Breadth First Search (BFS) | Iterative & Recursive Implementation

Breadth first search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a ‘search key’) and explores the neighbor nodes first, before moving to the next level neighbors.


 

Below graph shows order in which the nodes are discovered in BFS

Breadth first search (BFS) tree
 

 
Breadth first search (BFS) is a graph traversal algorithm that explores vertices in the order of their distance from the source vertex, where distance is the minimum length of a path from source vertex to the node as evident from above example.

 

Applications of BFS –

  • Copying garbage collection, Cheney’s algorithm
  • Finding the shortest path between two nodes u and v, with path length measured by number of edges (an advantage over depth first search)
  • Testing a graph for bipartiteness
  • Minimum Spanning Tree for unweighted graph
  • Web crawler
  • Finding nodes in any connected component of a graph
  • Ford–Fulkerson method for computing the maximum flow in a flow network
  • Serialization/Deserialization of a binary tree vs serialization in sorted order, allows the tree to be re-constructed in an efficient manner.

 

Iterative Implementation of BFS –

Non-recursive implementation of BFS is similar to the non-recursive implementation of DFS, but differs from it in two ways:

  • It uses a queue instead of a stack
  • It checks whether a vertex has been discovered before pushing the vertex rather than delaying this check until the vertex is dequeued from the queue

 

C++

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Java

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Output:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

 

Recursive Implementation of BFS –

 

C++

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Java

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Output:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

 

The time complexity of BFS traversal is O(n + m) where n is number of vertices and m is number of edges in the graph. Please note that O(m) may vary between O(1) and O(n2), depending on how dense the graph is.

 
Breadth-first Search (BFS) Practice Problems

 
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Rafael
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This is great code… thanks for making this so easy to understand.

Abhishek
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Awesome!!

Nitin
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In first program, loop should be executed from 1 to N at line #83. What if Nth node is disconnected.

Wang
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If it is a directed graph , we don’t need discover[] ?
since the edges will be tested only one time right?
I just want to know if my understanding right or wrong , thx in advance!

Coder
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discover[] has nothing to do with the edges. It tracks vertices, which can be involved in multiple edges. Consider the directed graph a->b->c->a. If we remove discover[], nodes will be visited again and again. Also, the code will then print only one connected component of the graph.