksum = " << checksum << std::endl;
srand (0);
checksum = 0;
std::cout << "Quite Complex: Ticks = " << QuiteComplex (count, window, CreateData, OutputResults) << ", checksum = " << checksum << std::endl;
srand (0);
checksum = 0;
std::cout << "Complex: Ticks = " << Complex (count, window, CreateData, OutputResults) << ", checksum = " << checksum << std::endl;
}
Simple.cpp:
#include "Range.h"
// Function to actually process the data.
// A circular buffer of min/max values for the current window is filled
// and once full, the oldest min/max pair is sent to the output callback
// and replaced with the newest input value. Each value inputted is
// compared against all min/max pairs.
void ProcessData
(
int count,
int window,
GeneratorCallback input,
OutputCallback output,
int *min_buffer,
int *max_buffer
)
{
int
i;
for (i = 0 ; i < window ; ++i)
{
int
value = input ();
min_buffer [i] = max_buffer [i] = value;
for (int j = 0 ; j < i ; ++j)
{
min_buffer [j] = min (min_buffer [j], value);
max_buffer [j] = max (max_buffer [j], value);
}
}
for ( ; i < count ; ++i)
{
int
index = i % window;
output (min_buffer [index], max_buffer [index]);
int
value = input ();
min_buffer [index] = max_buffer [index] = value;
for (int k = (i + 1) % window ; k != index ; k = (k + 1) % window)
{
min_buffer [k] = min (min_buffer [k], value);
max_buffer [k] = max (max_buffer [k], value);
}
}
output (min_buffer [count % window], max_buffer [count % window]);
}
// A simple method of calculating the results.
// Memory management is done here outside of the timing portion.
clock_t Simple
(
int count,
int window,
GeneratorCallback input,
OutputCallback output
)
{
int
*min_buffer = new int [window],
*max_buffer = new int [window];
clock_t
start = clock ();
ProcessData (count, window, input, output, min_buffer, max_buffer);
clock_t
end = clock ();
delete [] max_buffer;
delete [] min_buffer;
return end - start;
}
QuiteComplex.cpp:
#include "Range.h"
template <class T>
class Range
{
private:
// Class Types
// Node Data
// Stores a value and its position in various lists.
struct Node
{
Node
*m_queue_next,
*m_list_greater,
*m_list_lower;
T
m_value;
};
public:
// Constructor
// Allocates memory for the node data and adds all the allocated
// nodes to the unused/free list of nodes.
Range
(
int window_size
) :
m_nodes (new Node [window_size]),
m_queue_tail (m_nodes),
m_queue_head (0),
m_list_min (0),
m_list_max (0),
m_free_list (m_nodes)
{
for (int i = 0 ; i < window_size - 1 ; ++i)
{
m_nodes [i].m_list_lower = &m_nodes [i + 1];
}
m_nodes [window_size - 1].m_list_lower = 0;
}
// Destructor
// Tidy up allocated data.
~Range ()
{
delete [] m_nodes;
}
// Function to add a new value into the data structure.
void AddValue
(
T value
)
{
Node
*node = GetNode ();
// clear links
node->m_queue_next = 0;
// set value of node
node->m_value = value;
// find place to add node into linked list
Node
*search;
for (search = m_list_max ; search ; search = search->m_list_lower)
{
if (search->m_value < value)
{
if (search->m_list_greater)
{
node->m_list_greater = search->m_list_greater;
search->m_list_greater->m_list_lower = node;
}
else
{
m_list_max = node;
}
node->m_list_lower = search;
search->m_list_greater = node;
}
}
if (!search)
{
m_list_min->m_list_lower = node;
node->m_list_greater = m_list_min;
m_list_min = node;
}
}
// Accessor to determine if the first output value is ready for use.
bool RangeAvailable ()
{
return !m_free_list;
}
// Accessor to get the minimum value of all values in the current window.
T Min ()
{
return m_list_min->m_value;
}
// Accessor to get the maximum value of all values in the current window.
T Max ()
{
return m_list_max->m_value;
}
private:
// Function to get a node to store a value into.
