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
int getNumComponents(graph &g)
{
g.clearMark();
g.clearVisit();
int 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);
g.visit(i);
currentMoves.push(i);
}
}
}
}
}
return numComponents;
}
bool isConnected(graph &g)
// Returns true if the graph g is connected. Otherwise returns false.
{
queue<int> que;
int id=0,count=1;
que.push(id);
g.visit(id);
while(count<g.numNodes() && !que.empty())
{
id=que.front();
for(int i=0;i<g.numNodes();i++)
{
if (g.isEdge(id,i) && !g.isVisited(i))
{
g.visit(i);
que.push(i);
count++;
}
}
que.pop();
}
for (int z=0;z<g.numNodes();z++)
g.unVisit(z);
if(count==g.numNodes())
return true;
else return false;
}
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 findMSF(graph &g, graph &sf, int start)
// finds a minimum spanning tree in graph 'g'
{
priority_queue<edge, vector<edge>, CompareEdge> pq;
vector<int> lst = getNeighbors(start, g);
// build our priority queue
for (int i = 0; i < lst.size(); i++)
{
pq.push(g.getEdge(start, lst[i]));
g.mark(start, lst[i]);
}
// visit the start node
g.visit(start);
int src, dst, w;
edge top;
while (!pq.empty())
{
top = pq.top();
pq.pop();
src = top.getSource();
dst = top.getDest();
w = top.getWeight();
// add edges
if (!sf.isEdge(src, dst))
{
sf.addEdge(src, dst, w);
sf.addEdge(dst, src, w);
// delete edges if we make a cycle
if (isCyclic(sf))
{
sf.removeEdge(src, dst);
sf.removeEdge(dst, src);
}
else
{
g.visit(src);
lst = getNeighbors(dst, g);
for (int i = 0; i < lst.size(); i++)
{
if (!g.isMarked(dst, lst[i]))
{
pq.push(g.getEdge(dst, lst[i]));
g.mark(dst, lst[i]);
}
} // for
} // else
} // if
} // while
} // findMSF
vector<int> getNeighbors(graph &g, int current)
// loops through nodes and check if there is an edge between
// current and node, returns a vector of neighboring nodes
{
vector<int> neighbors;
for (int i = 0; i < g.numNodes(); i++)
{
if (g.isEdge(current, i))
neighbors.push_back(i);
}
return neighbors;
}
bool isCyclic(graph &g)
// Returns true if the graph g contains a cycle. Otherwise, returns false.
{
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))
{
g.visit(i);
que.push(i);
count++;
parentCount[i]=id;
}
else if(parentCount[id]==i)
continue;
else
{
for (int z=0;z<g.numNodes();z++)
g.unVisit(z);
return true;
}
}
}
que.pop();
}
for (int z=0;z<g.numNodes();z++)
g.unVisit(z);
return false;
}
vector<int> getNeighbors(int id, graph &g)
// get all neighbors of the node (id) in the graph (g)
{
vector<int> lst;
for (int i = 0; i < g.numNodes(); i++)
{
if (g.isEdge(id, i))
{
lst.push_back(i);
}
} // for
return lst;
} // getNeighbors
vector<int> getNeighbors(int id, graph &g)
// get all neighbors of the node with given id in graph g
{
vector<int> lst;
for (int i = 0; i < g.numNodes(); i++)
{
if (g.isEdge(id, i))
{
lst.push_back(i);
}
}
return lst;
}
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);
}
bool isCyclic(graph &g,int nodeNumber)
// Returns true if the graph g contains a cycle. Otherwise, returns false.
{
if (g.isVisited(nodeNumber))
{
return true;
}
//Visit the node
g.visit(nodeNumber);
for (int i=0;i<g.numNodes();i++)
{
if (g.isEdge(nodeNumber,i))
{
return isCyclic(g,i);
}
}
return false;
}
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 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);
}
// Helper Functions
void visitNodes(int start, graph &g)
// Visit all nodes reachable from the start node
{
bool found = false;
// Mark the start node as visited.
g.visit(start);
int v = 0;
// Keep looking for legal moves as long as there are more neighbors
// to check.
while (!found && v < g.numNodes())
{
// if v is an unvisited neighbor of the start node, recurse.
if (g.isEdge(start, v) && !g.isVisited(v))
{
visitNodes(v, g);
}
v++;
}
} // visitNodes
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;
}
}
}
}
