DFS implementation in C<\/h3>\n#include <stdio.h>\r\n#include <stdlib.h>\r\n\r\nstruct node \r\n{\r\n int vertex;\r\n struct node* next;\r\n};\r\n\r\nstruct node* createNode(int v);\r\n\r\nstruct Graph \r\n{\r\n int numVertices;\r\n int* visited;\r\n\r\n struct node** adjLists;\r\n};\r\n\r\nvoid DFS(struct Graph* graph, int vertex) \r\n{\r\n struct node* adjList = graph->adjLists[vertex];\r\n struct node* temp = adjList;\r\n\r\n graph->visited[vertex] = 1;\r\n printf(\"Visited %d \\n\", vertex);\r\n\r\n while (temp != NULL) \r\n {\r\n int connected_Vertex = temp->vertex;\r\n\r\n if (graph->visited[connected_Vertex] == 0) \r\n {\r\n DFS(graph, connected_Vertex);\r\n }\r\n temp = temp->next;\r\n }\r\n}\r\n\r\nstruct node* createNode(int vert) \r\n{\r\n struct node* newNode = malloc(sizeof(struct node));\r\n newNode->vertex = vert;\r\n newNode->next = NULL;\r\n return newNode;\r\n}\r\n\r\nstruct Graph* createGraph(int vertices) \r\n{\r\n struct Graph* graph = malloc(sizeof(struct Graph));\r\n graph->numVertices = vertices;\r\n\r\n graph->adjLists = malloc(vertices * sizeof(struct node*));\r\n\r\n graph->visited = malloc(vertices * sizeof(int));\r\n\r\n int i;\r\n \r\n for (i = 0; i < vertices; i++) \r\n {\r\n graph->adjLists[i] = NULL;\r\n graph->visited[i] = 0;\r\n }\r\n return graph;\r\n}\r\n\r\nvoid addEdge(struct Graph* graph, int src, int dest) \r\n{\r\n struct node* newNode = createNode(dest);\r\n newNode->next = graph->adjLists[src];\r\n graph->adjLists[src] = newNode;\r\n\r\n newNode = createNode(src);\r\n newNode->next = graph->adjLists[dest];\r\n graph->adjLists[dest] = newNode;\r\n}\r\n\r\nvoid printDFS(struct Graph* graph) \r\n{\r\n int v;\r\n for (v = 0; v < graph->numVertices; v++) \r\n {\r\n struct node* temp = graph->adjLists[v];\r\n printf(\"\\nvertex %d\\ : \", v);\r\n while (temp) {\r\n printf(\"%d -> \", temp->vertex);\r\n temp = temp->next;\r\n }\r\n printf(\"\\n\");\r\n }\r\n}\r\n\r\nint main() \r\n{\r\n struct Graph* graph = createGraph(5);\r\n addEdge(graph, 0, 1);\r\n addEdge(graph, 0, 2);\r\n addEdge(graph, 0, 3);\r\n addEdge(graph, 1, 4);\r\n addEdge(graph, 2, 3);\r\n\r\n printDFS(graph);\r\n\r\n DFS(graph, 0);\r\n\r\n return 0;\r\n}\r\n<\/pre>\nDFS implementation in C++<\/h3>\n#include <iostream>\r\n#include <list>\r\nusing namespace std;\r\n\r\nclass DSGraph \r\n{\r\n int numVertices;\r\n list<int> *adjLists;\r\n bool *visited;\r\n\r\n public:\r\n DSGraph(int V);\r\n void addEdge(int src, int dest);\r\n void DFS(int vertex);\r\n};\r\n\r\nDSGraph::DSGraph(int vert) \r\n{\r\n numVertices = vert;\r\n adjLists = new list<int>[vert];\r\n visited = new bool[vert];\r\n}\r\n\r\nvoid DSGraph::addEdge(int S_node, int D_node) \r\n{\r\n adjLists[S_node].push_front(D_node);\r\n}\r\n\r\nvoid DSGraph::DFS(int vertex) \r\n{\r\n visited[vertex] = true;\r\n list<int> adjList = adjLists[vertex];\r\n\r\n cout << vertex << \" \";\r\n\r\n list<int>::iterator i;\r\n for (i = adjList.begin(); i != adjList.end(); ++i)\r\n if (!visited[*i])\r\n DFS(*i);\r\n}\r\n\r\nint main() {\r\n DSGraph g(5);\r\n g.addEdge(0, 1);\r\n g.addEdge(0, 2);\r\n g.addEdge(0, 3);\r\n g.addEdge(1, 4);\r\n g.addEdge(2, 3);\r\n\r\n g.DFS(3);\r\n\r\n return 0;\r\n}<\/pre>\nImplementation of Depth First Search in JAVA<\/h3>\nimport java.util.