datastructure@ Find If there is a path between the vertices in a directed graph

Given a Directed Graph and both vertices in it, check whether there are a path from the first Given vertex to second. For example, in the following graph, there are a path from vertex 1 to 3. As another example, there is no path from 3 to 0.

We can either use Breadth First search (BFS) or Depth first search (DFS) to find path between and vertices. Take the first vertex as source in a BFS (or Dfs), follow the standard BFS (or DFS). If we see the second vertex in our traversal and then return true. Else return FALSE.

Following is C + + code, uses BFS for finding reachability of second vertex from first vertex.

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <limits>5#include <vector>6 using namespacestd;7 Const intMAXN =4;8 structedge{9     intto, cost;TenEdgeintt) { One          This->to = t; This->cost =0; A     } - }; - voidAddedge (vector<edge> &edgelist, vector<vector<int> > &g,int  from,intTo ) { the Edgelist.push_back (Edge (To)); -g[ from].push_back (Edgelist.size ()-1); - } - voidAdddoubleedge (vector<edge> &edgelist, vector<vector<int> > &g,int  from,intTo ) { +Addedge (Edgelist,g, from, to); -Addedge (Edgelist,g,to, from); + } A BOOLIscyclic (vector<edge> edgelist, vector<vector<int> > g,vector<BOOL> Vis, vector<BOOL> Recstack,intv) { at      for(intI=0; I<g[v].size (); + +i) { -Edge E =Edgelist[g[v][i]]; -         if(Recstack[e.to])return true; -         if(!Vis[e.to]) { -Vis[e.to] =true; Recstack[e.to] =true; -             if(Iscyclic (edgelist,g,vis,recstack,e.to))return true; inRecstack[e.to] =false; -         } to     } +     return false; - } the voidIscyclicutil (vector<edge> edgelist, vector<vector<int> > G) {//find all cycles. *vector<BOOL>Vis (G.size ()); $vector<BOOL>Recstack (G.size ());Panax Notoginseng      for(intI=0; I<vis.size (); ++i) vis[i]=false; -      for(intI=0; I<recstack.size (); ++i) recstack[i]=false; the      +      for(intI=0; I<g.size (); + +i) { A         if(!Vis[i]) { theVis[i] =true; Recstack[i] =true; +             if(Iscyclic (edgelist,g,vis,recstack,i)) { -cout<<i<<"starts a cycle"<<Endl; $             } $Recstack[i] =false; -         } -     } the } - BOOLDFS (vector<edge> edgelist, vector<vector<int> > G, vector<BOOL> Vis,int  from,intTo ) {Wuyi     if( from= = to)return true; the      for(intI=0; i<g[ from].size (); + +i) { -Edge E = edgelist[g[ from][i]]; Wu         if(e.to = = to)return true; -         if(!Vis[e.to]) { AboutVis[e.to] =true; $             if(Dfs (edgelist, G, Vis, e.to, to))return true; -         } -     } -     return false; A } + voidIsreachable (vector<edge> edgelist, vector<vector<int> > G,int  from,intTo ) { thevector<BOOL>Vis (G.size ()); -      for(intI=0; I<vis.size (); ++i) Vis[i] =false; $vis[ from] =true; the     if(Dfs (edgelist, G, Vis, from, to)) cout<< from<<" and"<<to<<"is reachable to all other"<<Endl; the     Elsecout<< from<<" and"<<to<<"is not reachable"<<Endl; the } the voidBuildmap (vector<edge> &edgelist, vector<vector<int> > &G) { -Addedge (Edgelist,g,0,1); inAddedge (Edgelist,g,0,2); theAddedge (Edgelist,g,2,0); theAddedge (Edgelist,g,1,2); AboutAddedge (Edgelist,g,2,3); theAddedge (Edgelist,g,3,3); the } the intMain () { +Vector<edge>edgelist; -vector<vector<int> >G (MAXN); the     Bayi Buildmap (edgelist,g); the      the Iscyclicutil (edgelist, G); -      -Isreachable (Edgelist, G,1,1); the      the     return 0; the}

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