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<title>Graph Breadth First Search BFS</title>
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<h1>Breadth first search</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn about breadth first search algorithm. Also, you will find working examples of bfs algorithm in C, C++, Java and Python.</p>
<div id="node-1052" class="node node-algorithm clearfix" about="/dsa/graph-bfs" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Breadth first search" class="rdf-meta element-hidden"></span>
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<p id="introduction">Traversal means visiting all the nodes of a graph. Breadth First Traversal or Breadth First Search is a recursive algorithm for searching all the vertices of a graph or tree data structure.</p>
<hr><h2 id="algorithm">BFS algorithm</h2>
<p>A standard BFS implementation puts each vertex of the graph into one of two categories:</p>
<ol><li>Visited</li>
<li>Not Visited</li>
</ol><p>The purpose of the algorithm is to mark each vertex as visited while avoiding cycles.</p>
<p>The algorithm works as follows:</p>
<ol><li>Start by putting any one of the graph's vertices at the back of a queue.</li>
<li>Take the front item of the queue and add it to the visited list.</li>
<li>Create a list of that vertex's adjacent nodes. Add the ones which aren't in the visited list to the back of the queue.</li>
<li>Keep repeating steps 2 and 3 until the queue is empty.</li>
</ol><p>The graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the BFS algorithm on every node</p>
<hr><h2 id="example">BFS example</h2>
<p>Let's see how the Breadth First Search algorithm works with an example. We use an undirected graph with 5 vertices.</p>
<figure><img alt="undirected graph with 5 vertices" src="//cdn.programiz.com/sites/tutorial2program/files/graph-bfs-step-0.png" title="Undirected graph with 5 vertices" width="1460" height="556"><figcaption>Undirected graph with 5 vertices</figcaption></figure><p>We start from vertex 0, the BFS algorithm starts by putting it in the Visited list and putting all its adjacent vertices in the stack.</p>
<figure><img alt="visit start vertex and add its adjacent vertices to queue" src="//cdn.programiz.com/sites/tutorial2program/files/graph-bfs-step-1.png" title="BFS example" width="1460" height="556"><figcaption>Visit start vertex and add its adjacent vertices to queue</figcaption></figure><p>Next, we visit the element at the front of queue i.e. 1 and go to its adjacent nodes. Since 0 has already been visited, we visit 2 instead.</p>
<figure><img alt="visit the first neighbour of start node 0, which is 1" src="//cdn.programiz.com/sites/tutorial2program/files/graph-bfs-step-2_2.png" title="BFS example" width="1460" height="566"><figcaption>Visit the first neighbour of start node 0, which is 1</figcaption></figure><p></p><div class="clearfix"></div><p>Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the back of the queue and visit 3, which is at the front of the queue.</p>
<figure><img alt="visit 2 which was added to queue earlier to add its neighbours" src="//cdn.programiz.com/sites/tutorial2program/files/graph-bfs-step-3.png" title="BFS algorithm" width="1460" height="566"><figcaption>Visit 2 which was added to queue earlier to add its neighbours</figcaption></figure><figure><img alt="visit " src="//cdn.programiz.com/sites/tutorial2program/files/graph-bfs-step-4.png" title="BFS example" width="1460" height="566"><figcaption>4 remains in the queue</figcaption></figure><p>Only 4 remains in the queue since the only adjacent node of 3 i.e. 0 is already visited. We visit it.</p>
<figure><img alt="visit last remaining item in queue to check if it has unvisited neighbours" src="//cdn.programiz.com/sites/tutorial2program/files/graph-bfs-step-5.png" title="BFS example" width="1460" height="566"><figcaption>Visit last remaining item in the queue to check if it has unvisited neighbors</figcaption></figure><p>Since the queue is empty, we have completed the Breadth First Traversal of the graph.</p>
<hr><h2 id="pseudocode">BFS pseudocode</h2>
<pre>create a queue Q
mark v as visited and put v into Q
while Q is non-empty
remove the head u of Q
mark and enqueue all (unvisited) neighbours of u</pre>
<hr><h2 id="code">Python, Java and C/C++ Examples</h2>
<p>The code for the Breadth First Search Algorithm with an example is shown below. The code has been simplified so that we can focus on the algorithm rather than other details.</p>
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<div id='py1'class="tabbed-editor__node tabbed-editor__node--active" onclick="changepy()"><a href="#python-code">Python</a></div>
<div id="java1" class="tabbed-editor__node" onclick="changejava()"><a href="#java-code">Java</a></div>
