예제 #1
0
void AdjecencyList::Kruskals() {
    vector<Edge> path; //the minimal spanning tree of the graph

    //sort the edges in the graph, since Kruskals cannot do directed graphs, make
    //sure the input file was made as such (it will not crash, just not account extra edges
    EdgeSort(EdgeRef);

    for(int i = 0; i < EdgeRef.size(); i++) {
        //to check if there is a cycle, I will test for it by seeing if both of sides of the new
        //edge is within the current minimal spanning tree
        bool firstMatch = false; //source is already in path
        bool secondMatch = false; //target is already in path
        for(int j = 0; j < path.size(); j++) {
            //source check
            if (EdgeRef[i].source == path[j].source || EdgeRef[i].source == path[j].target) {
                firstMatch = true;
            }
            //target check
            if (EdgeRef[i].target == path[j].source || EdgeRef[i].target == path[j].target) {
                secondMatch = true;
            }
        }
        //only one or both verticies exist at the moment, adding that edge is legal
        if (!firstMatch || !secondMatch) {
            path.push_back(EdgeRef[i]);
        }
    }

    cout << "Kruskal's Algorithm: " << endl;
    //print out the path
    for (int i = 0; i < path.size(); i++) {
        cout << path[i].source.value << " -" << path[i].weight << "- " << path[i].target.value << endl;
    }
} //do Kruskal's algorithm
예제 #2
0
void CCmpPathfinder::ComputeShortPath(const IObstructionTestFilter& filter,
	entity_pos_t x0, entity_pos_t z0, entity_pos_t r,
	entity_pos_t range, const Goal& goal, pass_class_t passClass, Path& path)
{
	UpdateGrid(); // TODO: only need to bother updating if the terrain changed

	PROFILE("ComputeShortPath");
//	ScopeTimer UID__(L"ComputeShortPath");

	m_DebugOverlayShortPathLines.clear();

	if (m_DebugOverlay)
	{
		// Render the goal shape
		m_DebugOverlayShortPathLines.push_back(SOverlayLine());
		m_DebugOverlayShortPathLines.back().m_Color = CColor(1, 0, 0, 1);
		switch (goal.type)
		{
		case CCmpPathfinder::Goal::POINT:
		{
			SimRender::ConstructCircleOnGround(GetSimContext(), goal.x.ToFloat(), goal.z.ToFloat(), 0.2f, m_DebugOverlayShortPathLines.back(), true);
			break;
		}
		case CCmpPathfinder::Goal::CIRCLE:
		{
			SimRender::ConstructCircleOnGround(GetSimContext(), goal.x.ToFloat(), goal.z.ToFloat(), goal.hw.ToFloat(), m_DebugOverlayShortPathLines.back(), true);
			break;
		}
		case CCmpPathfinder::Goal::SQUARE:
		{
			float a = atan2f(goal.v.X.ToFloat(), goal.v.Y.ToFloat());
			SimRender::ConstructSquareOnGround(GetSimContext(), goal.x.ToFloat(), goal.z.ToFloat(), goal.hw.ToFloat()*2, goal.hh.ToFloat()*2, a, m_DebugOverlayShortPathLines.back(), true);
			break;
		}
		}
	}

	// List of collision edges - paths must never cross these.
	// (Edges are one-sided so intersections are fine in one direction, but not the other direction.)
	std::vector<Edge> edges;
	std::vector<Edge> edgesAA; // axis-aligned squares

	// Create impassable edges at the max-range boundary, so we can't escape the region
	// where we're meant to be searching
	fixed rangeXMin = x0 - range;
	fixed rangeXMax = x0 + range;
	fixed rangeZMin = z0 - range;
	fixed rangeZMax = z0 + range;
	{
		// (The edges are the opposite direction to usual, so it's an inside-out square)
		Edge e0 = { CFixedVector2D(rangeXMin, rangeZMin), CFixedVector2D(rangeXMin, rangeZMax) };
		Edge e1 = { CFixedVector2D(rangeXMin, rangeZMax), CFixedVector2D(rangeXMax, rangeZMax) };
		Edge e2 = { CFixedVector2D(rangeXMax, rangeZMax), CFixedVector2D(rangeXMax, rangeZMin) };
		Edge e3 = { CFixedVector2D(rangeXMax, rangeZMin), CFixedVector2D(rangeXMin, rangeZMin) };
		edges.push_back(e0);
		edges.push_back(e1);
		edges.push_back(e2);
		edges.push_back(e3);
	}

	// List of obstruction vertexes (plus start/end points); we'll try to find paths through
	// the graph defined by these vertexes
	std::vector<Vertex> vertexes;

