implementation of Breadth First Search in C<\/h3>\n#include <stdio.h>\r\n#include <stdlib.h>\r\n#define SIZE 40\r\n\r\nstruct queue \r\n{\r\n int items[SIZE];\r\n int front;\r\n int rear;\r\n};\r\n\r\nstruct queue* createQueue();\r\nvoid enqueue(struct queue* q, int);\r\nint dequeue(struct queue* q);\r\nvoid display(struct queue* q);\r\nint isEmpty(struct queue* q);\r\nvoid printQueue(struct queue* q);\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);\r\n\r\nstruct Graph \r\n{\r\n int numVertices;\r\n struct node** adjLists;\r\n int* visited;\r\n};\r\n\r\nvoid bfs(struct Graph* graph, int startNode) \r\n{\r\n struct queue* q = createQueue();\r\n\r\n graph->visited[startNode] = 1;\r\n enqueue(q, startNode);\r\n\r\n while (!isEmpty(q)) \r\n {\r\n printQueue(q);\r\n int currentNode = dequeue(q);\r\n printf(\"Visited %d\\n\", currentNode);\r\n\r\n struct node* temp = graph->adjLists[currentNode];\r\n\r\n while (temp) \r\n {\r\n int adjVertex = temp->vertex;\r\n\r\n if (graph->visited[adjVertex] == 0) \r\n {\r\n graph->visited[adjVertex] = 1;\r\n enqueue(q, adjVertex);\r\n }\r\n temp = temp->next;\r\n }\r\n }\r\n}\r\n\r\nstruct node* createNode(int ver) \r\n{\r\n struct node* newNode = malloc(sizeof(struct node));\r\n newNode->vertex = ver;\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 graph->visited = malloc(vertices * sizeof(int));\r\n\r\n int i;\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\r\n return graph;\r\n}\r\n\r\nvoid addEdge(struct Graph* graph, int s_node, int d_node) \r\n{\r\n struct node* newNode = createNode(d_node);\r\n newNode->next = graph->adjLists[s_node];\r\n graph->adjLists[s_node] = newNode;\r\n\r\n newNode = createNode(s_node);\r\n newNode->next = graph->adjLists[d_node];\r\n graph->adjLists[d_node] = newNode;\r\n}\r\n\r\nstruct queue* createQueue() \r\n{\r\n struct queue* q = malloc(sizeof(struct queue));\r\n q->front = -1;\r\n q->rear = -1;\r\n return q;\r\n}\r\n\r\nint isEmpty(struct queue* q) \r\n{\r\n if (q->rear == -1)\r\n return 1;\r\n else\r\n return 0;\r\n}\r\n\r\nvoid enqueue(struct queue* q, int val) \r\n{\r\n if (q->rear == SIZE - 1)\r\n printf(\"\\nQueue is Full!!\");\r\n else {\r\n if (q->front == -1)\r\n q->front = 0;\r\n q->rear++;\r\n q->items[q->rear] = val;\r\n }\r\n}\r\n\r\nint dequeue(struct queue* q) \r\n{\r\n int item;\r\n if (isEmpty(q)) \r\n {\r\n printf(\"Queue is empty\");\r\n item = -1;\r\n } \r\n else \r\n {\r\n item = q->items[q->front];\r\n q->front++;\r\n if (q->front > q->rear) \r\n {\r\n q->front = q->rear = -1;\r\n }\r\n }\r\n return item;\r\n}\r\n\r\nvoid printQueue(struct queue* q) \r\n{\r\n int i = q->front;\r\n\r\n if (isEmpty(q))\r\n {\r\n printf(\"Queue empty\");\r\n } \r\n else \r\n {\r\n printf(\"\\n current Queue \\n\");\r\n for (i = q->front; i < q->rear + 1; i++) \r\n {\r\n printf(\"%d \", q->items[i]);\r\n }\r\n }\r\n}\r\n\r\nint main() \r\n{\r\n struct Graph* graph = createGraph(6);\r\n addEdge(graph, 0, 1);\r\n addEdge(graph, 0, 2);\r\n addEdge(graph, 0, 3);\r\n addEdge(graph, 1, 2);\r\n addEdge(graph, 1, 3);\r\n addEdge(graph, 2, 4);\r\n addEdge(graph, 3, 4);\r\n\r\n bfs(graph, 0);\r\n\r\n return 0;\r\n}\r\n<\/pre>\nBFS implementation in C++<\/h3>\n#include <iostream>\r\n#include <list>\r\nusing namespace std;\r\n\r\nclass BFSGraph \r\n{\r\n int numVertices;\r\n list<int>* adjLists;\r\n bool* visited;\r\n\r\n public:\r\n BFSGraph(int vertices);\r\n void addEdge(int src, int dest);\r\n void BFS(int startVertex);\r\n};\r\n\r\nBFSGraph::BFSGraph(int vertices) \r\n{\r\n numVertices = vertices;\r\n adjLists = new list<int>[vertices];\r\n}\r\n\r\nvoid BFSGraph::addEdge(int s_node, int d_node) \r\n{\r\n adjLists[s_node].push_back(d_node);\r\n adjLists[d_node].push_back(s_node);\r\n}\r\n\r\nvoid BFSGraph::BFS(int startVertex) \r\n{\r\n visited = new bool[numVertices];\r\n for (int i = 0; i < numVertices; i++)\r\n visited[i] = false;\r\n\r\n list<int> queue;\r\n\r\n visited[startVertex] = true;\r\n queue.push_back(startVertex);\r\n\r\n list<int>::iterator i;\r\n\r\n while (!queue.empty())\r\n {\r\n int currentVertex = queue.front();\r\n cout << \"Visited \" << currentVertex << \"\\n\";\r\n queue.pop_front();\r\n\r\n for (i = adjLists[currentVertex].begin(); i != adjLists[currentVertex].end(); ++i) \r\n {\r\n int adjVertex = *i;\r\n if (!visited[adjVertex]) \r\n {\r\n visited[adjVertex] = true;\r\n queue.push_back(adjVertex);\r\n }\r\n }\r\n }\r\n}\r\n\r\nint main() \r\n{\r\n BFSGraph g(4);\r\n g.addEdge(0, 1);\r\n g.addEdge(0, 2);\r\n g.addEdge(0, 3);\r\n g.addEdge(2, 0);\r\n g.addEdge(2, 1);\r\n g.addEdge(3, 3);\r\n g.addEdge(3, 1);\r\n\r\n g.BFS(2);\r\n\r\n return 0;\r\n}\r\n<\/pre>\nImplementation of BFS in JAVA<\/h3>\nimport java.util.