Merge pull request #430 from Aarushi11H/aarushi

graph algos cpp

cpp/Graphs/Cycle_Detection_in_DAG.cpp

@@ -0,0 +1,66 @@
+#include<iostream>
+#include<set>
+#define NODE 5
+using namespace std;
+
+//DIRECTED ACYCLIC GRAPH ( A directed graph with no self cycle)
+int graph[NODE][NODE] = {
+   {0, 1, 1, 0, 0},
+   {0, 0, 0, 0, 0},
+   {0, 0, 0, 1, 0},
+   {0, 1, 0, 0, 0},
+   {0, 1, 0, 1, 0}
+};
+
+/*
+ 1 -> 2 ,3
+ 3 -> 4
+ 4 -> 2
+ 5 -> 2,4
+*/
+
+bool dfs(int curr, set<int>&wSet, set<int>&gSet, set<int>&bSet) {
+   //moving curr to white set to grey set.
+   wSet.erase(wSet.find(curr));
+   gSet.insert(curr);
+
+   for(int v = 0; v < NODE; v++) {
+      if(graph[curr][v] != 0) {    //for all neighbour vertices
+         if(bSet.find(v) != bSet.end())
+            continue;    //if the vertices are in the black set
+         if(gSet.find(v) != gSet.end())
+            return true;    //it is a cycle
+         if(dfs(v, wSet, gSet, bSet))
+            return true;    //cycle found
+      }
+   }
+
+   //moving v to grey set to black set.
+   gSet.erase(gSet.find(curr));
+   bSet.insert(curr);
+   return false;
+}
+
+bool hasCycle() {
+   set<int> wSet, gSet, bSet;    //three set as white, grey and black
+   for(int i = 0; i<NODE; i++)
+      wSet.insert(i);    //initially add all node into the white set
+
+   while(wSet.size() > 0) {
+      for(int current = 0; current < NODE; current++) {
+         if(wSet.find(current) != wSet.end())
+            if(dfs(current, wSet, gSet, bSet))
+               return true;
+      }
+   }
+   return false;
+}
+
+int main() {
+   bool res;
+   res = hasCycle();
+   if(res)
+      cout << "The graph has cycle." << endl;
+   else
+      cout << "The graph has no cycle." << endl;
+}

cpp/Graphs/Ford_Fulkerson_Algorithm.cpp

@@ -0,0 +1,112 @@
+
+#include <iostream> 
+#include <limits.h> 
+#include <string.h> 
+#include <queue> 
+using namespace std; 
+
+// Number of vertices in given graph 
+#define V 6 
+
+/* Returns true if there is a path from source 's' to sink 't' in 
+  residual graph. Also fills parent[] to store the path */
+bool bfs(int rGraph[V][V], int s, int t, int parent[]) 
+{ 
+    // Create a visited array and mark all vertices as not visited 
+    bool visited[V]; 
+    memset(visited, 0, sizeof(visited)); 
+
+    // Create a queue, enqueue source vertex and mark source vertex 
+    // as visited 
+    queue <int> q; 
+    q.push(s); 
+    visited[s] = true; 
+    parent[s] = -1; 
+
+    // Standard BFS Loop 
+    while (!q.empty()) 
+    { 
+        int u = q.front(); 
+        q.pop(); 
+
+        for (int v=0; v<V; v++) 
+        { 
+            if (visited[v]==false && rGraph[u][v] > 0) 
+            { 
+                q.push(v); 
+                parent[v] = u; 
+                visited[v] = true; 
+            } 
+        } 
+    } 
+
+    // If we reached sink in BFS starting from source, then return 
+    // true, else false 
+    return (visited[t] == true); 
+} 
+
+// Returns the maximum flow from s to t in the given graph 
+int fordFulkerson(int graph[V][V], int s, int t) 
+{ 
+    int u, v; 
+
+    int rGraph[V][V]; // Residual graph where rGraph[i][j] indicates  
+                     // residual capacity of edge from i to j (if there 
+                     // is an edge. If rGraph[i][j] is 0, then there is not)   
+    for (u = 0; u < V; u++) 
+        for (v = 0; v < V; v++) 
+             rGraph[u][v] = graph[u][v]; 
+
+    int parent[V];  // This array is filled by BFS and to store path 
+
+    int max_flow = 0;  // There is no flow initially 
+
+    // Augment the flow while there is path from source to sink 
+    while (bfs(rGraph, s, t, parent)) 
+    { 
+        // Find minimum residual capacity of the edges along the 
+        // path filled by BFS. Or we can say find the maximum flow 
+        // through the path found. 
+        int path_flow = INT_MAX; 
+        for (v=t; v!=s; v=parent[v]) 
+        { 
+            u = parent[v]; 
+            path_flow = min(path_flow, rGraph[u][v]); 
+        } 
+
+        // update residual capacities of the edges and reverse edges 
+        // along the path 
+        for (v=t; v != s; v=parent[v]) 
+        { 
+            u = parent[v]; 
+            rGraph[u][v] -= path_flow; 
+            rGraph[v][u] += path_flow; 
+        } 
+
+        // Add path flow to overall flow 
+        max_flow += path_flow; 
+    } 
+
+    // Return the overall flow 
+    return max_flow; 
+} 
+
+
+int main() 
+{ 
+    // Creating a graph with 6 vertices as  defined earlier. 
+    //to change the vertices value, change it in the #define V <your vertex value>
+    //may change the edge values here  
+    int graph[V][V] = { {0, 16, 13, 0, 0, 0}, 
+                        {0, 0, 10, 12, 0, 0}, 
+                        {0, 4, 0, 0, 14, 0}, 
+                        {0, 0, 9, 0, 0, 20}, 
+                        {0, 0, 0, 7, 0, 4}, 
+                        {0, 0, 0, 0, 0, 0} 
+                      }; 
+
+
+    cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5); 
+
+    return 0; 
+} 

