Merge pull request #210 from Iamtripathisatyam/main

Breadth First Search

Author: prathimacode-hub

Graphs/Breadth First Search/Images/input.jpg

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+## Overview:
+Two techniques are frequently used for graph traversal: These techniques are called depth-first search (DFS) and breadth-first search (BFS), although we will just talk about BFS. Breadth-first search (BFS) is used to solve many problems, including finding the shortest path in a graph or solving puzzle games such as Rubik’s Cubes.
+
+## What is Breadth First Search in Python?
+Breadth-first search (BFS) is an algorithm for traversing graphs or trees. Breath-first search for trees and graphs are almost the same. BFS uses a queue data structure for finding the shortest path in a graph.
+
+## Algorithm of DFS in Python
+The algorithm works as follows:
+
+* Create a queue and insert any one vertex of the graph at the back of the queue.
+* Initialize a visited array and mark that vertex as visited.
+* Follow the below process till the queue becomes empty:
+  * Remove a front vertex from the queue.
+  * Get all the adjacent vertices of the removed vertex.
+  * If the adjacent vertex has not been visited, mark it as visited and insert it at the back of the queue.
+
+## Time & Space Complexity
+* Time complexity is `O(V+E)`, where V denotes the number of vertices and E denotes the number of edges. 
+* Space complexity is `O(V)`.
+
+## Input & Output
+### Input:
+
+ <img width=50% src="../Breadth First Search/Images/input.jpg"> 
+
+```python
+graph = {
+    'A': ['B', 'C', 'D'],
+    'B': ['A'],
+    'C': ['A', 'D'],
+    'D': ['A', 'C', 'E'],
+    'E': ['D']
+}
+```
+### Output:
+ <img width=50% src="../Breadth First Search/Images/output.jpg"> 
+ 
+```python
+Breadth-first Search: A B C D E
+```

Graphs/Breadth First Search/Images/output.jpg

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+# Create a graph given in the above diagram.
+graph = {
+    'A': ['B', 'C', 'D'],
+    'B': ['A'],
+    'C': ['A', 'D'],
+    'D': ['A', 'C', 'E'],
+    'E': ['D']
+}
+
+# to print a BFS of a graph
+def bfs(node):
+
+    # mark vertices as False means not visited
+    visited = [False] * (len(graph))
+
+    # make a empty queue for bfs
+    queue = []
+
+    # mark given node as visited and add it to the queue
+    visited.append(node)
+    queue.append(node)
+
+    while queue:
+        # Remove the front vertex or the vertex at 0th index from the queue and print that vertex.
+        v = queue.pop(0)
+        print(v, end=" ")
+
+        for neigh in graph[v]:
+            if neigh not in visited:
+                visited.append(neigh)
+                queue.append(neigh)
+
+
+# Driver Code
+if __name__ == "__main__":
+    bfs('A')