Dijkstra's Algorithm Explained — Shortest Paths, Visualized

On a real road network the possible routes are beyond counting — yet Dijkstra's algorithm finds the shortest one almost at once. This is the whole idea, built up visually from a single picture: pour water in at the start, let it spread down every road at one speed, and the instant it reaches a city it has arrived by the shortest route. End to end, nothing skipped: • The shortest-path problem, and the one rule that makes it work (non-negative weights) • What it means to "relax" an edge • Why breadth-first search isn't enough — distance, not number of hops • The key insight: the nearest unfinished city is always final • A full worked example, settling city by city — with a moment to predict the next step yourself • The code, line by line, including the min-heap and the stale-entry skip • Four gotchas that quietly break it • Why the time and space costs are what they are • Where it actually shows up: routing, networks, and more Rudrite Academy is the structured on-ramp to coding interviews for career-switchers and non-CS engineers. Learn it, practise it on 500+ problems, and remember it: → https://academy.rudrite.com New explainers weekly. #Dijkstra #Algorithms #ShortestPath #GraphAlgorithms #CodingInterview ------------------ Timestamps: 0:00 - What is Dijkstra's algorithm? 0:18 - The shortest-path problem 0:37 - The wave: a way to see it 0:59 - The setup & the one rule 1:19 - Relaxing an edge 1:38 - Why not breadth-first search? 2:03 - The key insight 2:25 - Settled vs. frontier 2:46 - Worked example, start to finish 4:04 - The code, line by line 4:40 - Four gotchas that bite 5:14 - Why the time complexity 5:55 - Why the space complexity 6:23 - Route explosion vs. one clean wave 6:49 - Where it's really used 7:27 - Recap ------------------