cpp/Graphs/Johnson's_Algorithm.cpp

@@ -0,0 +1,53 @@
+#include<iostream>
+#define INF 9999
+using namespace std;
+int min(int a, int b);
+int cost[10][10], adj[10][10];
+inline int min(int a, int b){
+   return (a<b)?a:b;
+}
+main() {
+   int vert, edge, i, j, k, c;
+   cout << "Enter no of vertices: ";
+   cin >> vert;
+   cout << "Enter no of edges: ";
+   cin >> edge;
+   cout << "Enter the EDGE Costs:\n";
+   for (k = 1; k <= edge; k++) { 
+      cin >> i >> j >> c;
+      adj[i][j] = cost[i][j] = c;
+   }
+   for (i = 1; i <= vert; i++)
+      for (j = 1; j <= vert; j++) {
+         if (adj[i][j] == 0 && i != j)
+            adj[i][j] = INF; //if there is no edge, put infinity
+      }
+   for (k = 1; k <= vert; k++)
+      for (i = 1; i <= vert; i++)
+         for (j = 1; j <= vert; j++)
+            adj[i][j] = min(adj[i][j], adj[i][k] + adj[k][j]); 
+   cout << "Resultant adj matrix\n";
+   for (i = 1; i <= vert; i++) {
+      for (j = 1; j <= vert; j++) {
+            if (adj[i][j] != INF)
+               cout << adj[i][j] << " ";
+      }
+      cout << "\n";
+   }
+}
+/* Example input and output
+Enter no of vertices: 3
+Enter no of edges: 5
+Enter the EDGE Cost:
+1 2 4
+2 1 6
+1 3 11
+3 1 3
+2 3 2
+Resultant adj matrix
+0 4 6 
+5 0 2 
+3 7 0 
+*/
+
+

cpp/Graphs/Kosaraju's_Algorithm.cpp

@@ -0,0 +1,113 @@
+// Kosaraju's algorithm to find strongly connected components in C++
+
+#include <iostream>
+#include <list>
+#include <stack>
+
+using namespace std;
+
+class Graph {
+  int V;
+  list<int> *adj;
+  /* Fills Stack with vertices (in increasing order of finishing 
+     times). The top element of stack has the maximum finishing  
+    */
+  void fillOrder(int s, bool visitedV[], stack<int> &Stack);
+  // A recursive function to print DFS starting from v 
+  void DFS(int s, bool visitedV[]);
+
+   public:
+  Graph(int V);
+  void addEdge(int s, int d);
+  void printSCC();
+  Graph transpose();
+};
+
+Graph::Graph(int V) {
+  this->V = V;
+  adj = new list<int>[V];
+}
+
+// DFS
+void Graph::DFS(int s, bool visitedV[]) {
+  visitedV[s] = true;
+  cout << s << " ";
+
+  list<int>::iterator i;
+  for (i = adj[s].begin(); i != adj[s].end(); ++i)
+    if (!visitedV[*i])
+      DFS(*i, visitedV);
+}
+
+// Transpose
+Graph Graph::transpose() {
+  Graph g(V);
+  for (int s = 0; s < V; s++) {
+  	// Recur for all the vertices adjacent to this vertex 
+    list<int>::iterator i;
+    for (i = adj[s].begin(); i != adj[s].end(); ++i) {
+      g.adj[*i].push_back(s);
+    }
+  }
+  return g;
+}
+
+// Add edge into the graph
+void Graph::addEdge(int s, int d) {
+  adj[s].push_back(d);
+}
+
+void Graph::fillOrder(int s, bool visitedV[], stack<int> &Stack) {
+  visitedV[s] = true;
+ // Recur for all the vertices adjacent to this vertex
+  list<int>::iterator i;
+  for (i = adj[s].begin(); i != adj[s].end(); ++i)
+    if (!visitedV[*i])
+      fillOrder(*i, visitedV, Stack);
+
+  Stack.push(s);
+}
+
+// Print strongly connected component
+void Graph::printSCC() {
+  stack<int> Stack;
+
+  bool *visitedV = new bool[V];
+  for (int i = 0; i < V; i++)
+    visitedV[i] = false;
+
+  for (int i = 0; i < V; i++)
+    if (visitedV[i] == false)
+      fillOrder(i, visitedV, Stack);
+
+  Graph gr = transpose();
+
+  for (int i = 0; i < V; i++)
+    visitedV[i] = false;
+
+  while (Stack.empty() == false) {
+    int s = Stack.top();
+    Stack.pop();
+
+    if (visitedV[s] == false) {
+      gr.DFS(s, visitedV);
+      cout << endl;
+    }
+  }
+}
+
+int main() {
+  Graph g(8);
+  g.addEdge(0, 1);
+  g.addEdge(1, 2);
+  g.addEdge(2, 3);
+  g.addEdge(2, 4);
+  g.addEdge(3, 0);
+  g.addEdge(4, 5);
+  g.addEdge(5, 6);
+  g.addEdge(6, 4);
+  g.addEdge(6, 7);
+
+  cout << "Strongly Connected Components through Kosaraju's Algorithm:\n";
+  g.printSCC();
+}