---
id:"kb-2026-00132"
title:"Dijkstra's Algorithm"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
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ai_citations:
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secondary_sources:
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---

## TL;DR

Dijkstra (1956) finds shortest paths from a source vertex to all others in graphs with non-negative weights. O((V+E) log V) with binary heap. Does not work with negative weights — use Bellman-Ford.

## Core Explanation

Algorithm: maintain distance array (∞ initially), extract min from priority queue, relax neighbors (update if shorter path found via current vertex). Bellman-Ford handles negative weights (O(VE), detects negative cycles). A* algorithm extends Dijkstra with a heuristic for goal-directed search.

## Further Reading

- [Introduction to Algorithms (CLRS)](undefined)