// This function gets nodes from one of two places:
// 1. From the unused/free list
// 2. From the end of the fifo queue, this requires removing the node from the list and tree
Node *GetNode ()
{
Node
*node;
if (m_free_list)
{
// get new node from unused/free list and place at head
node = m_free_list;
m_free_list = node->m_list_lower;
if (m_queue_head)
{
m_queue_head->m_queue_next = node;
}
m_queue_head = node;
}
else
{
// get node from tail of queue and place at head
node = m_queue_tail;
m_queue_tail = node->m_queue_next;
m_queue_head->m_queue_next = node;
m_queue_head = node;
// remove node from linked list
if (node->m_list_lower)
{
node->m_list_lower->m_list_greater = node->m_list_greater;
}
else
{
m_list_min = node->m_list_greater;
}
if (node->m_list_greater)
{
node->m_list_greater->m_list_lower = node->m_list_lower;
}
else
{
m_list_max = node->m_list_lower;
}
}
return node;
}
// Member Data.
Node
*m_nodes,
*m_queue_tail,
*m_queue_head,
*m_list_min,
*m_list_max,
*m_free_list;
};
// A reasonable complex but more efficent method of calculating the results.
// Memory management is done here outside of the timing portion.
clock_t QuiteComplex
(
int size,
int window,
GeneratorCallback input,
OutputCallback output
)
{
Range <int>
range (window);
clock_t
start = clock ();
for (int i = 0 ; i < size ; ++i)
{
range.AddValue (input ());
if (range.RangeAvailable ())
{
output (range.Min (), range.Max ());
}
}
clock_t
end = clock ();
return end - start;
}
Complex.cpp:
#include "Range.h"
template <class T>
class Range
{
private:
// Class Types
// Red/Black tree node colours.
enum NodeColour
{
Red,
Black
};
// Node Data
// Stores a value and its position in various lists and trees.
struct Node
{
// Function to get the sibling of a node.
// Because leaves are stored as null pointers, it must be possible
// to get the sibling of a null pointer. If the object is a null pointer
// then the parent pointer is used to determine the sibling.
Node *Sibling
(
Node *parent
)
{
Node
*sibling;
if (this)
{
sibling = m_tree_parent->m_tree_less == this ? m_tree_parent->m_tree_more : m_tree_parent->m_tree_less;
}
else
{
sibling = parent->m_tree_less ? parent->m_tree_less : parent->m_tree_more;
}
return sibling;
}
// Node Members
Node
*m_queue_next,
*m_tree_less,
*m_tree_more,
*m_tree_parent,
*m_list_greater,
*m_list_lower;
NodeColour
m_colour;
T
m_value;
};
public:
// Constructor
// Allocates memory for the node data and adds all the allocated
// nodes to the unused/free list of nodes.
Range
(
int window_size
) :
m_nodes (new Node [window_size]),
m_queue_tail (m_nodes),
m_queue_head (0),
m_tree_root (0),
m_list_min (0),
m_list_max (0),
m_free_list (m_nodes)
{
for (int i = 0 ; i < window_size - 1 ; ++i)
{
m_nodes [i].m_list_lower = &m_nodes [i + 1];
}
m_nodes [window_size - 1].m_list_lower = 0;
}
// Destructor
// Tidy up allocated data.
~Range ()
{
delete [] m_nodes;
}
// Function to add a new value into the data structure.
void AddValue
(
T value
)
{
Node
*node = GetNode ();
// clear links
node->m_queue_next = node->m_tree_more = node->m_tree_less = node->m_tree_parent = 0;
// set value of node
node->m_value = value;
// insert node into tree
if (m_tree_root)
{
InsertNodeIntoTree (node);
BalanceTreeAfterInsertion (node);
}
else
{
m_tree_root = m_list_max = m_list_min = node;
node->m_tree_parent = node->m_list_greater = node->m_list_lower = 0;
}
m_tree_root->m_colour = Black;
}
// Accessor to determine if the first output value is ready for use.
bool RangeAvailable ()
{
return !m_free_list;
}
// Accessor to get the minimum value of all values in the current window.
T Min ()
{
return m_list_min->m_value;
}
// Accessor to get the maximum value of all values in the current window.