<div id="c1" class="tabbed-editor__node" onclick="changec()"><a href="#c-code">C</a></div>
<div id="cpp1" class="tabbed-editor__node" onclick="changecpp()"><a href="#cpp-code">C++</a></div>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># BFS algorithm in Python</span>
<span class="hljs-keyword">import</span> collections
<span class="hljs-comment"># BFS algorithm</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">bfs</span><span class="hljs-params">(graph, root)</span>:</span>
visited, queue = set(), collections.deque([root])
visited.add(root)
<span class="hljs-keyword">while</span> queue:
<span class="hljs-comment"># Dequeue a vertex from queue</span>
vertex = queue.popleft()
<span class="hljs-keyword">print</span>(str(vertex) + <span class="hljs-string">" "</span>, end=<span class="hljs-string">""</span>)
<span class="hljs-comment"># If not visited, mark it as visited, and</span>
<span class="hljs-comment"># enqueue it</span>
<span class="hljs-keyword">for</span> neighbour <span class="hljs-keyword">in</span> graph[vertex]:
<span class="hljs-keyword">if</span> neighbour <span class="hljs-keyword">not</span> <span class="hljs-keyword">in</span> visited:
visited.add(neighbour)
queue.append(neighbour)
<span class="hljs-keyword">if</span> __name__ == <span class="hljs-string">'__main__'</span>:
graph = {<span class="hljs-number">0</span>: [<span class="hljs-number">1</span>, <span class="hljs-number">2</span>], <span class="hljs-number">1</span>: [<span class="hljs-number">2</span>], <span class="hljs-number">2</span>: [<span class="hljs-number">3</span>], <span class="hljs-number">3</span>: [<span class="hljs-number">1</span>, <span class="hljs-number">2</span>]}
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Following is Breadth First Traversal: "</span>)
bfs(graph, <span class="hljs-number">0</span>)
</code></pre></div>
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<div class="code-editor__area" id="java-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// BFS algorithm in Java</span>
<span class="hljs-keyword">import</span> java.util.*;
<span class="hljs-keyword">public</span> <span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Graph</span> </span>{
<span class="hljs-keyword">private</span> <span class="hljs-keyword">int</span> V;
<span class="hljs-keyword">private</span> LinkedList<Integer> adj[];
<span class="hljs-comment">// Create a graph</span>
Graph(<span class="hljs-keyword">int</span> v) {
V = v;
adj = <span class="hljs-keyword">new</span> LinkedList[v];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < v; ++i)
adj[i] = <span class="hljs-keyword">new</span> LinkedList();
}
<span class="hljs-comment">// Add edges to the graph</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">addEdge</span><span class="hljs-params">(<span class="hljs-keyword">int</span> v, <span class="hljs-keyword">int</span> w)</span> </span>{
adj[v].add(w);
}
<span class="hljs-comment">// BFS algorithm</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">BFS</span><span class="hljs-params">(<span class="hljs-keyword">int</span> s)</span> </span>{
<span class="hljs-keyword">boolean</span> visited[] = <span class="hljs-keyword">new</span> <span class="hljs-keyword">boolean</span>[V];
LinkedList<Integer> queue = <span class="hljs-keyword">new</span> LinkedList();
visited[s] = <span class="hljs-keyword">true</span>;
queue.add(s);
<span class="hljs-keyword">while</span> (queue.size() != <span class="hljs-number">0</span>) {
s = queue.poll();
System.out.print(s + <span class="hljs-string">" "</span>);
Iterator<Integer> i = adj[s].listIterator();
<span class="hljs-keyword">while</span> (i.hasNext()) {
<span class="hljs-keyword">int</span> n = i.next();
<span class="hljs-keyword">if</span> (!visited[n]) {
visited[n] = <span class="hljs-keyword">true</span>;
queue.add(n);
}
}
}
}
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span> </span>{
Graph g = <span class="hljs-keyword">new</span> Graph(<span class="hljs-number">4</span>);
g.addEdge(<span class="hljs-number">0</span>, <span class="hljs-number">1</span>);
g.addEdge(<span class="hljs-number">0</span>, <span class="hljs-number">2</span>);
g.addEdge(<span class="hljs-number">1</span>, <span class="hljs-number">2</span>);
g.addEdge(<span class="hljs-number">2</span>, <span class="hljs-number">0</span>);
g.addEdge(<span class="hljs-number">2</span>, <span class="hljs-number">3</span>);
g.addEdge(<span class="hljs-number">3</span>, <span class="hljs-number">3</span>);
System.out.println(<span class="hljs-string">"Following is Breadth First Traversal "</span> + <span class="hljs-string">"(starting from vertex 2)"</span>);
g.BFS(<span class="hljs-number">2</span>);
}
}</code></pre></div>
