![]() ![]() With this additional information itineraries can be computed very fast. The main idea is to do a preprocessing on the graph once, to speed up all following queries. This question has been an active area of research in the last years. The former seems to use prominent Boulevard de Sebastopol even though it's slightly out of the way.Įdit: Neither of these examples seem to work anymore, but both did at the time of the original post. Here's another violation of the triangle inequality that suggests (to me) that they use some kind of tiered approach: X-Z versus X-Y-Z. But maybe their walking directions optimize for another parameter, too? Contrary to the triangle inequality, sometimes Google Maps thinks that X-Z takes longer and is farther than using an intermediate point as in X-Y-Z. This question was motivated by finding quirks in online mapping directions. What algorithms are actually used in practice? Then directions for two far-away points will involve local directions to a key points, global directions to another key point, and then local directions again.) However, our data is very structured, and perhaps some kind of tiered approach might work? (For example, store precomputed directions between certain "key" points far apart, as well as some local directions. Luckily, heuristic algorithms like A* will probably work. Graph algorithms like Dijkstra's algorithm will not work because the graph is enormous. Sometimes these points will be close together (within one city) while sometimes they will be far apart (cross-country). I want to be able to quickly compute directions from one arbitrary point to another. But suppose the data were in a simpler format, say a very large directed graph with edge weights reflecting distances. I mean, they probably have real-world data in some form, certainly including distances but also perhaps things like driving speeds, presence of sidewalks, train schedules, etc. How do map providers (such as Google or Yahoo! Maps) suggest directions? ![]()
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![]() ![]() For example, Todoist is one of our favorite to-do apps, but it's not one of our favorite to-do apps for Mac. This can include supporting macOS features like notifications, widgets, and a menu bar app, but it also extends to the general feel of the app. In my opinion, the very best Mac to-do list apps need to do five key things: Which one you prefer may well boil down to personal taste. There's an incredible range of Mac to-do list apps out there, all looking to serve different kinds of users. For more details on our process, read the full rundown of how we select apps to feature on the Zapier blog. We're never paid for placement in our articles from any app or for links to any site-we value the trust readers put in us to offer authentic evaluations of the categories and apps we review. ![]() We spend dozens of hours researching and testing apps, using each app as it's intended to be used and evaluating it against the criteria we set for the category. What makes the best to-do list app for Mac?Īll of our best apps roundups are written by humans who've spent much of their careers using, testing, and writing about software. TickTick for a cross-platform option that feels native to the Mac GoodTask for making Reminders more powerfulĢDo for a fully customizable to-do list with multiple syncing options Reminders for a simple option for Apple-only users Things for a blend of powerful features with elegant design ![]() ![]() So here are the best to-do list apps you can find for macOS. I've been a Mac user, to-do list maker, and tech writer for over a decade, and I thought about all of these things while I tested every Mac to-do list app I could get my hands on. It doesn't matter how good the app is on Windows or the web, if it doesn't respect macOS conventions, it will disrupt people's workflows-defeating the entire purpose of productivity software. Things like keyboard shortcuts, notifications, and menus won't work as expected. 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