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AkashGit21AkashGit21
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Added some graph Algorithms
1 parent 8d30ebf commit c05bfdc

14 files changed

+645
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lines changed

‎Graph/articulationPoints.cpp

+38
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void Graph::traversalArt(int root,int cur,int src,int id,int &outEC,vector<bool> &isArt){
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if(src==root) outEC++;
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visited[cur]=true;
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lowLink[cur]=ids[cur]=id++;
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for(int child:G[cur]){
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if(src==child) continue;
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if(!visited[child]){
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traversalArt(root,child,cur,id,outEC,isArt);
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lowLink[cur]=min(lowLink[cur],lowLink[child]);
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if(ids[cur]<=lowLink[child])
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isArt[cur]=true;
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}
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else
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lowLink[cur] = min(lowLink[cur],ids[child]);
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}
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}
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vector<bool> Graph::findArticulationPoints(){
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vector<bool> isArt(numOfNodes+1,false);
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visited.resize(numOfNodes+1,false);
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lowLink.resize(numOfNodes+1);
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ids.resize(numOfNodes+1);
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int outEdgeCount;
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for(int i=1;i<=numOfNodes;i++){
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if(visited[i]) continue;
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outEdgeCount=0;
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traversalArt(i,i,-1,0,outEdgeCount,isArt);
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isArt[i] = (outEdgeCount>1);
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}
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for(int node=1;node<=numOfNodes;node++)
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if(isArt[node]) cout<<" "<<node;
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cout<<"\n";
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return isArt;
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}

‎Graph/bellmanFord.cpp

+35
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vector<ll> Graph::bellmanFord(int startingNode){
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vector<ll> dist(numOfNodes+1,INF);
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int V=numOfNodes;
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dist[startingNode]=0;
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for(int i=0;i<V-1;i++){
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for(auto edge:edgeW){
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int from=edge.first.first, to=edge.first.second;
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ll wt=edge.second;
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if(dist[to]>dist[from]+wt)
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dist[to]= dist[from]+wt;
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}
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}
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for(int i=0;i<V-1;i++){
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for(auto edge:edgeW){
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int from=edge.first.first, to=edge.first.second;
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ll wt=edge.second;
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if(dist[to]>dist[from]+wt){
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dist[to]=-1*INF;
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}
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}
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}
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/*
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for(int node=1;node<=numOfNodes;node++){
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cout<<"\n"<<node<<": ";
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if(dist[node]<=-1*INF)
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cout<<"-INF ";
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else cout<<dist[node];
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}
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cout<<"\n";
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*/
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return dist;
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}

‎Graph/bfs.cpp

+38
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vector<int> Graph::bfs(int node){
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vector<int> prev(numOfNodes+1,-1);
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visited.resize(numOfNodes+1,false);
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queue<int> q;
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q.push(node);
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visited[node]=true;
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while(!q.empty()){
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node = q.front(); q.pop();
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for(int child:G[node]){
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if(!visited[child]){
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q.push(child);
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visited[child]=true;
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prev[child]=node;
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}
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}
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}
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return prev;
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}
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//To get the path from StartingNode to lastNode
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vector<int> Graph::reconstructPathFromBFS(
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vector<int> prev, int startingNode, int endingNode){
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vector<int> path; //To store the path
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int ind=endingNode;
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path.push_back(endingNode);
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while(prev[ind]!=-1){
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path.push_back(prev[ind]);
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ind = prev[ind];
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}
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reverse(path.begin(), path.end());
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if(path[0]==startingNode) return path;
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else return {-1};
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}

‎Graph/bridge.cpp

+35
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void Graph::traversal(int cur, int par, int val,
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vector<pair<int,int> > &bridges){
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visited[cur] = true;
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lowLink[cur] = ids[cur] = val++;
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for(int child:G[cur]){
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if(child==par) continue;
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if(!visited[child]){
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traversal(child,cur,val,bridges);
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lowLink[cur] = min(lowLink[child],lowLink[cur]);
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if(ids[cur] < lowLink[child])
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bridges.push_back({cur,child});
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}
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else
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lowLink[cur] = min(lowLink[cur],ids[child]);
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}
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}
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vector<pair<int,int> > Graph::findBridges(){
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ids.resize(numOfNodes+1);
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lowLink.resize(numOfNodes+1);
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vector<pair<int,int> > bridges;
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visited.resize(numOfNodes+1,false);
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for(int node=1;node<=numOfNodes;node++){
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if(visited[node]) continue;
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traversal(node,-1,0,bridges);
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}
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for(auto bridge:bridges){
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cout<<bridge.first<<" "<<bridge.second<<"\n";
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}
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return bridges;
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}

‎Graph/dfs.cpp

+26
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//Time Complexity - O(N)
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void Graph::dfsUtil(int node,int src){
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cout<<" "<<node;
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visited[node]=true;
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for(int child:G[node]){
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if(child==src) continue;
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dfsUtil(child,node);
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}
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}
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//Considering Disconnected Graph as well
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int Graph::dfs(int node){
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int connectedComponents = 0;
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visited.resize(numOfNodes+1,false);
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//Considering Disconnected Graph as well
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for(int i=1;i<=numOfNodes;i++){
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if(visited[i]) continue;
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connectedComponents++;
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dfsUtil(i,-1);
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}
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//returns the number of connected components
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return connectedComponents;
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}