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<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// BFS algorithm in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdlib.h></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> SIZE 40</span>
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">queue</span> {</span>
<span class="hljs-keyword">int</span> items[SIZE];
<span class="hljs-keyword">int</span> front;
<span class="hljs-keyword">int</span> rear;
};
<span class="hljs-function">struct <span class="hljs-built_in">queue</span>* <span class="hljs-title">createQueue</span><span class="hljs-params">()</span></span>;
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">enqueue</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q, <span class="hljs-keyword">int</span>)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">dequeue</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">display</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isEmpty</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printQueue</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span></span>;
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">node</span> {</span>
<span class="hljs-keyword">int</span> vertex;
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">node</span>* <span class="hljs-title">next</span>;</span>
};
<span class="hljs-function">struct node* <span class="hljs-title">createNode</span><span class="hljs-params">(<span class="hljs-keyword">int</span>)</span></span>;
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">Graph</span> {</span>
<span class="hljs-keyword">int</span> numVertices;
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">node</span>** <span class="hljs-title">adjLists</span>;</span>
<span class="hljs-keyword">int</span>* visited;
};
<span class="hljs-comment">// BFS algorithm</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">bfs</span><span class="hljs-params">(struct Graph* graph, <span class="hljs-keyword">int</span> startVertex)</span> </span>{
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">queue</span>* <span class="hljs-title">q</span> = <span class="hljs-title">createQueue</span>();</span>
graph->visited[startVertex] = <span class="hljs-number">1</span>;
enqueue(q, startVertex);
<span class="hljs-keyword">while</span> (!isEmpty(q)) {
printQueue(q);
<span class="hljs-keyword">int</span> currentVertex = dequeue(q);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Visited %d\n"</span>, currentVertex);
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">node</span>* <span class="hljs-title">temp</span> = <span class="hljs-title">graph</span>-><span class="hljs-title">adjLists</span>[<span class="hljs-title">currentVertex</span>];</span>
<span class="hljs-keyword">while</span> (temp) {
<span class="hljs-keyword">int</span> adjVertex = temp->vertex;
<span class="hljs-keyword">if</span> (graph->visited[adjVertex] == <span class="hljs-number">0</span>) {
graph->visited[adjVertex] = <span class="hljs-number">1</span>;
enqueue(q, adjVertex);
}
temp = temp->next;
}
}
}
<span class="hljs-comment">// Creating a node</span>
<span class="hljs-function">struct node* <span class="hljs-title">createNode</span><span class="hljs-params">(<span class="hljs-keyword">int</span> v)</span> </span>{
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">node</span>* <span class="hljs-title">newNode</span> = <span class="hljs-title">malloc</span>(<span class="hljs-title">sizeof</span>(<span class="hljs-title">struct</span> <span class="hljs-title">node</span>));</span>
newNode->vertex = v;
newNode->next = <span class="hljs-literal">NULL</span>;
<span class="hljs-keyword">return</span> newNode;
}
<span class="hljs-comment">// Creating a graph</span>
<span class="hljs-function">struct Graph* <span class="hljs-title">createGraph</span><span class="hljs-params">(<span class="hljs-keyword">int</span> vertices)</span> </span>{
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">Graph</span>* <span class="hljs-title">graph</span> = <span class="hljs-title">malloc</span>(<span class="hljs-title">sizeof</span>(<span class="hljs-title">struct</span> <span class="hljs-title">Graph</span>));</span>
graph->numVertices = vertices;
graph->adjLists = <span class="hljs-built_in">malloc</span>(vertices * <span class="hljs-keyword">sizeof</span>(struct node*));
graph->visited = <span class="hljs-built_in">malloc</span>(vertices * <span class="hljs-keyword">sizeof</span>(<span class="hljs-keyword">int</span>));
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < vertices; i++) {
graph->adjLists[i] = <span class="hljs-literal">NULL</span>;
graph->visited[i] = <span class="hljs-number">0</span>;
}
<span class="hljs-keyword">return</span> graph;
}