	// Add the start point to the graph
	CFixedVector2D posStart(x0, z0);
	fixed hStart = (posStart - NearestPointOnGoal(posStart, goal)).Length();
	Vertex start = { posStart, fixed::Zero(), hStart, 0, Vertex::OPEN, QUADRANT_NONE, QUADRANT_ALL };
	vertexes.push_back(start);
	const size_t START_VERTEX_ID = 0;

	// Add the goal vertex to the graph.
	// Since the goal isn't always a point, this a special magic virtual vertex which moves around - whenever
	// we look at it from another vertex, it is moved to be the closest point on the goal shape to that vertex.
	Vertex end = { CFixedVector2D(goal.x, goal.z), fixed::Zero(), fixed::Zero(), 0, Vertex::UNEXPLORED, QUADRANT_NONE, QUADRANT_ALL };
	vertexes.push_back(end);
	const size_t GOAL_VERTEX_ID = 1;

	// Add terrain obstructions
	{
		u16 i0, j0, i1, j1;
		NearestTile(rangeXMin, rangeZMin, i0, j0);
		NearestTile(rangeXMax, rangeZMax, i1, j1);
		AddTerrainEdges(edgesAA, vertexes, i0, j0, i1, j1, r, passClass, *m_Grid);
	}

	// Find all the obstruction squares that might affect us
	CmpPtr<ICmpObstructionManager> cmpObstructionManager(GetSimContext(), SYSTEM_ENTITY);
	std::vector<ICmpObstructionManager::ObstructionSquare> squares;
	cmpObstructionManager->GetObstructionsInRange(filter, rangeXMin - r, rangeZMin - r, rangeXMax + r, rangeZMax + r, squares);

	// Resize arrays to reduce reallocations
	vertexes.reserve(vertexes.size() + squares.size()*4);
	edgesAA.reserve(edgesAA.size() + squares.size()); // (assume most squares are AA)

	// Convert each obstruction square into collision edges and search graph vertexes
	for (size_t i = 0; i < squares.size(); ++i)
	{
		CFixedVector2D center(squares[i].x, squares[i].z);
		CFixedVector2D u = squares[i].u;
		CFixedVector2D v = squares[i].v;

		// Expand the vertexes by the moving unit's collision radius, to find the
		// closest we can get to it

		CFixedVector2D hd0(squares[i].hw + r + EDGE_EXPAND_DELTA, squares[i].hh + r + EDGE_EXPAND_DELTA);
		CFixedVector2D hd1(squares[i].hw + r + EDGE_EXPAND_DELTA, -(squares[i].hh + r + EDGE_EXPAND_DELTA));

		// Check whether this is an axis-aligned square
		bool aa = (u.X == fixed::FromInt(1) && u.Y == fixed::Zero() && v.X == fixed::Zero() && v.Y == fixed::FromInt(1));

		Vertex vert;
		vert.status = Vertex::UNEXPLORED;
		vert.quadInward = QUADRANT_NONE;
		vert.quadOutward = QUADRANT_ALL;
		vert.p.X = center.X - hd0.Dot(u); vert.p.Y = center.Y + hd0.Dot(v); if (aa) vert.quadInward = QUADRANT_BR; vertexes.push_back(vert);
		vert.p.X = center.X - hd1.Dot(u); vert.p.Y = center.Y + hd1.Dot(v); if (aa) vert.quadInward = QUADRANT_TR; vertexes.push_back(vert);
		vert.p.X = center.X + hd0.Dot(u); vert.p.Y = center.Y - hd0.Dot(v); if (aa) vert.quadInward = QUADRANT_TL; vertexes.push_back(vert);
		vert.p.X = center.X + hd1.Dot(u); vert.p.Y = center.Y - hd1.Dot(v); if (aa) vert.quadInward = QUADRANT_BL; vertexes.push_back(vert);

		// Add the edges:

		CFixedVector2D h0(squares[i].hw + r, squares[i].hh + r);
		CFixedVector2D h1(squares[i].hw + r, -(squares[i].hh + r));

		CFixedVector2D ev0(center.X - h0.Dot(u), center.Y + h0.Dot(v));
		CFixedVector2D ev1(center.X - h1.Dot(u), center.Y + h1.Dot(v));
		CFixedVector2D ev2(center.X + h0.Dot(u), center.Y - h0.Dot(v));
		CFixedVector2D ev3(center.X + h1.Dot(u), center.Y - h1.Dot(v));
		if (aa)
		{
			Edge e = { ev1, ev3 };
			edgesAA.push_back(e);
		}
		else
		{
			Edge e0 = { ev0, ev1 };
			Edge e1 = { ev1, ev2 };
			Edge e2 = { ev2, ev3 };
			Edge e3 = { ev3, ev0 };
			edges.push_back(e0);
			edges.push_back(e1);
			edges.push_back(e2);
			edges.push_back(e3);
		}

