We have introduced Graph basics in Graph and its representations.
In this post, a different STL-based representation is used that can be helpful to quickly implement graphs using vectors. The implementation is for the adjacency list representation of the graph.
Following is an example undirected and unweighted graph with 5 vertices.
Below is an adjacency list representation of the graph.
We use vectors in STL to implement graphs using adjacency list representation.
- vector: A sequence container. Here we use it to store adjacency lists of all vertices. We use vertex numbers as the index in this vector.
The idea is to represent a graph as an array of vectors such that every vector represents the adjacency list of a vertex. Below is a complete STL-based C++ program for DFS Traversal.
Implementation:
C++
// A simple representation of graph using STL,// for the purpose of competitive programming#include<bits/stdc++.h>using namespace std;// A utility function to add an edge in an// undirected graph.void addEdge(vector<int> adj[], int u, int v){ adj[u].push_back(v); adj[v].push_back(u);}// A utility function to do DFS of graph// recursively from a given vertex u.void DFSUtil(int u, vector<int> adj[], vector<bool> &visited){ visited[u] = true; cout << u << " "; for (int i=0; i<adj[u].size(); i++) if (visited[adj[u][i]] == false) DFSUtil(adj[u][i], adj, visited);}// This function does DFSUtil() for all // unvisited vertices.void DFS(vector<int> adj[], int V){ vector<bool> visited(V, false); for (int u=0; u<V; u++) if (visited[u] == false) DFSUtil(u, adj, visited);}// Driver codeint main(){ int V = 5; // The below line may not work on all // compilers. If it does not work on // your compiler, please replace it with // following // vector<int> *adj = new vector<int>[V]; vector<int> adj[V]; // Vertex numbers should be from 0 to 4. addEdge(adj, 0, 1); addEdge(adj, 0, 4); addEdge(adj, 1, 2); addEdge(adj, 1, 3); addEdge(adj, 1, 4); addEdge(adj, 2, 3); addEdge(adj, 3, 4); DFS(adj, V); return 0;} |
Java
import java.util.*;class Graph { // A utility function to add an edge in an // undirected graph. static void addEdge(List<List<Integer>> adj, int u, int v) { adj.get(u).add(v); adj.get(v).add(u); } // A utility function to do DFS of graph // recursively from a given vertex u. static void DFSUtil(int u, List<List<Integer>> adj, boolean[] visited) { visited[u] = true; System.out.print(u + " "); for (int i = 0; i < adj.get(u).size(); i++) { if (!visited[adj.get(u).get(i)]) { DFSUtil(adj.get(u).get(i), adj, visited); } } } // This function does DFSUtil() for all // unvisited vertices. static void DFS(List<List<Integer>> adj, int V) { boolean[] visited = new boolean[V]; for (int u = 0; u < V; u++) { if (!visited[u]) { DFSUtil(u, adj, visited); } } } public static void main(String[] args) { int V = 5; // The below line may not work on all // compilers. If it does not work on // your compiler, please replace it with // following // List<List<Integer>> adj = new ArrayList<>(V); List<List<Integer>> adj = new ArrayList<>(V); for (int i = 0; i < V; i++) { adj.add(new ArrayList<Integer>()); } // Vertex numbers should be from 0 to 4. addEdge(adj, 0, 1); addEdge(adj, 0, 4); addEdge(adj, 1, 2); addEdge(adj, 1, 3); addEdge(adj, 1, 4); addEdge(adj, 2, 3); addEdge(adj, 3, 4); DFS(adj, V); }}// this code is contributed by devendrasalunke |
Python3
# A simple representation of graph using STL,# for the purpose of competitive programming# A utility function to add an edge in an# undirected graph.def addEdge(adj, u, v): adj[u].append(v) adj[v].append(u) return adj# A utility function to do DFS of graph# recursively from a given vertex u.def DFSUtil(u, adj, visited): visited[u] = True print(u, end = " ") for i in range(len(adj[u])): if (visited[adj[u][i]] == False): DFSUtil(adj[u][i], adj, visited)# This function does DFSUtil() for all# unvisited vertices.def DFS(adj, V): visited = [False]*(V+1) for u in range(V): if (visited[u] == False): DFSUtil(u, adj, visited)# Driver codeif __name__ == '__main__': V = 5 # The below line may not work on all # compilers. If it does not work on # your compiler, please replace it with # following # vector<int> *adj = new vector<int>[V] adj = [[] for i in range(V)] # Vertex numbers should be from 0 to 4. adj = addEdge(adj, 0, 1) adj = addEdge(adj, 0, 4) adj = addEdge(adj, 1, 2) adj = addEdge(adj, 1, 3) adj = addEdge(adj, 1, 4) adj = addEdge(adj, 2, 3) adj = addEdge(adj, 3, 4) DFS(adj, V)# This code is contributed by mohit kumar 29. |
C#
