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Breadth First Search with example and solutions
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- 2. Breadth-first search ļ Breadth-firstsearch (BFS) is an algorithm for traversing or searching tree or graph data structures. ļ It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a āsearch keyā), and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. ļ It is implemented using a queue(FIFO). ļ BFS traverses the tree āshallowest node firstā, it would always pick the shallower branch until it reaches the solution (or it runs out of nodes, and goes to the next branch).
- 3. Algorithm 3 ļ Declare aqueue and insert the starting vertex. ļ Initialize a visited array and mark the starting vertex as visited. ļ Follow the below process till the queue becomes empty: ļ Remove the first vertex of the queue. ļ Mark that vertex as visited. ļ Insert all the unvisited neighbors of the vertex into the queue.
- 4. ā«Consider the FollowingExample Example-1
- 5. Breadth First Search-STEP1 ļ Choose the Starting Vertex as A ļ VISIT A ļ Insert A into the Queue A QUEUE:
- 6. Breadth First Search-STEP2 ā«Visit all adjacent vertices of A which are not visited(Here: D,E,B) ā«Insert newly visited vertices into the queue and delete A from the Queue D E B QUEUE: RESULT: A
- 7. Breadth First Search-STEP3 ā«Visit all adjacent vertices of D which are not visited (No Vertex) ā«Delete D from the Queue E B QUEUE: RESULT: A D
- 8. Breadth First Search-STEP4 ā« Visit all adjacent vertices of E which are not visited(Here C, F) ā« Insert newly visited vertices into the queue and delete E from the Queue B C F QUEUE: RESULT: A D E
- 9. Breadth First Search-STEP5 ā«Visit all adjacent vertices of B which are not visited(No Vertex) ā«Delete B from the Queue C F QUEUE: RESULT: A D E B
- 10. Breadth First Search-STEP6 ā« Visit all adjacent vertices of C which are not visited(Here G) ā« Insert newly visited vertices into the queue and delete C from the Queue F G QUEUE: RESULT: A D E B C
- 11. Breadth First Search-STEP7 ā« Visit all adjacent vertices of F which are not visited(Here No Vertex) ā« Delete F from the Queue G QUEUE: RESULT: A D E B C F
- 12. Breadth First Search-STEP8 ā«Visit all adjacent vertices of G which are not visited(Here No Vertex) ā«Delete G from the Queue QUEUE: Queue Empty, End the Process RESULT: A D E B C F G
- 13. BFS Traversal -Result Aļ D ļ Eļ Bļ Cļ F ļ G
- 14. 14 Advantages ā¢ BFS willprovide a solution if any solution exists. ā¢ If there are more than one solution for a given problem, then BFS will provide minimum solution which requires the least number of steps. Disadvantage ā¢ It requires lot of memory since each level of the tree must be saved into memory to expand the next level. ā¢ BFS needs lot of time if the solution is far a way from the root.
- 15. Example 15 ļ BFS Outputwill be ? ļ Output of BFS : 1 2 3 4 5 6 7 8 9 10 11 12
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- 19. 19 Time complexity: Equivalentto the number of nodes traversed in BFS until the shallowest solution. T(n) = 1 + n^2 + n^3 + ... + n^s = O(n^s) ā¢ s = the depth of the shallowest solution. ā¢ n^i = number of nodes in level i. Space complexity: Equivalent to how large can the fringe get. S(n) = O(n^s)
- 20. 20 ā¢ Completeness: BFSis complete, meaning for a given search tree, BFS will come up with a solution if it exists. ā¢ Optimality: BFS is optimal as long as the costs of all edges are equal.
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