		// TODO: should clip out vertexes and edges that are outside the range,
		// to reduce the search space
	}

	ENSURE(vertexes.size() < 65536); // we store array indexes as u16

	if (m_DebugOverlay)
	{
		// Render the obstruction edges
		for (size_t i = 0; i < edges.size(); ++i)
		{
			m_DebugOverlayShortPathLines.push_back(SOverlayLine());
			m_DebugOverlayShortPathLines.back().m_Color = CColor(0, 1, 1, 1);
			std::vector<float> xz;
			xz.push_back(edges[i].p0.X.ToFloat());
			xz.push_back(edges[i].p0.Y.ToFloat());
			xz.push_back(edges[i].p1.X.ToFloat());
			xz.push_back(edges[i].p1.Y.ToFloat());
			SimRender::ConstructLineOnGround(GetSimContext(), xz, m_DebugOverlayShortPathLines.back(), true);
		}

		for (size_t i = 0; i < edgesAA.size(); ++i)
		{
			m_DebugOverlayShortPathLines.push_back(SOverlayLine());
			m_DebugOverlayShortPathLines.back().m_Color = CColor(0, 1, 1, 1);
			std::vector<float> xz;
			xz.push_back(edgesAA[i].p0.X.ToFloat());
			xz.push_back(edgesAA[i].p0.Y.ToFloat());
			xz.push_back(edgesAA[i].p0.X.ToFloat());
			xz.push_back(edgesAA[i].p1.Y.ToFloat());
			xz.push_back(edgesAA[i].p1.X.ToFloat());
			xz.push_back(edgesAA[i].p1.Y.ToFloat());
			xz.push_back(edgesAA[i].p1.X.ToFloat());
			xz.push_back(edgesAA[i].p0.Y.ToFloat());
			xz.push_back(edgesAA[i].p0.X.ToFloat());
			xz.push_back(edgesAA[i].p0.Y.ToFloat());
			SimRender::ConstructLineOnGround(GetSimContext(), xz, m_DebugOverlayShortPathLines.back(), true);
		}
	}

	// Do an A* search over the vertex/visibility graph:

	// Since we are just measuring Euclidean distance the heuristic is admissible,
	// so we never have to re-examine a node once it's been moved to the closed set.

	// To save time in common cases, we don't precompute a graph of valid edges between vertexes;
	// we do it lazily instead. When the search algorithm reaches a vertex, we examine every other
	// vertex and see if we can reach it without hitting any collision edges, and ignore the ones
	// we can't reach. Since the algorithm can only reach a vertex once (and then it'll be marked
	// as closed), we won't be doing any redundant visibility computations.

	PROFILE_START("A*");

	PriorityQueue open;
	PriorityQueue::Item qiStart = { START_VERTEX_ID, start.h };
	open.push(qiStart);

	u16 idBest = START_VERTEX_ID;
	fixed hBest = start.h;

	while (!open.empty())
	{
		// Move best tile from open to closed
		PriorityQueue::Item curr = open.pop();
		vertexes[curr.id].status = Vertex::CLOSED;

		// If we've reached the destination, stop
		if (curr.id == GOAL_VERTEX_ID)
		{
			idBest = curr.id;
			break;
		}

		// Sort the edges so ones nearer this vertex are checked first by CheckVisibility,
		// since they're more likely to block the rays
		std::sort(edgesAA.begin(), edgesAA.end(), EdgeSort(vertexes[curr.id].p));

		std::vector<EdgeAA> edgesLeft;
		std::vector<EdgeAA> edgesRight;
		std::vector<EdgeAA> edgesBottom;
		std::vector<EdgeAA> edgesTop;
		SplitAAEdges(vertexes[curr.id].p, edgesAA, edgesLeft, edgesRight, edgesBottom, edgesTop);

		// Check the lines to every other vertex
		for (size_t n = 0; n < vertexes.size(); ++n)
		{
			if (vertexes[n].status == Vertex::CLOSED)
				continue;

			// If this is the magical goal vertex, move it to near the current vertex
			CFixedVector2D npos;
			if (n == GOAL_VERTEX_ID)
			{
				npos = NearestPointOnGoal(vertexes[curr.id].p, goal);

				// To prevent integer overflows later on, we need to ensure all vertexes are
				// 'close' to the source. The goal might be far away (not a good idea but
				// sometimes it happens), so clamp it to the current search range
				npos.X = clamp(npos.X, rangeXMin, rangeXMax);
				npos.Y = clamp(npos.Y, rangeZMin, rangeZMax);
			}
			else
			{
				npos = vertexes[n].p;
			}