using System;using System.Collections.Generic;class Graph { // A utility function to add an edge in an // undirected graph. static void AddEdge(List<List<int> > adj, int u, int v) { adj[u].Add(v); adj[v].Add(u); } // A utility function to do DFS of graph // recursively from a given vertex u. static void DFSUtil(int u, List<List<int> > adj, bool[] visited) { visited[u] = true; Console.Write(u + " "); for (int i = 0; i < adj[u].Count; i++) { if (!visited[adj[u][i]]) { DFSUtil(adj[u][i], adj, visited); } } } // This function does DFSUtil() for all // unvisited vertices. static void DFS(List<List<int> > adj, int V) { bool[] visited = new bool[V]; for (int u = 0; u < V; u++) { if (!visited[u]) { DFSUtil(u, adj, visited); } } } public static void Main(string[] args) { int V = 5; // The below line may not work on all // compilers. If it does not work on // your compiler, please replace it with // following // List<List<int>> adj = new List<List<int>>(V); List<List<int> > adj = new List<List<int> >(); for (int i = 0; i < V; i++) { adj.Add(new List<int>()); } // Vertex numbers should be from 0 to 4. AddEdge(adj, 0, 1); AddEdge(adj, 0, 4); AddEdge(adj, 1, 2); AddEdge(adj, 1, 3); AddEdge(adj, 1, 4); AddEdge(adj, 2, 3); AddEdge(adj, 3, 4); DFS(adj, V); }} // this code is contributed by devendra |
Javascript
<script>// A simple representation of graph using STL,// for the purpose of competitive programming // A utility function to add an edge in an// undirected graph. function addEdge(adj,u,v) { adj[u].push(v); adj[v].push(u); } // A utility function to do DFS of graph// recursively from a given vertex u. function DFSUtil(u,adj,visited) { visited[u] = true; document.write(u+" "); for (let i=0; i<adj[u].length; i++) if (visited[adj[u][i]] == false) DFSUtil(adj[u][i], adj, visited); } // This function does DFSUtil() for all// unvisited vertices. function DFS(adj,V) { let visited=new Array(V); for(let i=0;i<V;i++) { visited[i]=false; } for (let u=0; u<V; u++) if (visited[u] == false) DFSUtil(u, adj, visited); } // Driver code let V = 5; // The below line may not work on all // compilers. If it does not work on // your compiler, please replace it with // following // vector<int> *adj = new vector<int>[V]; let adj=new Array(V); for(let i=0;i<V;i++) { adj[i]=[]; } // Vertex numbers should be from 0 to 4. addEdge(adj, 0, 1); addEdge(adj, 0, 4); addEdge(adj, 1, 2); addEdge(adj, 1, 3); addEdge(adj, 1, 4); addEdge(adj, 2, 3); addEdge(adj, 3, 4); DFS(adj, V); // This code is contributed by unknown2108</script> |
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Time complexity : O(V+E), where V is the number of vertices in the graph and E is the number of edges in the graph. This is because the code performs a Depth First Search (DFS) on the graph, which takes O(V+E) time, as it visits each vertex once and visits all its adjacent vertices.
Space complexity : O(V), where V is the number of vertices in the graph. This is because the code uses an adjacency list representation of the graph and maintains a visited array to keep track of visited vertices, both of which have a size of O(V). Additionally, the call stack of the DFSUtil function has a space complexity of O(V) in the worst case, when all vertices are reachable from a single vertex.
Below are related articles:
Graph implementation using STL for competitive programming | Set 2 (Weighted graph)
Dijkstra’s Shortest Path Algorithm using priority_queue of STL
Dijkstra’s shortest path algorithm using set in STL
Kruskal’s Minimum Spanning Tree using STL in C++
Prim’s algorithm using priority_queue in STL
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