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Merge pull request #214 from makjn10/add-graph-algos
 Added following new graph algorithms in folder Graph Algorithms (all in C++):
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‎Graph Algorithms/Articulation_Points/C++/articulationpoints.cpp

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//this code can be used to find Articulation points in a Graph
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#include <bits/stdc++.h>
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using namespace std;
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int timee;// a variable to keep track of the time at which a particular vertex is encounterd
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vector<int> graph[100];//adjacency list for the graph (100 is the max number of vertices.. you can change as per your needs)
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bool visited[100] , AP[100];
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//visited - bool array used in DFS to know whether the node is visited or not
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//AP - bool array to tell whether ith vertex is a AP or NOT
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int disc[100] , low[100] , parent[100];
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//disc - discovery time of a vertex
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//low - exit time of a source
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//parent - array to tell the parent of ith vertex
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//finding all APs
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void printAP2(int source){
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visited[source] = true;
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disc[source] = timee++;
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low[source] = disc[source];
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int child = 0;
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for(auto i : graph[source]){
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if(!visited[i]){
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child++;
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parent[i] = source;
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printAP2(i);
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low[source] = min(low[i] , low[source]);
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if(parent[source] == source){
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if(child > 1) AP[source] = true;
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}
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else{
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if(low[i] >= disc[source]) AP[source] = true; // IMP
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}
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}
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else if(i != parent[source]) low[source] = min(low[i] , low[source]);
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}
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}
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//find and print all APs
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void printAP(int n , int source){
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for(int i = 0 ; i < n ; i++) low[i] = INT_MAX;
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parent[source] = source; //initializing source os source vertex to itself
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printAP2(source);
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for(int i = 0 ; i < n ; i++){
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if(!visited[i]){
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parent[i] = i;
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printAP2(i);
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}
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}
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for(int i = 0 ; i < n ; i++){
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if(AP[i]) cout << i << " ";
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}
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cout << endl;
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}
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int main(){
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//n - no. of vertices , e - no. of edges
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int n , e , u , v;
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cin >> n >> e;
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//inputting e edges
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for(int i = 0 ; i < e ; i++){
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cin >> u >> v;
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graph[u].push_back(v);
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graph[v].push_back(u);
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}
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printAP(n , 0);
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}

‎Graph Algorithms/Articulation_Points/C++/articulationpoints.cpp~

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//this code can be used to find Articulation points in a Graph
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#include <bits/stdc++.h>
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using namespace std;
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int timee;// a variable to keep track of the time at which a particular vertex is encounterd
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vector<int> graph[100];//adjacency list for the graph (100 is the max number of vertices.. you can change as per your needs)
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bool visited[100] , AP[100];
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//visited - bool array used in DFS to know whether the node is visited or not
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//AP - bool array to tell whether ith vertex is a AP or NOT
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int disc[100] , low[100] , parent[100];
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//disc - discovery time of a vertex
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//low - exit time of a source
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//parent - array to tell the parent of ith vertex
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//finding all APs
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void printAP2(int source){
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visited[source] = true;
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disc[source] = timee++;
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low[source] = disc[source];
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int child = 0;
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for(auto i : graph[source]){
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if(!visited[i]){
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child++;
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parent[i] = source;
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printAP2(i);
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low[source] = min(low[i] , low[source]);
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if(parent[source] == source){
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if(child > 1) AP[source] = true;
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}
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else{
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if(low[i] >= disc[source]) AP[source] = true; // IMP
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}
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}
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else if(i != parent[source]) low[source] = min(low[i] , low[source]);
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}
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}
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//find and print all APs
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void printAP(int n , int source){
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for(int i = 0 ; i < n ; i++) low[i] = INT_MAX;
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parent[source] = source;
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printAP2(source);
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for(int i = 0 ; i < n ; i++){
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if(!visited[i]){
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parent[i] = i;
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printAP2(i);
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}
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}
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for(int i = 0 ; i < n ; i++){
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if(AP[i]) cout << i << " ";
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}
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cout << endl;
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}
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int main(){
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//n - no. of vertices , e - no. of edges
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int n , e , u , v;
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cin >> n >> e;
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//inputting e edges
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for(int i = 0 ; i < e ; i++){
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cin >> u >> v;
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graph[u].push_back(v);
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graph[v].push_back(u);
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}
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printAP(n , 0);
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}