T Max ()
{
return m_list_max->m_value;
}
private:
// Function to get a node to store a value into.
// This function gets nodes from one of two places:
// 1. From the unused/free list
// 2. From the end of the fifo queue, this requires removing the node from the list and tree
Node *GetNode ()
{
Node
*node;
if (m_free_list)
{
// get new node from unused/free list and place at head
node = m_free_list;
m_free_list = node->m_list_lower;
if (m_queue_head)
{
m_queue_head->m_queue_next = node;
}
m_queue_head = node;
}
else
{
// get node from tail of queue and place at head
node = m_queue_tail;
m_queue_tail = node->m_queue_next;
m_queue_head->m_queue_next = node;
m_queue_head = node;
// remove node from tree
node = RemoveNodeFromTree (node);
RebalanceTreeAfterDeletion (node);
// remove node from linked list
if (node->m_list_lower)
{
node->m_list_lower->m_list_greater = node->m_list_greater;
}
else
{
m_list_min = node->m_list_greater;
}
if (node->m_list_greater)
{
node->m_list_greater->m_list_lower = node->m_list_lower;
}
else
{
m_list_max = node->m_list_lower;
}
}
return node;
}
// Rebalances the tree after insertion
void BalanceTreeAfterInsertion
(
Node *node
)
{
node->m_colour = Red;
while (node != m_tree_root && node->m_tree_parent->m_colour == Red)
{
if (node->m_tree_parent == node->m_tree_parent->m_tree_parent->m_tree_more)
{
Node
*uncle = node->m_tree_parent->m_tree_parent->m_tree_less;
if (uncle && uncle->m_colour == Red)
{
node->m_tree_parent->m_colour = Black;
uncle->m_colour = Black;
node->m_tree_parent->m_tree_parent->m_colour = Red;
node = node->m_tree_parent->m_tree_parent;
}
else
{
if (node == node->m_tree_parent->m_tree_less)
{
node = node->m_tree_parent;
LeftRotate (node);
}
node->m_tree_parent->m_colour = Black;
node->m_tree_parent->m_tree_parent->m_colour = Red;
RightRotate (node->m_tree_parent->m_tree_parent);
}
}
else
{
Node
*uncle = node->m_tree_parent->m_tree_parent->m_tree_more;
if (uncle && uncle->m_colour == Red)
{
node->m_tree_parent->m_colour = Black;
uncle->m_colour = Black;
node->m_tree_parent->m_tree_parent->m_colour = Red;
node = node->m_tree_parent->m_tree_parent;
}
else
{
if (node == node->m_tree_parent->m_tree_more)
{
node = node->m_tree_parent;
RightRotate (node);
}
node->m_tree_parent->m_colour = Black;
node->m_tree_parent->m_tree_parent->m_colour = Red;
LeftRotate (node->m_tree_parent->m_tree_parent);
}
}
}
}
// Adds a node into the tree and sorted linked list
void InsertNodeIntoTree
(
Node *node
)
{
Node
*parent = 0,
*child = m_tree_root;
bool
greater;
while (child)
{
parent = child;
child = (greater = node->m_value > child->m_value) ? child->m_tree_more : child->m_tree_less;
}
node->m_tree_parent = parent;
if (greater)
{
parent->m_tree_more = node;
// insert node into linked list
if (parent->m_list_greater)
{
parent->m_list_greater->m_list_lower = node;
}
else
{
m_list_max = node;
}
node->m_list_greater = parent->m_list_greater;
node->m_list_lower = parent;
parent->m_list_greater = node;
}
else
{
parent->m_tree_less = node;
// insert node into linked list
if (parent->m_list_lower)
{
parent->m_list_lower->m_list_greater = node;
}
else
{
m_list_min = node;
}
node->m_list_lower = parent->m_list_lower;
node->m_list_greater = parent;
parent->m_list_lower = node;
}
}
// Red/Black tree manipulation routine, used for removing a node
Node *RemoveNodeFromTree
(
Node *node
)
{
if (node->m_tree_less && node->m_tree_more)
{
// the complex case, swap node with a child node
Node
