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;
}
void maze::findPathNonRecursive(graph &g)
// method for finding a path in the maze given a graph g representing the maze
// uses a stack based DFS
{
g.clearVisit();
g.clearMark();
int start = getMap(0, 0);
int end = getMap(numRows() - 1, numCols() - 1);
vector< stack<int> > rpaths = nonRecursiveDFS(start, end, g);
stack<int> reverse_path;
for(int i = 0; i < rpaths.size(); i++)
if (rpaths[i].size() > reverse_path.size())
reverse_path = rpaths[i];
stack<int> path;
while (!reverse_path.empty())
{
int top = reverse_path.top();
reverse_path.pop();
if (g.isVisited(top))
{
path.push(top);
}
}
printPath(path);
}
bool maze::findShortestPath1(graph &g)
//finds the shortest path in the given graph using DFS
{
g.clearVisit();
g.clearMark();
int start = getMap(0, 0);
int end = getMap(numRows() - 1, numCols() - 1);
vector< stack<int> > rpaths = nonRecursiveDFS(start, end, g);
stack<int> reverse_path;
for(int i = 0; i < rpaths.size(); i++)
if (rpaths[i].size() > reverse_path.size())
reverse_path = rpaths[i];
stack<int> path;
while (!reverse_path.empty())
{
int top = reverse_path.top();
reverse_path.pop();
if (g.isVisited(top))
{
path.push(top);
}
}
printPath(path);
}
// Project Functions
bool isCyclic(graph &g)
// Returns true if the graph g contains a cycle. Otherwise, returns false.
{
g.clearVisit();
g.clearMark();
bool cycle = false;
for (int i = 0; i < g.numNodes(); i++)
{
if (!g.isVisited(i))
findCycle(i, i, cycle, g);
}
g.clearMark();
g.clearVisit();
return cycle;
} // isCyclic
bool maze::findShortestPath2(graph &g)
// finds the shortest path in the given graph using BFS
{
g.clearVisit();
g.clearMark();
int start = getMap(0, 0);
int end = getMap(numRows() - 1, numCols() - 1);
stack<int> path = nonRecursiveBFS(start, end, g);
printPath(path);
}
void findSpanningForest(graph &g, graph &sf)
// Create a graph sf that contains a spanning forest on the graph g.
{
g.clearVisit();
// if a node is not visited, call dfsAddEdges on it
// to create a tree with the node as the start
for (int i = 0; i < sf.numNodes(); i++)
{
if (!sf.isVisited(i))
dfsAddEdges(g, i, sf);
}
}
bool isConnected(graph &g)
// Returns true if the graph g is connected. Otherwise returns false.
{
g.clearVisit();
int start = 0;
dfs(g, start);
for (int i = 0; i < g.numNodes(); i++)
{
if (!g.isVisited(i))
return false;
}
return true;
}
void maze::findPathRecursive(graph &g)
// method for finding a path in the maze given a graph g representing the maze
// uses recursion based DFS
{
g.clearVisit();
g.clearMark();
stack<int> path;
int start = getMap(0, 0);
int end = getMap(numRows() - 1, numCols() - 1);
bool done = false;
recursiveDFS(start, end, g, path, done);
printPath(path);
}
int numComponents(graph &sf)
// given a spanning forest, finds the number of trees,
// or connected components in that forest
{
int components = 0;
sf.clearVisit();
for (int i = 0; i < sf.numNodes(); i++)
{
if (!sf.isVisited(i))
{
dfs(sf, i);
components++;
}
}
return components;
}
bool isCyclic(graph &g)
// Returns true if the graph g contains a cycle. Otherwise, returns false.
// checks all spanning tree components in the graph
{
g.clearVisit();
int prev = NONE;
for (int i = 0; i < g.numNodes(); i++)
{
// if node is not visited, call traversal with it as the start
if (!g.isVisited(i) && dfsCyclic(g, i, prev))
return true;
}
return false;
}
bool isConnected(graph &g)
// Returns true if the graph g is connected. Otherwise returns false.
{
g.clearVisit();
g.clearMark();
visitNodes(0, g); // start at '0' the 'first' node
for (int i = 0; i < g.numNodes(); i++)
{
if (!g.isVisited(i))
{
return false;
}
} // for
return true;
} // isConnected
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 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);
}
}
}
}
}
}
