Dijkstra's shortest paths
one step at a time.
Always settle the nearest unsettled node: with no negative edges, no route found later can beat it.
Free to use. Step forward and back at your pace, and share a link to the exact step you are stuck on.
What you actually watch.
The part a dry run on paper loses: the state, at every step.
Always settle the nearest unsettled node: with no negative edges, no route found later can beat it. That sentence is easy to agree with and hard to hold in your head on step nine, which is where most people lose the thread.
So the visualiser keeps it in front of you: the frontier spreading, and which nodes are settled for good. The line of code being executed is highlighted as the picture changes, so the drawing and the code never drift apart. Step forward, step back, or let it play.
Put your own input in. Dijkstra's shortest paths on a clean example teaches you the shape; dijkstra's shortest paths on an empty input, a single element, or one with duplicates teaches you the thing an interviewer asks about.
How it runs, step by step.
The same order the visualiser moves in, so the list and the picture match.
- 1Start from a source and mark it seen.
- 2Take the next node from the frontier: a queue spreads in layers, a stack goes deep.
- 3Look at its neighbours, and add the ones never seen before.
- 4Never revisit a node, so every edge is examined once.
What it costs.
The two numbers an interviewer will ask for, and what they mean here.
- Time
- O((V + E) log V)counted as real operations while it runs, not quoted from a table
- Space
- O(V + E)what the algorithm holds besides the input itself
- Pattern
- GraphsExplore in layers, or go deep, and never visit twice.
Once you can see it, go and use it.
Watching is the first ten minutes. The pattern sticks when you solve with it.
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About dijkstra's shortest paths.
Open it in the app and the answers are easier to see than to read.
Open the visualiserWhat does the dijkstra's shortest paths visualiser show?
Every step of the algorithm on input you choose: the frontier spreading, and which nodes are settled for good, with the line of code being executed highlighted beside it. You can step forward, step back, or let it play. Spelled visualizer or visualiser, it is the same tool.
What is the time complexity of dijkstra's shortest paths?
O((V + E) log V) time and O(V + E) space. The visualiser counts the real operations as it runs, so you can watch the number grow instead of taking the formula on trust.
Can I use my own input?
Yes. Type your own array, string or graph and the algorithm runs on that, including the edge cases that break a solution in an interview.
Is it free?
Yes. The app is free to start, with 100 AI credits when you sign up and 100 every month, and watching an algorithm costs no credits.