<span class="hljs-comment">// Add edge</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">addEdge</span><span class="hljs-params">(struct Graph* graph, <span class="hljs-keyword">int</span> src, <span class="hljs-keyword">int</span> dest)</span> </span>{
<span class="hljs-comment">// Add edge from src to dest</span>
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">node</span>* <span class="hljs-title">newNode</span> = <span class="hljs-title">createNode</span>(<span class="hljs-title">dest</span>);</span>
newNode->next = graph->adjLists[src];
graph->adjLists[src] = newNode;
<span class="hljs-comment">// Add edge from dest to src</span>
newNode = createNode(src);
newNode->next = graph->adjLists[dest];
graph->adjLists[dest] = newNode;
}
<span class="hljs-comment">// Create a queue</span>
<span class="hljs-function">struct <span class="hljs-built_in">queue</span>* <span class="hljs-title">createQueue</span><span class="hljs-params">()</span> </span>{
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">queue</span>* <span class="hljs-title">q</span> = <span class="hljs-title">malloc</span>(<span class="hljs-title">sizeof</span>(<span class="hljs-title">struct</span> <span class="hljs-title">queue</span>));</span>
q->front = <span class="hljs-number">-1</span>;
q->rear = <span class="hljs-number">-1</span>;
<span class="hljs-keyword">return</span> q;
}
<span class="hljs-comment">// Check if the queue is empty</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isEmpty</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span> </span>{
<span class="hljs-keyword">if</span> (q->rear == <span class="hljs-number">-1</span>)
<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;
<span class="hljs-keyword">else</span>
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
<span class="hljs-comment">// Adding elements into queue</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">enqueue</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q, <span class="hljs-keyword">int</span> value)</span> </span>{
<span class="hljs-keyword">if</span> (q->rear == SIZE - <span class="hljs-number">1</span>)
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nQueue is Full!!"</span>);
<span class="hljs-keyword">else</span> {
<span class="hljs-keyword">if</span> (q->front == <span class="hljs-number">-1</span>)
q->front = <span class="hljs-number">0</span>;
q->rear++;
q->items[q->rear] = value;
}
}
<span class="hljs-comment">// Removing elements from queue</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">dequeue</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span> </span>{
<span class="hljs-keyword">int</span> item;
<span class="hljs-keyword">if</span> (isEmpty(q)) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Queue is empty"</span>);
item = <span class="hljs-number">-1</span>;
} <span class="hljs-keyword">else</span> {
item = q->items[q->front];
q->front++;
<span class="hljs-keyword">if</span> (q->front > q->rear) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Resetting queue "</span>);
q->front = q->rear = <span class="hljs-number">-1</span>;
}
}
<span class="hljs-keyword">return</span> item;
}
<span class="hljs-comment">// Print the queue</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printQueue</span><span class="hljs-params">(struct <span class="hljs-built_in">queue</span>* q)</span> </span>{
<span class="hljs-keyword">int</span> i = q->front;
<span class="hljs-keyword">if</span> (isEmpty(q)) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Queue is empty"</span>);
} <span class="hljs-keyword">else</span> {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nQueue contains \n"</span>);
<span class="hljs-keyword">for</span> (i = q->front; i < q->rear + <span class="hljs-number">1</span>; i++) {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, q->items[i]);
}
}
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">Graph</span>* <span class="hljs-title">graph</span> = <span class="hljs-title">createGraph</span>(6);</span>
addEdge(graph, <span class="hljs-number">0</span>, <span class="hljs-number">1</span>);
addEdge(graph, <span class="hljs-number">0</span>, <span class="hljs-number">2</span>);
addEdge(graph, <span class="hljs-number">1</span>, <span class="hljs-number">2</span>);
addEdge(graph, <span class="hljs-number">1</span>, <span class="hljs-number">4</span>);
addEdge(graph, <span class="hljs-number">1</span>, <span class="hljs-number">3</span>);
addEdge(graph, <span class="hljs-number">2</span>, <span class="hljs-number">4</span>);
addEdge(graph, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>);
bfs(graph, <span class="hljs-number">0</span>);
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// BFS algorithm in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><list></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Graph</span> {</span>
