edgepair getMinEdge(graph &g) // iterate through whole graph and finds the edge from // marked node to unmarked node with minimum weight // returns a struct with marked, unmarked, and weight { int minCost = HIGH; int marked = NONE; int unmarked = NONE; // find the minimum edge for (int i = 0; i < g.numNodes() ; i++) { if (g.isMarked(i)) { for (int j = 0; j < g.numNodes(); j++) { if (!g.isMarked(j) && g.isEdge(i, j) && g.getEdgeWeight(i, j) < minCost) { minCost = g.getEdgeWeight(i,j); marked = i; unmarked = j; } } } } edgepair pair = {marked, unmarked, minCost}; return pair; }
void findSpanningForest(graph &g, graph &sf) // Create a graph sf that contains a spanning forest on the graph g. { if (isConnected(g) && !isCyclic(g)) { sf = g; } else { // add nodes to sf for (int i = 0; i < g.numNodes(); i++) { sf.addNode(g.getNode(i)); } // build sf for (int i = 0; i < g.numNodes(); i++) { for (int j = 0; j < g.numNodes(); j++) { if (g.isEdge(i, j) && !sf.isEdge(i, j)) { sf.addEdge(i, j, g.getEdgeWeight(i, j)); sf.addEdge(j, i, g.getEdgeWeight(j, i)); if(isCyclic(sf)) { sf.removeEdge(j, i); sf.removeEdge(i, j); } // if } // if } // for } // for } // else } // findSpanningForest
void kruskal(graph &g, graph &sf) // Given a weighted graph g, sets sf equal to a minimum spanning // forest on g. Uses Kruskal's algorithm. { g.clearMark(); g.clearVisit(); numComponents=0; while(!g.allNodesVisited()) { // find the smallest edge int smallestEdgeWeight = -1; int smallestEdgeBeg = -1; int smallestEdgeEnd = -1; for(int i = 0; i < g.numNodes(); i++) { for(int j = 0; j < g.numNodes(); j++) { if(g.isEdge(i, j) && !g.isVisited(i, j) && !g.isVisited(j, i) && (!g.isVisited(i) || !g.isVisited(j))) { if(g.getEdgeWeight(i, j) < smallestEdgeWeight || smallestEdgeWeight == -1) { smallestEdgeWeight = g.getEdgeWeight(i, j); smallestEdgeBeg = i; smallestEdgeEnd = j; } } } } // add the new edge g.visit(smallestEdgeBeg); g.visit(smallestEdgeEnd); g.visit(smallestEdgeBeg, smallestEdgeEnd); sf.addEdge(smallestEdgeBeg, smallestEdgeEnd); sf.setEdgeWeight(smallestEdgeBeg, smallestEdgeEnd, smallestEdgeWeight); } numComponents = getNumComponents(sf); }
void prim(graph &g, graph &sf) // Given a weighted graph g, sets sf equal to a minimum spanning // forest on g. Uses Prim's algorithm. { g.clearMark(); g.clearVisit(); numComponents=0; int currentNode = 0; while(!g.allNodesVisited()) { // find next currentNode while(g.isVisited(currentNode) && currentNode < g.numNodes()) { currentNode++; } g.visit(currentNode); int smallestEdgeWeight = -1; int smallestEdgeNode = -1; // find shortest new edge from currentNode for(int i = 0; i < g.numNodes(); i++) { if(g.isEdge(currentNode, i)) { if(g.getEdgeWeight(currentNode, i) < smallestEdgeWeight || smallestEdgeWeight == -1) { smallestEdgeWeight = g.getEdgeWeight(currentNode, i); smallestEdgeNode = i; } } } // add the new edge g.visit(smallestEdgeNode); sf.addEdge(currentNode, smallestEdgeNode); sf.setEdgeWeight(currentNode, smallestEdgeNode, smallestEdgeWeight); } numComponents = getNumComponents(sf); }
