In this article, you will learn to implement a Breadth-First Search (BFS) algorithm on a graph by using Java with iterative approaches

Breadth-First Search (BFS) is an algorithm for traversing and searching for a graph/tree layer-wise. It starts at an arbitrary node and explores all of the neighbor nodes before moving to the next depth level

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Problem

  • Give an undirected/directed graph G(V, E)

  • Write a Breadth-First search algorithm to print out each vertex value exactly once

Example

For the above graph with 0 as the starting vertex, assuming that the left edges are chosen before the right edges, the BFS traversal order will be 0 -> 1 -> 2 -> 3 -> 4

Approach 1: Iterative

  • Use an array to track visited nodes to avoid processing a node more than once

  • Use a queue to track which nodes to visit next


GraphUndirectedByAdjacencyList is defined in Graph Data Structure

  • Output
0 1 2 3 4  
  • Time complexity: O(V+E)

  • Space complexity: O(V)

Approach 2: Iterative with Color

  • Use a color array to track vertex states. Each vertex can have 3 states marked by color

    • White represents unvisited

    • Gray represents a visit in progress

    • Black represents visited

  • Use a queue to track which nodes to visit next


GraphUndirectedByAdjacencyList is defined in Graph Data Structure

  • Output
0 1 2 3 4  
  • Time complexity: O(V+E)

  • Space complexity: O(V)