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

Let's get started!

### 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)

### Applications

Find shortest paths between vertices

The shortest path is a path between two vertices in a graph such that the total sum of the weights of the constituent edges is minimum

You can implement an algorithm to find the shortest path by using Breadth-First Search (BFS), Dijkstra, Bellman-Ford, and Floyd-Warshall algorithms