**Directed Graph through DFS and classifying all edges**

Write a C Program for Traversing Directed Graph through DFS and classifying all edges. Here’s simple Program for Traversing Directed Graph through DFS and classifying all edges.

**Depth First Search (DFS)**

Depth First Search (DFS) algorithm traverses a graph in a depthward motion and uses a stack to remember to get the next vertex to start a search, when a dead end occurs in any iteration.

It employs the following rules.

**Rule 1**− Visit the adjacent unvisited vertex. Mark it as visited. Display it. Push it in a stack.**Rule 2**− If no adjacent vertex is found, pop up a vertex from the stack. (It will pop up all the vertices from the stack, which do not have adjacent vertices.)**Rule 3**− Repeat Rule 1 and Rule 2 until the stack is empty.

We shall not see the implementation of Depth First Traversal (or Depth First Search) in C programming language

**Also Read : : C Program for traversing a Directed Graph through DFS recursively**

Below is the source code for C Program for Traversing Directed Graph through DFS and classifying all edges in output which is successfully compiled and run on Windows System to produce desired output as shown below :

**SOURCE CODE : :**

**SOURCE CODE : :**

/* C Program for Traversing Directed Graph through DFS and classifying all edges */ #include<stdio.h> #define MAX 50 #define initial 1 #define visited 2 #define finished 3 int n; /*Number of vertices in the graph */ int adj[MAX][MAX]; void create_graph( ); int state[MAX]; int time; int d[MAX]; int f[MAX]; void DF_Traversal(); void DFS(int v); int main() { create_graph(); DF_Traversal(); return 0; }/*End of main()*/ void DF_Traversal() { int v; for(v=0; v<n; v++) state[v] = initial; printf("\nEnter starting vertex for Depth First Search : "); scanf("%d",&v); DFS(v); for(v=0; v<n; v++) { if(state[v] == initial) DFS(v); } printf("\n"); }/*End of DF_Traversal( )*/ void DFS(int v) { int i; time++; d[v] = time; state[v] = visited; for(i=0; i<n; i++) { if(adj[v][i] == 1) { if(state[i] == initial) { printf("\n(%d,%d) - Tree edge\n", v, i); DFS(i); } else if(state[i] == visited) { printf("\n(%d,%d) - Back edge\n", v, i); } else if(d[v] < d[i]) { printf("\n(%d,%d) - Forward edge\n", v, i); } else printf("\n(%d,%d) - Cross edge\n", v, i); } } state[v] = finished; f[v] = ++time; }/*End of DFS()*/ void create_graph() { int i,max_edges,origin,destin; printf("\nEnter number of vertices : "); scanf("%d",&n); max_edges=n*(n-1); for(i=1;i<=max_edges;i++) { printf("\nEnter edge %d( -1 -1 to quit ) : ",i); scanf("%d %d",&origin,&destin); if( (origin == -1) && (destin == -1) ) break; if( origin >= n || destin >= n || origin<0 || destin<0) { printf("\nInvalid edge!\n"); i--; } else { adj[origin][destin] = 1; } } }

**OUTPUT : :**

**OUTPUT : :**

/* C Program for Traversing Directed Graph through DFS and classifying all edges */ Enter number of vertices : 6 Enter edge 1( -1 -1 to quit ) : 0 1 Enter edge 2( -1 -1 to quit ) : 0 2 Enter edge 3( -1 -1 to quit ) : 0 3 Enter edge 4( -1 -1 to quit ) : 0 4 Enter edge 5( -1 -1 to quit ) : 1 3 Enter edge 6( -1 -1 to quit ) : 3 4 Enter edge 7( -1 -1 to quit ) : 2 5 Enter edge 8( -1 -1 to quit ) : 5 4 Enter edge 9( -1 -1 to quit ) : -1 -1 Enter starting vertex for Depth First Search : 0 (0,1) - Tree edge (1,3) - Tree edge (3,4) - Tree edge (0,2) - Tree edge (2,5) - Tree edge (5,4) - Cross edge (0,3) - Forward edge (0,4) - Forward edge Process returned 0

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