*child;
if (node->m_tree_less)
{
// find largest value in lesser half (node with no greater pointer)
for (child = node->m_tree_less ; child->m_tree_more ; child = child->m_tree_more)
{
}
}
else
{
// find smallest value in greater half (node with no lesser pointer)
for (child = node->m_tree_more ; child->m_tree_less ; child = child->m_tree_less)
{
}
}
swap (child->m_colour, node->m_colour);
if (child->m_tree_parent != node)
{
swap (child->m_tree_less, node->m_tree_less);
swap (child->m_tree_more, node->m_tree_more);
swap (child->m_tree_parent, node->m_tree_parent);
if (!child->m_tree_parent)
{
m_tree_root = child;
}
else
{
if (child->m_tree_parent->m_tree_less == node)
{
child->m_tree_parent->m_tree_less = child;
}
else
{
child->m_tree_parent->m_tree_more = child;
}
}
if (node->m_tree_parent->m_tree_less == child)
{
node->m_tree_parent->m_tree_less = node;
}
else
{
node->m_tree_parent->m_tree_more = node;
}
}
else
{
child->m_tree_parent = node->m_tree_parent;
node->m_tree_parent = child;
Node
*child_less = child->m_tree_less,
*child_more = child->m_tree_more;
if (node->m_tree_less == child)
{
child->m_tree_less = node;
child->m_tree_more = node->m_tree_more;
node->m_tree_less = child_less;
node->m_tree_more = child_more;
}
else
{
child->m_tree_less = node->m_tree_less;
child->m_tree_more = node;
node->m_tree_less = child_less;
node->m_tree_more = child_more;
}
if (!child->m_tree_parent)
{
m_tree_root = child;
}
else
{
if (child->m_tree_parent->m_tree_less == node)
{
child->m_tree_parent->m_tree_less = child;
}
else
{
child->m_tree_parent->m_tree_more = child;
}
}
}
if (child->m_tree_less)
{
child->m_tree_less->m_tree_parent = child;
}
if (child->m_tree_more)
{
child->m_tree_more->m_tree_parent = child;
}
if (node->m_tree_less)
{
node->m_tree_less->m_tree_parent = node;
}
if (node->m_tree_more)
{
node->m_tree_more->m_tree_parent = node;
}
}
Node
*child = node->m_tree_less ? node->m_tree_less : node->m_tree_more;
if (node->m_tree_parent->m_tree_less == node)
{
node->m_tree_parent->m_tree_less = child;
}
else
{
node->m_tree_parent->m_tree_more = child;
}
if (child)
{
child->m_tree_parent = node->m_tree_parent;
}
return node;
}
// Red/Black tree manipulation routine, used for rebalancing a tree after a deletion
void RebalanceTreeAfterDeletion
(
Node *node
)
{
Node
*child = node->m_tree_less ? node->m_tree_less : node->m_tree_more;
if (node->m_colour == Black)
{
if (child && child->m_colour == Red)
{
child->m_colour = Black;
}
else
{
Node
*parent = node->m_tree_parent,
*n = child;
while (parent)
{
Node
*sibling = n->Sibling (parent);
if (sibling && sibling->m_colour == Red)
{
parent->m_colour = Red;
sibling->m_colour = Black;
if (n == parent->m_tree_more)
{
LeftRotate (parent);
}
else
{
RightRotate (parent);
}
}
sibling = n->Sibling (parent);
if (parent->m_colour == Black &&
sibling->m_colour == Black &&
(!sibling->m_tree_more || sibling->m_tree_more->m_colour == Black) &&
(!sibling->m_tree_less || sibling->m_tree_less->m_colour == Black))
{
sibling->m_colour = Red;
n = parent;
parent = n->m_tree_parent;
continue;
}
else
{
if (parent->m_colour == Red &&
sibling->m_colour == Black &&
(!sibling->m_tree_more || sibling->m_tree_more->m_colour == Black) &&
(!sibling->m_tree_less || sibling->m_tree_less->m_colour == Black))
{
sibling->m_colour = Red;
parent->m_colour = Black;
break;
}
else
{
if (n == parent->m_tree_more &&
sibling->m_colour == Black &&
(sibling->m_tree_more && sibling->m_tree_more->m_colour == Red) &&