void dfsAddEdges(graph &g, int current, graph &sf) // depth first search to visit all nodes and add edges to unvisited nodes { g.visit(current); vector<int> neighbors = getNeighbors(g, current); for (int i = 0; i < (int) neighbors.size(); i++) { if (!g.isVisited(neighbors[i])) { sf.addEdge(current, neighbors[i], g.getEdgeWeight(current, neighbors[i])); sf.addEdge(neighbors[i], current, g.getEdgeWeight(neighbors[i], current)); dfsAddEdges(g, neighbors[i], sf); } } }
void findSpanningForest(graph &g, graph &sf) // Create a graph sf that contains a spanning forest on the graph g. { queue<int> que; int id=0,count=1; bool first=true; vector<int> parentCount(g.numNodes(),-1); que.push(id); g.visit(id); while(count<g.numNodes() || !que.empty()) { if (que.empty()) { id=count; que.push(id); g.visit(id); count++; } else id=que.front(); for(int i=0;i<g.numNodes();i++) { if (g.isEdge(id,i) && i!=que.front()) { if(!g.isVisited(i) && parentCount[id]!=i) { g.visit(i); sf.addEdge(id,i,g.getEdgeWeight(i,id)); sf.addEdge(i,id,g.getEdgeWeight(i,id)); que.push(i); count++; parentCount[id]++; } } } que.pop(); } for (int z=0;z<g.numNodes();z++) g.unVisit(z); }
pqueue getEdges(graph &g) // iterate through graph and construct a priority queue with minimum cost // only add an edgepair for edge between marked node and unmarked node { pqueue edges; for (int i = 0; i < g.numNodes(); i++) { g.mark(i); for (int j = 0; j < g.numNodes(); j++) { if (g.isMarked(i) && !g.isMarked(j) && g.isEdge(i, j)) { edgepair pair = {i, j, g.getEdgeWeight(i, j)}; edges.push(pair); } } } return edges; }
void findSpanningForest(graph &g, graph &sf) // Create a graph sf that contains a spanning forest on the graph g. { g.clearMark(); g.clearVisit(); numComponents=0; queue<int> currentMoves; for (int n=0;n<g.numNodes();n++) { if (!g.isVisited(n)) { numComponents++; int nodeNumber=n; g.visit(nodeNumber); currentMoves.push(nodeNumber); while(currentMoves.size() > 0) { int currentNode = currentMoves.front(); currentMoves.pop(); //Populate a list of nodes that can be visited for (int i=0;i<g.numNodes();i++) { if (g.isEdge(currentNode,i) && !g.isVisited(i)) { g.mark(currentNode,i); sf.addEdge(currentNode,i); sf.setEdgeWeight(currentNode, i, g.getEdgeWeight(currentNode, i)); g.visit(i); currentMoves.push(i); } } } } } }
void prim(graph &g, graph &sf) // Given a weighted graph g, sets sf equal to a minimum spanning // forest on g. Uses Prim's algorithm. { NodeWeight minWeight = 0; NodeWeight minR, minP; bool edgeFound; g.clearMark(); for(int i=0; i<g.numNodes(); i++) { if(!g.isMarked(i)) { g.mark(i); for(int j=0; j<g.numNodes()-1; j++) //start at i and grow a spanning tree untill no more can be added { edgeFound = false; minWeight = MaxEdgeWeight; for(int r=0; r<g.numNodes(); r++) { for(int p=0; p<g.numNodes(); p++) { if(g.isEdge(r,p) && g.isMarked(r) && !g.isMarked(p)) { if(g.getEdgeWeight(r,p) < minWeight) { minWeight = g.getEdgeWeight(r,p); minR= r; minP= p; edgeFound = true; } } } } //if edge was found add it to the tree if(edgeFound) { g.mark(minR,minP); g.mark(minP, minR); g.mark(minP); } } } } //add marked edges to spanning forest graph for(int i=0; i<g.numNodes(); i++) { for(int j=i+1; j<g.numNodes(); j++) { if(g.isEdge(i,j) && g.isMarked(i,j)) { sf.addEdge(i,j,g.getEdgeWeight(i,j)); sf.addEdge(j,i,g.getEdgeWeight(j,i)); cout<<"adding edge "<< i << " "<< j << endl; cout<<"num edges: "<<sf.numEdges() << endl; } } } }