*;\r\n\r\npublic class Graph \r\n{\r\n private LinkedList<Integer> adjLists[];\r\n private boolean visited[];\r\n\r\n Graph(int vert) \r\n {\r\n adjLists = new LinkedList[vert];\r\n visited = new boolean[vert];\r\n\r\n for (int i = 0; i < vert; i++)\r\n adjLists[i] = new LinkedList<Integer>();\r\n }\r\n\r\n void addEdge(int S_node, int D_node) \r\n {\r\n adjLists[S_node].add(D_node);\r\n }\r\n\r\n void DFS(int vertex) \r\n {\r\n visited[vertex] = true;\r\n System.out.print(vertex + \" \");\r\n\r\n Iterator<Integer> ite = adjLists[vertex].listIterator();\r\n while (ite.hasNext()) {\r\n int adj = ite.next();\r\n if (!visited[adj])\r\n DFS(adj);\r\n }\r\n }\r\n\r\n public static void main(String args[]) \r\n {\r\n Graph g = new Graph(5);\r\n\r\n g.addEdge(0, 1);\r\n g.addEdge(0, 2);\r\n g.addEdge(0, 3);\r\n g.addEdge(1, 4);\r\n g.addEdge(2, 3);\r\n\r\n System.out.println(\"DFS\");\r\n\r\n g.DFS(2);\r\n }\r\n}<\/pre>\nDFS implementation in Python<\/h3>\ngraph = {\r\n 'A' : ['B','C','D'],\r\n 'B' : ['E'],\r\n 'C' : ['D'],\r\n 'D' : ['C'],\r\n 'E' : ['C']\r\n }\r\n\r\nvisited = set() \r\n\r\ndef dfs(visited, graph, node):\r\n if node not in visited:\r\n print (node)\r\n visited.add(node)\r\n for neighbour in graph[node]:\r\n dfs(visited, graph, neighbour)\r\n\r\ndfs(visited, graph, 'A')<\/pre>\nDepth First Search Complexity<\/h3>\n
The time complexity of DFS is represented in the form O(V+E) where V is the number of vertices and E is the number of edges.<\/p>\n
The space complexity of DFS algorithms is O(V).<\/p>\n
Disconnected graph in DFS<\/h3>\n
It might be possible that all the vertices are not reachable from the starting vertex in the case of a disconnected graph. For complete DFS traversal, Run DFS traversal from all unvisited nodes after the connected graph is completely visited.<\/p>\n
Procedure<\/h3>\n
1. Create a recursive function that takes the index of the node and a visited array as the input.
\n2. Mark the current node as a visited node.
\n3. Traverse all the adjacent and unmarked nodes
\n4. Run a loop from 0 to the number of nodes and check if the node is unvisited. If yes, call the recursive function with the index of the unvisited node.<\/p>\n
Handling disconnected graph in C++<\/h3>\n#include <iostream>\r\n#include <list>\r\nusing namespace std;\r\n\r\nclass DSGraph \r\n{\r\n int numVertices;\r\n list<int> *adjLists;\r\n bool *visited;\r\n\r\n public:\r\n map<int, bool> visited;\r\n map<int, list<int>> adj;\r\n DSGraph(int V);\r\n void addEdge(int src, int dest);\r\n void DFS(int vertex);\r\n};\r\n\r\nDSGraph::DSGraph(int vert) \r\n{\r\n numVertices = vert;\r\n adjLists = new list<int>[vert];\r\n visited = new bool[vert];\r\n}\r\n\r\nvoid DSGraph::addEdge(int S_node, int D_node) \r\n{\r\n adjLists[S_node].push_front(D_node);\r\n}\r\n\r\nvoid DSGraph::DFS(int vertex) \r\n{\r\n visited[vertex] = true;\r\n list<int> adjList = adjLists[vertex];\r\n\r\n cout << vertex << \" \";\r\n\r\n list<int>::iterator i;\r\n for (i = adjList.begin(); i != adjList.end(); ++i)\r\n if (!visited[*i])\r\n DFS(*i);\r\n\r\n for (auto i:adj)\r\n if (visited[i.first] == false)\r\n DFSUtil(i.first);\r\n\r\n}\r\n\r\nint main() {\r\n DSGraph g(5);\r\n g.addEdge(0, 1);\r\n g.addEdge(0, 2);\r\n g.addEdge(0, 3);\r\n g.addEdge(1, 4);\r\n g.addEdge(2, 3);\r\n\r\n g.DFS(3);\r\n\r\n return 0;\r\n}<\/pre>\nHandling disconnected graph in JAVA<\/h3>\nimport java.util.