(!sibling->m_tree_less || sibling->m_tree_less->m_colour == Black))
{
sibling->m_colour = Red;
sibling->m_tree_more->m_colour = Black;
RightRotate (sibling);
}
else
{
if (n == parent->m_tree_less &&
sibling->m_colour == Black &&
(!sibling->m_tree_more || sibling->m_tree_more->m_colour == Black) &&
(sibling->m_tree_less && sibling->m_tree_less->m_colour == Red))
{
sibling->m_colour = Red;
sibling->m_tree_less->m_colour = Black;
LeftRotate (sibling);
}
}
sibling = n->Sibling (parent);
sibling->m_colour = parent->m_colour;
parent->m_colour = Black;
if (n == parent->m_tree_more)
{
sibling->m_tree_less->m_colour = Black;
LeftRotate (parent);
}
else
{
sibling->m_tree_more->m_colour = Black;
RightRotate (parent);
}
break;
}
}
}
}
}
}
// Red/Black tree manipulation routine, used for balancing the tree
void LeftRotate
(
Node *node
)
{
Node
*less = node->m_tree_less;
node->m_tree_less = less->m_tree_more;
if (less->m_tree_more)
{
less->m_tree_more->m_tree_parent = node;
}
less->m_tree_parent = node->m_tree_parent;
if (!node->m_tree_parent)
{
m_tree_root = less;
}
else
{
if (node == node->m_tree_parent->m_tree_more)
{
node->m_tree_parent->m_tree_more = less;
}
else
{
node->m_tree_parent->m_tree_less = less;
}
}
less->m_tree_more = node;
node->m_tree_parent = less;
}
// Red/Black tree manipulation routine, used for balancing the tree
void RightRotate
(
Node *node
)
{
Node
*more = node->m_tree_more;
node->m_tree_more = more->m_tree_less;
if (more->m_tree_less)
{
more->m_tree_less->m_tree_parent = node;
}
more->m_tree_parent = node->m_tree_parent;
if (!node->m_tree_parent)
{
m_tree_root = more;
}
else
{
if (node == node->m_tree_parent->m_tree_less)
{
node->m_tree_parent->m_tree_less = more;
}
else
{
node->m_tree_parent->m_tree_more = more;
}
}
more->m_tree_less = node;
node->m_tree_parent = more;
}
// Member Data.
Node
*m_nodes,
*m_queue_tail,
*m_queue_head,
*m_tree_root,
*m_list_min,
*m_list_max,
*m_free_list;
};
// A complex but more efficent method of calculating the results.
// Memory management is done here outside of the timing portion.
clock_t Complex
(
int count,
int window,
GeneratorCallback input,
OutputCallback output
)
{
Range <int>
range (window);
clock_t
start = clock ();
for (int i = 0 ; i < count ; ++i)
{
range.AddValue (input ());
if (range.RangeAvailable ())
{
output (range.Min (), range.Max ());
}
}
clock_t
end = clock ();
return end - start;
}
Idea of algorithm:
Take the first 1000 values of data and sort them
The last in the sort - the first is range(data + 0, data + 999).
Then remove from the sort pile the first element with the value data[0]
and add the element data[1000]
Now, the last in the sort - the first is range(data + 1, data + 1000).
Repeat until done
// This should run in (DATA_LEN - RANGE_WIDTH)log(RANGE_WIDTH)
#include <set>
#include <algorithm>
using namespace std;
const int DATA_LEN = 3600000;
double* const data = new double (DATA_LEN);
....
....
const int RANGE_WIDTH = 1000;
double range = new double(DATA_LEN - RANGE_WIDTH);
multiset<double> data_set;
data_set.insert(data[i], data[RANGE_WIDTH]);
for (int i = 0 ; i < DATA_LEN - RANGE_WIDTH - 1 ; i++)
{
range[i] = *data_set.end() - *data_set.begin();
multiset<double>::iterator iter = data_set.find(data[i]);
data_set.erase(iter);
data_set.insert(data[i+1]);
}
range[i] = *data_set.end() - *data_set.begin();
// range now holds the values you seek
You should probably check this for off by 1 errors, but the idea is there.