‎Graph Algorithms/Bridges_in_Graph/C++/APandbridges.cpp

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//this code can be used to find Articulation points(APs) and bridges in a Graph
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#include <bits/stdc++.h>
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using namespace std;
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int timee;// a variable to keep track of the time at which a particular vertex is encounterd
6+
vector<int> graph[10001];//adjacency list for the graph (10000 is the max number of vertices.. you can change as per your needs)
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bool visited[10001] , AP[10001];
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//visited - bool array used in DFS to know whether the node is visited or not
9+
//AP - bool array to tell whether ith vertex is a AP or NOT
10+
11+
int disc[10001] , low[10001] , parent[10001];
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//disc - discovery time of a vertex
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//low - exit time of a source
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//parent - array to tell the parent of ith vertex
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//function to find APs and Bridges
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void printAP2(int source , vector<int> &Ap , vector<pair<int , int> > &bridges){
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visited[source] = true;
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disc[source] = timee++;
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low[source] = disc[source];
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int child = 0;
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for(auto i : graph[source]){
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if(!visited[i]){
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child++;
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parent[i] = source;
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printAP2(i , Ap , bridges);
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low[source] = min(low[i] , low[source]);
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if(parent[source] == source){
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if(child > 1) Ap.push_back(source);
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}
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else{
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if(low[i] >= disc[source]) Ap.push_back(source); // IMP
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}
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if(low[i] > disc[source]){
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pair<int , int> temp;
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temp.first = source;
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temp.second = i;
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bridges.push_back(temp);
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}
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}
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else if(i != parent[source]) low[source] = min(low[source] , disc[i]);
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}
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}
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void printAP(int n , int source){
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vector<int> Ap;
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vector<pair<int , int> > bridges; //contains edges which are bridges
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parent[source] = source;
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printAP2(source , Ap , bridges);
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for(int i = 0 ; i < n ; i++){
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if(!visited[i]){
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parent[i] = i;
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printAP2(i , Ap , bridges);
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}
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}
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//print number of APs and Bridges
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//printing the APS and Bridges
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sort(Ap.begin() , Ap.end());
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sort(bridges.begin() , bridges.end());
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cout << Ap.size() << endl;
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for(int i = 0 ; i < Ap.size() ; i++){
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cout << Ap[i] << " ";
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}
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cout << endl;
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cout << bridges.size() << endl;
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for(int i = 0 ; i < bridges.size() ; i++){
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cout << bridges[i].first << " " << bridges[i].second << endl;
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}
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}
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int main(){
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//n - no. of vertices , e - no. of edges
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int n , e , u , v;
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cin >> n >> e;
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//inputting e edges
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for(int i = 0 ; i < e ; i++){
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cin >> u >> v;
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graph[u].push_back(v);
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graph[v].push_back(u);
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}
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printAP(n , 0);
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}