*;\r\n\r\npublic class Graph \r\n{\r\n private LinkedList<Integer> adjLists[];\r\n private boolean visited[];\r\n\r\n Graph(int vert) \r\n {\r\n adjLists = new LinkedList[vert];\r\n visited = new boolean[vert];\r\n\r\n for (int i = 0; i < vert; i++)\r\n adjLists[i] = new LinkedList<Integer>();\r\n }\r\n\r\n void addEdge(int S_node, int D_node) \r\n {\r\n adjLists[S_node].add(D_node);\r\n }\r\n\r\n void DFS(int vertex) \r\n {\r\n Boolean visited[] =new boolean[4]\r\n visited[vertex] = true;\r\n System.out.print(vertex + \" \");\r\n\r\n Iterator<Integer> ite = adjLists[vertex].listIterator();\r\n while (ite.hasNext()) {\r\n int adj = ite.next();\r\n if (!visited[adj])\r\n DFS(adj);\r\nfor (int i = 0; i < V; ++i)\r\n if (visited[i] == false)\r\n DFS(visited);\r\n\r\n }\r\n }\r\n\r\n public static void main(String args[]) \r\n {\r\n Graph g = new Graph(5);\r\n\r\n g.addEdge(0, 1);\r\n g.addEdge(0, 2);\r\n g.addEdge(0, 3);\r\n g.addEdge(1, 4);\r\n g.addEdge(2, 3);\r\n\r\n System.out.println(\"DFS\");\r\n\r\n g.DFS(2);\r\n }\r\n}\r\n\r\n<\/pre>\nDFS implementation in Python<\/h3>\ngraph = {\r\n 'A' : ['B','C','D'],\r\n 'B' : ['E'],\r\n 'C' : ['D'],\r\n 'D' : ['C'],\r\n 'E' : ['C']\r\n }\r\n\r\nvisited = set() \r\n\r\ndef dfs(visited, graph, node):\r\n if node not in visited:\r\n print (node)\r\n visited.add(node)\r\n for neighbour in graph[node]:\r\n dfs(visited, graph, neighbour)\r\n for vertex in list(self.graph):\r\n if vertex not in visited:\r\n self.dfs(vertex, graph, node)\r\n\r\n\r\ndfs(visited, graph, 'A')<\/pre>\nApplications of Depth First Search<\/h3>\n
1. Solving maze like puzzles with only one solution
\n2. Dfs is highly preferred approach for solving problem like, job scheduling, data serialization, etc using topological sorting
\n3. Network analysis and mapping routes
\n4. Detection of cycle in graphs<\/p>\n
Conclusion<\/h3>\n
DFS is the traversal algorithms for graphs and trees. In this article, we witnessed the DFS algorithm, its working, and its implementation in different programming languages. In the next article, we will learn about another graph traversal algorithm BFS ( Breadth-First Search ).<\/p>\n","protected":false},"excerpt":{"rendered":"
In the last article, we learned about graphs in data structures. Graphs are one of the efficient ways that are used to model daily life problems and find an optimal solution. In this article,...<\/p>\n","protected":false},"author":1,"featured_media":97909,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24020],"tags":[24709,24704,24705,24708,24707,24706],"class_list":["post-97883","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-structure-tutorials","tag-applications-of-depth-first-search","tag-depth-first-search","tag-depth-first-search-algorithm","tag-dfs-implementation-in-python","tag-disconnected-graph-in-c","tag-implementation-of-dfs"],"yoast_head":"\n
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![\"Depth](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image01.jpg\")
<\/a><\/p>\n![\"Adjacency](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image02.jpg\")
<\/a><\/p>\n![\"Push](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image03.jpg\")
<\/a><\/p>\n![\"Pushing](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image04.jpg\")
<\/a><\/p>\n![\"DFS](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image05.jpg\")
<\/a><\/p>\n![\"DFS](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image06.jpg\")
<\/a><\/p>\n![\"DFS](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Depth-First-Search-in-DS-normal-image07.jpg\")
<\/a><\/p>\n