*;\r\n\r\npublic class BFSGraph \r\n{\r\n private int V;\r\n private LinkedList<Integer> adj[];\r\n\r\n BFSGraph(int v) \r\n {\r\n V = v;\r\n adj = new LinkedList[v];\r\n for (int i = 0; i < v; ++i)\r\n adj[i] = new LinkedList();\r\n }\r\n\r\n void addEdge(int v, int w) \r\n {\r\n adj[v].add(w);\r\n }\r\n\r\n void BFS(int s) \r\n {\r\n\r\n boolean visited[] = new boolean[V];\r\n\r\n LinkedList<Integer> queue = new LinkedList();\r\n\r\n visited[s] = true;\r\n queue.add(s);\r\n\r\n while (queue.size() != 0) \r\n {\r\n s = queue.poll();\r\n System.out.print(s + \" \");\r\n\r\n Iterator<Integer> i = adj[s].listIterator();\r\n while (i.hasNext()) \r\n {\r\n int n = i.next();\r\n if (!visited[n]) \r\n {\r\n visited[n] = true;\r\n queue.add(n);\r\n }\r\n }\r\n }\r\n }\r\n\r\n public static void main(String args[]) \r\n {\r\n BFSGraph g = new BFSGraph(4);\r\n\r\n g.addEdge(0, 1);\r\n g.addEdge(0, 2);\r\n g.addEdge(0, 3);\r\n g.addEdge(2, 1);\r\n g.addEdge(2, 3);\r\n g.addEdge(3, 3);\r\n g.addEdge(3, 0);\r\n\r\n System.out.println(\"Breadth First Traversal \");\r\n\r\n g.BFS(2);\r\n }\r\n}\r\n<\/pre>\nBFS implementation in python<\/h3>\nimport collections\r\n\r\ndef bfs(graph, root):\r\n\r\n visited, queue = set(), collections.deque([root])\r\n visited.add(root)\r\n\r\n while queue:\r\n\r\n ver = queue.popleft()\r\n print(str(ver) + \" \", end=\"\")\r\n\r\n for near in graph[ver]:\r\n if near not in visited:\r\n visited.add(near)\r\n queue.append(near)\r\n\r\n\r\nif __name__ == '__main__':\r\n graph = {0: [1, 2], 1: [2,0], 2: [3], 3: [1, 2]}\r\n print(\"Breadth First Traversal: \")\r\n bfs(graph, 1)\r\n<\/pre>\nComplexity of Breadth-First Search<\/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
Applications of BFS<\/h3>\n
BFS Algorithm is used in<\/p>\n
1. Pathfinding algorithms
\n2. GPS Navigation
\n3. Minimum spanning trees
\n4. Building index by search index
\n5. Ford Fulkerson algorithm. Finds maximum flow in a network
\n6. Detection of a cycle in an undirected graph<\/p>\n
Conclusion<\/h3>\n
With this article, the graph data structure is complete. We now have a complete understanding of the Graphs in Data structures and their different representation in form of an adjacency list and an adjacency matrix.<\/p>\n
In other articles, we have seen traversal algorithms for finding a node in the graph or tree and its implementation in different programming languages. In future articles, we will learn about the tree data structures and everything related to them.<\/p>\n","protected":false},"excerpt":{"rendered":"
Just like DFS, BFS (Breadth-first Search ) is also a recursive traversal algorithm for searching all vertices of the graph or tree data structure. In this article, we will learn about BFS, its implementation,...<\/p>\n","protected":false},"author":1,"featured_media":98171,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24020],"tags":[24717,24718,24715,24716,24714],"class_list":["post-97936","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-structure-tutorials","tag-bfs-algorithm","tag-bfs-implementation","tag-bfs-in-data-structure","tag-bfs-working","tag-breadth-first-search"],"yoast_head":"\n
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![\"Breadth](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Breadth-First-Search-in-DS-normal-image01.jpg\")
<\/a><\/p>\n![\"Steps](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Breadth-First-Search-in-DS-normal-image02.jpg\")
<\/a><\/p>\n![\"Breadth](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Breadth-First-Search-in-DS-normal-image03.jpg\")
<\/a><\/p>\n![\"Breadth](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Breadth-First-Search-in-DS-normal-image04.jpg\")
<\/a><\/p>\n![\"BFS](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Breadth-First-Search-in-DS-normal-image05.jpg\")
<\/a><\/p>\n![\"Working](\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2021\/07\/Breadth-First-Search-in-DS-normal-image06.jpg\")
<\/a><\/p>\n