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elimelt committed Jan 1, 2025
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6 changes: 1 addition & 5 deletions algorithms/BFS.md
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---
title: Breadth First Search Algorithm Implementation and Analysis
category: algorithms
tags:
- graph-traversal
- shortest-paths
- graph-theory
- complexity-analysis
tags: [graph-traversal, shortest-paths, graph-theory, complexity-analysis]
description: A comprehensive explanation of the Breadth First Search (BFS) algorithm, including implementation, complexity analysis, and mathematical proofs. The document covers the algorithm's properties for finding shortest paths in graphs and includes Python implementations with detailed theoretical foundations and lemmas about level ordering.
---
# Breadth First Search
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<meta charset="UTF-8">
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<title>Breadth First Search Algorithm Implementation and Analysis</title>

<meta name="description" content="A comprehensive explanation of the Breadth First Search (BFS) algorithm, including implementation, complexity analysis, and mathematical proofs. The document covers the algorithm's properties for finding shortest paths in graphs and includes Python implementations with detailed theoretical foundations and lemmas about level ordering.">
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<span>Category: <a href="/categories/algorithms.html">algorithms</a></span>
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<ul>
<li>graph-traversal</li>
<li>shortest-paths</li>
<li>graph-theory</li>
<li>complexity-analysis
description: A comprehensive explanation of the Breadth First Search (BFS) algorithm, including implementation, complexity analysis, and mathematical proofs. The document covers the algorithm's properties for finding shortest paths in graphs and includes Python implementations with detailed theoretical foundations and lemmas about level ordering.</li>
</ul>
<hr />
<h1 id="breadth-first-search">Breadth First Search</h1>
<h1 id="breadth-first-search">Breadth First Search</h1>
<p>Completely explore the vertices of a graph in order of their distance from the starting node.</p>
<p>There are three states of a vertex in BFS:
- <strong>Undiscovered</strong>: The vertex has not been seen yet.
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queue.append((neighbor, level + 1))
</code></pre>
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