Merge pull request #267 from PalAditya/master

Added code to find strongly connected components

data_structures/graphs/strongly_connected_components.c

@@ -0,0 +1,211 @@
+#include <stdio.h>
+#include <stdlib.h>
+#define MAX_SIZE 40//Assume 40 nodes at max in graph
+//A vertex of the graph 
+struct node
+{
+    int vertex;
+    struct node* next;
+};
+//Some declarations
+struct node* createNode(int v);
+struct Graph
+{
+    int numVertices;
+    int* visited;
+    struct node** adjLists; // we need int** to store a two dimensional array. Similary, we need struct node** to store an array of Linked lists
+};
+//Structure to create a stack, necessary for topological sorting
+struct Stack
+{
+	int arr[MAX_SIZE];
+	int top;
+};
+struct Graph* createGraph(int);
+void addEdge(struct Graph*, int, int);
+void printGraph(struct Graph*);
+struct Graph* transpose(struct Graph*);
+void fillOrder(int,struct Graph*, struct Stack*);
+void scc(struct Graph*);
+void dfs(struct Graph*, int);
+struct Stack* createStack();
+void push(struct Stack*, int);
+int pop(struct Stack*);
+
+int main()
+{	
+	int vertices,edges,i,src,dst;
+	printf("Enter the number of vertices\n");
+	scanf("%d",&vertices);
+	struct Graph* graph = createGraph(vertices);
+	printf("Enter the number of edges\n");
+	scanf("%d",&edges);
+	for(i=0; i<edges; i++)
+	{
+		printf("Edge %d \nEnter source: ",i+1);
+		scanf("%d",&src);
+		printf("Enter destination: ");
+		scanf("%d",&dst);
+		addEdge(graph, src, dst);
+	}
+	printf("The strongly connected conponents are:\n");
+	scc(graph);
+	printf("\n");
+	
+	//Uncomment below part to get a ready-made example
+    /*struct Graph* graph2 = createGraph(4);
+    addEdge(graph2, 0, 1);
+    addEdge(graph2, 1, 2);
+    addEdge(graph2, 2, 0);
+    addEdge(graph2, 2, 3);
+    printf("The strongly connected components are:\n");
+    scc(graph2);
+	printf("\n");*/
+    return 0;
+}
+//Creates a topological sorting of the graph
+void fillOrder(int vertex, struct Graph* graph, struct Stack* stack)
+{
+	graph->visited[vertex]=1;
+	struct node* adjList = graph->adjLists[vertex];
+    struct node* temp = adjList;
+    //First add all dependents (that is, children) to stack
+    while(temp!=NULL) {
+        int connectedVertex = temp->vertex;
+        if(graph->visited[connectedVertex] == 0) {
+               fillOrder(connectedVertex, graph, stack);
+            }
+        temp=temp->next;
+    }
+    //and then add itself
+    push(stack,vertex);
+}
+//Transpose the adjacency list
+struct Graph* transpose(struct Graph* g)
+{
+	struct Graph* graph = createGraph(g->numVertices);//Number of vertices is same
+	int i=0;
+	for(i=0;i<g->numVertices;i++)
+	{
+		struct node* temp=g->adjLists[i];
+		while(temp!=NULL)
+		{
+			addEdge(graph,temp->vertex,i);//Reverse all edges
+			temp=temp->next;
+		}
+	}
+	return graph;
+}
+//Recursive dfs aproach
+void dfs(struct Graph* graph, int vertex) {
+    struct node* adjList = graph->adjLists[vertex];
+    struct node* temp = adjList;
+        
+    //Add vertex to visited list and print it
+    graph->visited[vertex] = 1;
+    printf("%d ", vertex);
+        
+    //Recursively call the dfs function on all unvisited neighbours
+    while(temp!=NULL) {
+        int connectedVertex = temp->vertex;
+        if(graph->visited[connectedVertex] == 0) {
+        	dfs(graph, connectedVertex);
+        }
+        temp = temp->next;
+    }       
+}
+
+//Strongly connected components
+void scc(struct Graph* graph)
+{
+	//Step I: Create a topological sort of the graph and store it in a stack
+	struct Stack* stack=createStack();
+	int i=0;
+	for(i=0;i<graph->numVertices;i++)
+	{
+		//Execute topological sort on all elements
+		if(graph->visited[i]==0)
+		{
+			fillOrder(i,graph,stack);
+		}
+	}
+	//Step 2: Get the transpose graph
+	struct Graph* graphT=transpose(graph);
+	//Step 3: Perform a simple dfs by popping nodes from stack
+	while(stack->top!=-1)
+	{
+		int v=pop(stack);
+		if(graphT->visited[v]==0)
+		{
+			dfs(graphT,v);
+			printf("\n");
+		}		
+	}
+}
+	
+//Allocate memory for a node
+struct node* createNode(int v)
+{
+    struct node* newNode = malloc(sizeof(struct node));
+    newNode->vertex = v;
+    newNode->next = NULL;
+    return newNode;
+}
+//Allocate memory for the entire graph structure
+struct Graph* createGraph(int vertices)
+{
+    struct Graph* graph = malloc(sizeof(struct Graph));
+    graph->numVertices = vertices;
+    graph->adjLists = malloc(vertices * sizeof(struct node*));    
+    graph->visited = malloc(vertices * sizeof(int));
+ 
+    int i;
+    for (i = 0; i < vertices; i++) {
+        graph->adjLists[i] = NULL;
+        graph->visited[i] = 0;
+    }
+    return graph;
+}
+//Creates a unidirectional graph
+void addEdge(struct Graph* graph, int src, int dest)
+{
+    // Add edge from src to dest
+    struct node* newNode = createNode(dest);
+    newNode->next = graph->adjLists[src];
+    graph->adjLists[src] = newNode;
+}
+//Utility function to see state of graph at a given time 
+void printGraph(struct Graph* graph)
+{
+    int v;
+    for (v = 0; v < graph->numVertices; v++)
+    {
+        struct node* temp = graph->adjLists[v];
+        printf("\n Adjacency list of vertex %d\n ", v);
+        while (temp)
+        {
+            printf("%d -> ", temp->vertex);
+            temp = temp->next;
+        }
+        printf("\n");
+    }
+}
+//Creates a stack
+struct Stack* createStack()
+{
+	struct Stack* stack=malloc(sizeof(struct Stack));
+	stack->top=-1;
+}
+//Pushes element into stack
+void push(struct Stack* stack,int element)
+{
+	stack->arr[++stack->top]=element;//Increment then add, as we start from -1
+}
+//Removes element from stack, or returns INT_MIN if stack empty
+int pop(struct Stack* stack)
+{
+	if(stack->top==-1)
+		return INT_MIN;
+	else 
+		return stack->arr[stack->top--];
+}