‎Graph/dijkstra.cpp

+31
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vector<vector<ll> > Graph::lazyDijkstra(int startingNode){
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visited.resize(numOfNodes+1,false);
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vector<ll> dist(numOfNodes+1,1e18+1);
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vector<ll> prev(numOfNodes+1,-1);
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priority_queue<pil,vector<pil>,comparePILByWeight> pq;
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pq.push({startingNode,0LL});
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dist[startingNode]=0LL;
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while(!pq.empty()){
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auto cur = pq.top(); pq.pop();
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int curNode = cur.first; ll wt = cur.second;
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if(dist[curNode]<wt) continue;
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visited[curNode]=true;
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for(int child:G[curNode]){
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if(visited[child]) continue;
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ll newDist = dist[curNode]+
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edgeW[{min(curNode,child),max(curNode,child)}];
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if(newDist<dist[child]){
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dist[child]= newDist;
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prev[child]= curNode;
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pq.push({child,newDist});
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}
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}
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}
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//for(int i=1;i<=numOfNodes;i++)
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// cout<<i<<" "<<dist[i]<<"\n";
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return {dist,prev};
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}

‎Graph/eulerPath.cpp

+76
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bool Graph::hasEulerianPath(vector<int> &in, vector<int> &out){
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int inNodes=0, edNodes=0;
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for(int i=1;i<=numOfNodes;i++){
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out[i]=G[i].size();
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for(int child:G[i])
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in[child]++;
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}
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for(int i=1;i<=numOfNodes;i++){
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if(out[i]-in[i]>1 || in[i]-out[i]>1) return false;
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if(out[i]-in[i]==1) inNodes++;
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else if(in[i]-out[i]==1) edNodes++;
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}
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return ( (inNodes==0 && edNodes==0) ||
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(inNodes==1 && edNodes==1) );
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}
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int Graph::findStartingNode(vector<int> in, vector<int> out){
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int startingNode = 0;
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for(int i=1;i<=numOfNodes;i++){
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if(out[i]-in[i]==1) return i;
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if(out[i]) startingNode=i;
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}
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return startingNode;
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}
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int Graph::findEndingNode(vector<int> in, vector<int> out){
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int endingNode = 0;
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for(int i=1;i<=numOfNodes;i++){
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if(in[i]-out[i]==1) return i;
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if(in[i]) endingNode=i;
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}
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return endingNode;
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}
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void Graph::eulerianTraversal(int cur, vector<int> &path, vector<int> &order){
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//cout<<" "<<cur;
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order[cur]++;
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if(order[cur]>G[cur].size()) return;
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eulerianTraversal(G[cur][order[cur]-1], path, order);
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path.push_back(cur);
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}
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void Graph::eulerPath(){
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vector<int> path;
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vector<int> inDegree(numOfNodes+1,0);
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vector<int> outDegree(numOfNodes+1,0);
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vector<int> order(numOfNodes+1,0);
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bool isPath = hasEulerianPath(inDegree,outDegree);
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cout<<"\nisPath: "<<isPath<<"\n";
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if(!isPath){ cout<<"\nNo Eulerian Path!\n";return;}
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int st = findStartingNode(inDegree,outDegree);
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int ed = findEndingNode(inDegree,outDegree);
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cout<<"\nstartingNode: "<<st;
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eulerianTraversal(st, path, order);
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cout<<"\nendingNode: "<<ed;
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reverse(path.begin(),path.end());
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path.push_back(ed);
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//Make sure the graph is not disconnected
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if(path.size() != numOfEdges+1){
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cout<<"\nGraph is disconnected!!!\n";
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return;
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}
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cout<<"\nPath is: ";
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for(int node:path) cout<<" "<<node;
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}

‎Graph/floydWarshall.cpp

+52
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void Graph::propogateNegativeCycles(vector<vector<ll> > &dp, vector<vector<int> >&next){
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int V = numOfNodes;
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for(int k=1;k<=V;k++){
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for(int i=1;i<=V;i++){
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for(int j=1;j<=V;j++){
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if(dp[i][k]+dp[k][j]<dp[i][j]){
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dp[i][j] = -INF;
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next[i][j] = -1;
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}
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}
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}
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}
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}
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// O(V*V*V)
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vector<vector<ll> > Graph::floydWarshall(){
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int V=numOfNodes;
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vector<vector<ll> > dp(V+1,vector<ll>(V+1,INF));
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vector<vector<int> > next(V+1,vector<int>(V+1,-1));
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for(int i=1;i<=V;i++)
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dp[i][i]=0LL;
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for(auto edge:edgeW){
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int from=edge.first.first, to=edge.first.second;
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ll wt = edge.second;
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dp[from][to] = wt;
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next[from][to] = to;
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}
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for(int k=1;k<=V;k++){
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for(int i=1;i<=V;i++){
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for(int j=1;j<=V;j++){
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if(dp[i][k]+dp[k][j]<dp[i][j]){
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dp[i][j] = dp[i][k]+dp[k][j];
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next[i][j] = next[i][k];
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}
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}
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}
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}
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// propogateNegativeCycles(dp,next);
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for(int i=1;i<=V;i++){
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for(int j=1;j<=V;j++){
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if(dp[i][j]<=-INF) cout<<"-INF ";
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else if(dp[i][j]>=INF) cout<<"NP ";
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else cout<<dp[i][j]<<" ";
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}
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cout<<"\n";
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}
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return dp;
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}

‎Graph/getPath.cpp

+13
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vector<int> Graph::getPath(vector<vector<ll> > dist,
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int startingNode, int endingNode){
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vector<int> path;
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while(endingNode!=-1){
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//cout<<endingNode<<"\n";
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path.push_back(endingNode);
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endingNode = dist[1][endingNode];
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}
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reverse(path.begin(),path.end());
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if(path[0]!=startingNode) return {-1};
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else return path;
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}

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