			// Work out which quadrant(s) we're approaching the new vertex from
			u8 quad = 0;
			if (vertexes[curr.id].p.X <= npos.X && vertexes[curr.id].p.Y <= npos.Y) quad |= QUADRANT_BL;
			if (vertexes[curr.id].p.X >= npos.X && vertexes[curr.id].p.Y >= npos.Y) quad |= QUADRANT_TR;
			if (vertexes[curr.id].p.X <= npos.X && vertexes[curr.id].p.Y >= npos.Y) quad |= QUADRANT_TL;
			if (vertexes[curr.id].p.X >= npos.X && vertexes[curr.id].p.Y <= npos.Y) quad |= QUADRANT_BR;

			// Check that the new vertex is in the right quadrant for the old vertex
			if (!(vertexes[curr.id].quadOutward & quad))
			{
				// Hack: Always head towards the goal if possible, to avoid missing it if it's
				// inside another unit
				if (n != GOAL_VERTEX_ID)
				{
					continue;
				}
			}

			bool visible =
				CheckVisibilityLeft(vertexes[curr.id].p, npos, edgesLeft) &&
				CheckVisibilityRight(vertexes[curr.id].p, npos, edgesRight) &&
				CheckVisibilityBottom(vertexes[curr.id].p, npos, edgesBottom) &&
				CheckVisibilityTop(vertexes[curr.id].p, npos, edgesTop) &&
				CheckVisibility(vertexes[curr.id].p, npos, edges);

			/*
			// Render the edges that we examine
			m_DebugOverlayShortPathLines.push_back(SOverlayLine());
			m_DebugOverlayShortPathLines.back().m_Color = visible ? CColor(0, 1, 0, 0.5) : CColor(1, 0, 0, 0.5);
			std::vector<float> xz;
			xz.push_back(vertexes[curr.id].p.X.ToFloat());
			xz.push_back(vertexes[curr.id].p.Y.ToFloat());
			xz.push_back(npos.X.ToFloat());
			xz.push_back(npos.Y.ToFloat());
			SimRender::ConstructLineOnGround(GetSimContext(), xz, m_DebugOverlayShortPathLines.back(), false);
			//*/

			if (visible)
			{
				fixed g = vertexes[curr.id].g + (vertexes[curr.id].p - npos).Length();

				// If this is a new tile, compute the heuristic distance
				if (vertexes[n].status == Vertex::UNEXPLORED)
				{
					// Add it to the open list:
					vertexes[n].status = Vertex::OPEN;
					vertexes[n].g = g;
					vertexes[n].h = DistanceToGoal(npos, goal);
					vertexes[n].pred = curr.id;

					// If this is an axis-aligned shape, the path must continue in the same quadrant
					// direction (but not go into the inside of the shape).
					// Hack: If we started *inside* a shape then perhaps headed to its corner (e.g. the unit
					// was very near another unit), don't restrict further pathing.
					if (vertexes[n].quadInward && !(curr.id == START_VERTEX_ID && g < fixed::FromInt(8)))
						vertexes[n].quadOutward = ((~vertexes[n].quadInward) & quad) & 0xF;

					if (n == GOAL_VERTEX_ID)
						vertexes[n].p = npos; // remember the new best goal position

					PriorityQueue::Item t = { (u16)n, g + vertexes[n].h };
					open.push(t);

					// Remember the heuristically best vertex we've seen so far, in case we never actually reach the target
					if (vertexes[n].h < hBest)
					{
						idBest = (u16)n;
						hBest = vertexes[n].h;
					}
				}
				else // must be OPEN
				{
					// If we've already seen this tile, and the new path to this tile does not have a
					// better cost, then stop now
					if (g >= vertexes[n].g)
						continue;

					// Otherwise, we have a better path, so replace the old one with the new cost/parent
					vertexes[n].g = g;
					vertexes[n].pred = curr.id;

					// If this is an axis-aligned shape, the path must continue in the same quadrant
					// direction (but not go into the inside of the shape).
					if (vertexes[n].quadInward)
						vertexes[n].quadOutward = ((~vertexes[n].quadInward) & quad) & 0xF;

					if (n == GOAL_VERTEX_ID)
						vertexes[n].p = npos; // remember the new best goal position

					open.promote((u16)n, g + vertexes[n].h);
				}
			}
		}
	}

	// Reconstruct the path (in reverse)
	for (u16 id = idBest; id != START_VERTEX_ID; id = vertexes[id].pred)
	{
		Waypoint w = { vertexes[id].p.X, vertexes[id].p.Y };
		path.m_Waypoints.push_back(w);
	}

	PROFILE_END("A*");
}