‎Graph Algorithms/Bridges_in_Graph/C++/APandbridges.cpp~

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//this code can be used to find Articulation points(APs) and bridges in a Graph
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#include <bits/stdc++.h>
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using namespace std;
4+
5+
int timee;// a variable to keep track of the time at which a particular vertex is encounterd
6+
vector<int> graph[10001];//adjacency list for the graph (10000 is the max number of vertices.. you can change as per your needs)
7+
bool visited[10001] , AP[10001];
8+
//visited - bool array used in DFS to know whether the node is visited or not
9+
//AP - bool array to tell whether ith vertex is a AP or NOT
10+
11+
int disc[10001] , low[10001] , parent[10001];
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//disc - discovery time of a vertex
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//low - exit time of a source
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//parent - array to tell the parent of ith vertex
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void printAP2(int source , vector<int> &Ap , vector<pair<int , int> > &bridges){
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visited[source] = true;
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disc[source] = timee++;
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low[source] = disc[source];
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int child = 0;
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for(auto i : graph[source]){
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if(!visited[i]){
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child++;
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parent[i] = source;
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printAP2(i , Ap , bridges);
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low[source] = min(low[i] , low[source]);
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if(parent[source] == source){
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if(child > 1) Ap.push_back(source);
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}
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else{
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if(low[i] >= disc[source]) Ap.push_back(source); // IMP
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}
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if(low[i] > disc[source]){
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pair<int , int> temp;
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temp.first = source;
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temp.second = i;
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bridges.push_back(temp);
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}
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}
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else if(i != parent[source]) low[source] = min(low[source] , disc[i]);
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}
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}
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void printAP(int n , int source){
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vector<int> Ap;
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vector<pair<int , int> > bridges;
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parent[source] = source;
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printAP2(source , Ap , bridges);
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for(int i = 0 ; i < n ; i++){
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if(!visited[i]){
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parent[i] = i;
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printAP2(i , Ap , bridges);
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}
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}
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//print number of APs and Bridges
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//printing the APS and Bridges
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sort(Ap.begin() , Ap.end());
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sort(bridges.begin() , bridges.end());
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cout << Ap.size() << endl;
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for(int i = 0 ; i < Ap.size() ; i++){
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cout << Ap[i] << " ";
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}
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cout << endl;
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cout << bridges.size() << endl;
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for(int i = 0 ; i < bridges.size() ; i++){
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cout << bridges[i].first << " " << bridges[i].second << endl;
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}
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}
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int main(){
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//n - no. of vertices , e - no. of edges
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int n , e , u , v;
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cin >> n >> e;
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//inputting e edges
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for(int i = 0 ; i < e ; i++){
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cin >> u >> v;
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graph[u].push_back(v);
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graph[v].push_back(u);
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}
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printAP(n , 0);
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}

‎Graph Algorithms/MST/Kruskals_Algo/C++/kruskals.cpp

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#include <bits/stdc++.h>
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using namespace std;
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#define pb push_back
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#define mp make_pair
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// edge class
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class edge{
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public:
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int u , v , weight; // u and v are the end points of an edge
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// weight is the weight of the edge
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edge(){}
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edge(int a , int b , int c){
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u = a , v = b , weight = c;
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}
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};
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bool compare(edge a , edge b){
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return a.weight < b.weight;
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}
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vector<edge> edges; //vector of all the edges of the graph
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vector<edge> result; //vector that will contain the edges present in MST
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//creating a DSU (DISJOINT SET UNION) - to find and detect cycles
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int parent[100001] , ranks[100001];
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void make_set(int v){
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parent[v] = v;
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}
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int find_set(int v){
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if(v == parent[v])
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return v;
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return parent[v] = find_set(parent[v]);
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}
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bool check(int a , int b){
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a = find_set(a);
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b = find_set(b);
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if(a == b) return false;
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if(ranks[a] < ranks[b]) swap(a , b);
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parent[b] = a;
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if(ranks[a] == ranks[b]) ranks[a]++;
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return true;
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}
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// function to find the MST that returns the overall weight os the MST
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int calcMST(int n , int m){
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int weight = 0 , totaledges = 0;
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//sorting the edges as per their weights
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sort(edges.begin() , edges.end() , compare);
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//initializing dsu
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for(int i = 1 ; i <= n ; i++){
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make_set(i);
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}
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//picking edges and checking
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for(auto i : edges){
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if(check(i.u , i.v)){
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result.pb(i);
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weight += i.weight;
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totaledges++;
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if(totaledges == n - 1) break;
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}
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}
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return weight;
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}
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int main(){
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//n - no. of vertices , m - no. of edges
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int n , m , u , v , weight;
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cin >> n >> m;
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//inputting m edges
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for(int i = 0 ; i < m ; i++){
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cin >> u >> v >> weight;
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edge temp(u , v , weight);
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edges.pb(temp);
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}
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int ans = calcMST(n , m);
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cout << ans << endl;
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//printing all the edges present in result vector
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for(int i = 0 ; i < result.size() ; i++){
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cout << result[i].u << " " << result[i].v << " " << result[i].weight << endl;
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}
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}

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