Find all reachable nodes from every node present in a given set in C++

Suppose we have one undirected graph and a set of vertices; we have to find all reachable nodes from every vertex present in the given set.

So, if the input is like

then the output will be [1,2,3] and [4,5] as these are two connected components.

To solve this, we will follow these steps −

• nodes := number of nodes in the graph
• Define an array visited of size: nodes+1. And fill with 0
• Define one map m
• comp_sum := 0
• for initialize i := 0, when i < n, update (increase i by 1), do −
  • u := arr[i]
  • if visited[u] is false, then −
    • (increase comp_sum by 1)
    • m[visited[u]] := bfs traversal of g from node u, also calculate comp_sum
  • print traversal of m[visited[u]]

Example

Let us see the following implementation to get better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Graph{
   public:
      int nodes;
      list<int> *adj_list;
      Graph(int);
      void insert_edge(int, int);
      vector<int> BFS(int, int, int []);
};
Graph::Graph(int nodes) {
   this->nodes = nodes;
   adj_list = new list<int>[nodes+1];
}
void Graph::insert_edge(int u, int v) {
   adj_list[u].push_back(v);
   adj_list[v].push_back(u);
}
vector<int> Graph::BFS(int comp_sum, int src,int visited[]){
   queue<int> queue;
   queue.push(src);
   visited[src] = comp_sum;
   vector<int> reachableNodes;
   while(!queue.empty()) {
      int u = queue.front();
      queue.pop();
      reachableNodes.push_back(u);
      for (auto itr = adj_list[u].begin(); itr != adj_list[u].end(); itr++) {
         if (!visited[*itr]) {
            visited[*itr] = comp_sum;
            queue.push(*itr);
         }
      }
   }
   return reachableNodes;
}
void displayReachableNodes(int n, unordered_map <int, vector<int> > m) {
   vector<int> temp = m[n];
   for (int i=0; i<temp.size(); i++)
      cout << temp[i] << " ";
   cout << endl;
}
void get_all_reachable(Graph g, int arr[], int n) {
   int nodes = g.nodes;
   int visited[nodes+1];
   memset(visited, 0, sizeof(visited));
   unordered_map <int, vector<int> > m;
   int comp_sum = 0;
   for (int i = 0 ; i < n ; i++) {
      int u = arr[i];
      if (!visited[u]) {
         comp_sum++;
         m[visited[u]] = g.BFS(comp_sum, u, visited);
      }
      cout << "Reachable Nodes from " << u <<" are\n";
      displayReachableNodes(visited[u], m);
   }
}
int main() {
   int nodes = 5;
   Graph g(nodes);
   g.insert_edge(1, 2);
   g.insert_edge(2, 3);
   g.insert_edge(4, 5);
   int arr[] = {2, 4, 1};
   int n = sizeof(arr)/sizeof(int);
   get_all_reachable(g, arr, n);
}

Input

g.insert_edge(1, 2);
g.insert_edge(2, 3);
g.insert_edge(4, 5);

Output

Reachable Nodes from 2 are
2 1 3
Reachable Nodes from 4 are
4 5
Reachable Nodes from 1 are
2 1 3