Tag Archives: algorithms

Implementation of Dijkstra’s Single-Source Shortest-Paths in JavaScript

I’m working on a project where the client wants a cool sliding navigation effect. We’re implementing this with JavaScript/AJAX/DHTML.

One of the constraints is that pages can only be reached via certain other pages. For example, if you’re on the /portland/contact page and want to go to the /seattle/contact page, you’ll first slide up to /portland, then over to /seattle, then finally down to /seattle/contact.

After a while, it occurred to me that there were some similarities with another project I’ve been working on off and on for the last few years, byCycle.org, which is a bicycle trip planner a la Google Maps.

I had written a Python version of Dijkstra’s Single-Source Shortest-Paths (SSSP) for byCycle.org. That’s available on Bitbucket as Dijkstar (so named because it also does has the potential to do A*). I figured it wouldn’t be too hard to port the Python version to JavaScript, and it wasn’t.

There were a few snags, though. Most of it was just syntactic and semantic differences between the two languages. The biggest issue was that I use “heapq“ in the Python version to maintain the costs to previously visited nodes in sorted order. JavaScript has no priority queue implementation that I could find, so I came up with a different solution that involves updating an Object (AKA hash) with costs to newly visited nodes and sorting the keys to pick the next node to visit. I’m assuming/hoping the underlying sort implementation is highly optimized.

Interestingly, I think I found at least one bug in the Python version, although I’ve been using that version for a couple years now with no known problems, so it must only be applicable in certain edge (no pun intended) cases (or maybe it’s due to some difference in the languages–need to take a closer look). I think the JS version came out cleaner, too.

If anyone’s interested, I’m releasing this under an MIT license. You can get it from here. Note that it depends on the util module that you can get from here. The util module contains some other Python-inspired JavaScript, in particular a couple of functions for generating namespaces and classes. I might write another post about that at some point.

Google Maps Encoded Polylines

Update 6/30/07: Fixed links to glineenc.py so that it’s actually accessible.
Update 7/15/08: Fixed links to glineenc.py again because of change to HTTPS on Trac site.

Here’s some Python code (complete with unit and doc tests) for converting a series of latitude/longitude points (i.e., a polyline) to the Base64 encoding that Google Maps understands. It’s particularly useful for long and/or complicated lines.

It’s based on the algorithm listed here and the JavaScript code here [page disappeared].

This site gives some more insight into it and has a pretty cool example of a fractal line here.

Here’s the code:

Previously, I had pasted the Python code right into this article, but I recently made a bunch of revisions and it was way too long. Here’s a link to the Bitbucket project instead:

glineenc on Bitbucket

Please note that this code is still in somewhat of a rough state. I have plans to polish and package it up, but for now, I’m using it as is and it’s working quite well (you’ll have to be patient to click that link as it takes ~20-30 seconds to generate the route, even though the line drawing itself is almost instantaneous).

JavaScript that uses results from `glineenc` looks something like this (assuming you’ve returned some JSON, say, with `encoded_points` and `encoded_lines` keys):

 map.addOverlay(new GPolyline.fromEncoded({ color: "#0000ff", weight: 4, opacity: 0.8, points: result.encoded_points, levels: result.encoded_levels, zoomFactor: 32, numLevels: 4 })); 

`points` is the encoded lat/long points. `levels` indicates which zoom levels each point should displayed at; there is one character per point. See the links above for a more complete explanation.