<span class="hljs-keyword">int</span> numVertices;
<span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>>* adjLists;
<span class="hljs-keyword">bool</span>* visited;
<span class="hljs-keyword">public</span>:
Graph(<span class="hljs-keyword">int</span> vertices);
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">addEdge</span><span class="hljs-params">(<span class="hljs-keyword">int</span> src, <span class="hljs-keyword">int</span> dest)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">BFS</span><span class="hljs-params">(<span class="hljs-keyword">int</span> startVertex)</span></span>;
};
<span class="hljs-comment">// Create a graph with given vertices,</span>
<span class="hljs-comment">// and maintain an adjacency list</span>
Graph::Graph(<span class="hljs-keyword">int</span> vertices) {
numVertices = vertices;
adjLists = <span class="hljs-keyword">new</span> <span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>>[vertices];
}
<span class="hljs-comment">// Add edges to the graph</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">Graph::addEdge</span><span class="hljs-params">(<span class="hljs-keyword">int</span> src, <span class="hljs-keyword">int</span> dest)</span> </span>{
adjLists[src].push_back(dest);
adjLists[dest].push_back(src);
}
<span class="hljs-comment">// BFS algorithm</span>
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">Graph::BFS</span><span class="hljs-params">(<span class="hljs-keyword">int</span> startVertex)</span> </span>{
visited = <span class="hljs-keyword">new</span> <span class="hljs-keyword">bool</span>[numVertices];
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < numVertices; i++)
visited[i] = <span class="hljs-literal">false</span>;
<span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>> <span class="hljs-built_in">queue</span>;
visited[startVertex] = <span class="hljs-literal">true</span>;
<span class="hljs-built_in">queue</span>.push_back(startVertex);
<span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>>::iterator i;
<span class="hljs-keyword">while</span> (!<span class="hljs-built_in">queue</span>.empty()) {
<span class="hljs-keyword">int</span> currVertex = <span class="hljs-built_in">queue</span>.front();
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Visited "</span> << currVertex << <span class="hljs-string">" "</span>;
<span class="hljs-built_in">queue</span>.pop_front();
<span class="hljs-keyword">for</span> (i = adjLists[currVertex].begin(); i != adjLists[currVertex].end(); ++i) {
<span class="hljs-keyword">int</span> adjVertex = *i;
<span class="hljs-keyword">if</span> (!visited[adjVertex]) {
visited[adjVertex] = <span class="hljs-literal">true</span>;
<span class="hljs-built_in">queue</span>.push_back(adjVertex);
}
}
}
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-function">Graph <span class="hljs-title">g</span><span class="hljs-params">(<span class="hljs-number">4</span>)</span></span>;
g.addEdge(<span class="hljs-number">0</span>, <span class="hljs-number">1</span>);
g.addEdge(<span class="hljs-number">0</span>, <span class="hljs-number">2</span>);
g.addEdge(<span class="hljs-number">1</span>, <span class="hljs-number">2</span>);
g.addEdge(<span class="hljs-number">2</span>, <span class="hljs-number">0</span>);
g.addEdge(<span class="hljs-number">2</span>, <span class="hljs-number">3</span>);
g.addEdge(<span class="hljs-number">3</span>, <span class="hljs-number">3</span>);
g.BFS(<span class="hljs-number">2</span>);
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
</div>
<hr><h2 id="complexity">BFS Algorithm Complexity</h2>
<p>The time complexity of the BFS algorithm is represented in the form of <code>O(V + E)</code>, where <var>V</var> is the number of nodes and E is the number of edges.</p>
<p>The space complexity of the algorithm is <code>O(V)</code>.</p>
<hr><h2 id="applications">BFS Algorithm Applications</h2>
<ol><li>To build index by search index</li>
<li>For GPS navigation</li>
<li>Path finding algorithms</li>
<li>In Ford-Fulkerson algorithm to find maximum flow in a network</li>
<li>Cycle detection in an undirected graph</li>
<li>In <a href="/dsa/spanning-tree-and-minimum-spanning-tree">minimum spanning tree</a></li>
</ol></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#introduction">Introduction</a></li>
<li><a href="#algorithm">BFS algorithm</a></li>
<li><a href="#example">BFS example</a></li>
<li><a href="#pseudocode">BFS pseudocode</a></li>
<li><a href="#code">Python, Java and C/C++ Examples</a></li>
<li><a href="#complexity">BFS Algorithm Complexity</a></li>
<li><a href="#applications">BFS Algorithm Applications</a></li>
</ul></div></div></div> </div>
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