# Optimal walking route across a full parking lot **URL:** \ **Category:** Factual Questions\ **Created:** [April 20, 2018, 2:23am UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751 "2018-04-20T02:23:12Z")\ **Posts on this page:** 17\ **Page:** 2
**Author:** ![doorhinge](https://avatars.discourse-cdn.com/v4/letter/d/a5b964/32.png) [@doorhinge](https://boards.straightdope.com/u/doorhinge)\ **Post date:** [April 26, 2018, 2:21am UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/21 "2018-04-26T02:21:26Z")
for historical reference - _Originally Posted by doorhinge Left, right, left, right, left, right. Travel directly towards the exit in areas where there are no cars._ > [@Chessic\_Sense](#): > > This is guaranteed not to work. When you hit a row of cars, you’re forced off-course. Then you have to spent time getting back on course, when you could’ve used the earlier space to prepare for this eventuality. Of course you’re going to hit a row of cars, you’re walking thru a parking lot. It’s a bit like sailing a boat directly into the wind. You have to jibe port and starboard until you reach your intended destination. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [April 26, 2018, 7:20am UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/22 "2018-04-26T07:20:20Z")
> [@Chessic\_Sense](#): > > Perhaps it’s your drawing, but I don’t see how I can touch all the asterisks and still be on the optimal path. The asterisks _are_ on the optimal path, but your sub-paths _aren’t_ all subsets of that path, but will still be a shorter distance than pure rectilinear motion - is how I read it. For instance, in that example, I’d make my path out to be one steeper diagonals and one shallower one, and then a second set of same: Starting top left, I’d go down one row against the left edge, across between the cars, then diagonally across the aisle through the asterisk (in the centre of the aisle) to the start of the fourth-fifth inter-car space. That’s a “steep” diagonal. Across in that space, and then through the asterisk gets me to the 5-6 space. That’s a “shallow” diagonal. Across 5-6, then diagonal to the 8-9 (another “steep” one), then across and diagonal to the 9-10 (“shallow” slope) and then either down and across or across and down, to the exit. Did that make any sense? I think there are probably other combos (shallow-steep-shallow-steep also look like it might work and be the same length, and that’s not considering doglegs while between the cars) Oh, and **septimus** , that’s a lovely diagram. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [April 26, 2018, 1:11pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/23 "2018-04-26T13:11:22Z")
> [@septimus](#): > > (But that lot has other issues: often there won’t be room to pass between cars.) How can people get out of their cars if there isn’t even enough room to walk between them? ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [April 26, 2018, 2:37pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/24 "2018-04-26T14:37:09Z")
You can walk faster if you don’t have to worry about hitting other peoples cars if you swing your arms too wide or take one false step. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [April 26, 2018, 2:56pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/25 "2018-04-26T14:56:47Z")
> [@MrDibble](#): > > Oh, and **septimus** , that’s a lovely diagram. Thank you! 🙂 **Chessic Sense** is correct that I should have spent more effort making it more exact :o , but I was in a hurry to convey the general concept. > [@CookingWithGas](#): > > How can people get out of their cars if there isn’t even enough room to walk between them? I should photograph that parking lot and post pictures. It’s an almost unbelievable parking lot, with cars also parked perpendicular blocking the paths. Getting out can be like a Traffic Jam puzzle. (For that reason I never park in the main lot, but park in one of the distant annexes.) The “can’t fit between cars” problem applies _after_ shopping when I’m returning to car _with a shopping cart._ ---
**Author:** ![Jim\_Peebles](https://avatars.discourse-cdn.com/v4/letter/j/5f9b8f/32.png) [@Jim\_Peebles](https://boards.straightdope.com/u/Jim_Peebles)\ **Post date:** [April 26, 2018, 3:01pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/26 "2018-04-26T15:01:23Z")
You can walk diagonal down your vertical aisle, and then diagonal across the horizontal to the entrance. But those are two rectangle diagonals. The diagonal of one square (or rectangle with almost equal side lengths) could be much shorter. But your zigzags to get past aisles of cars would add some extra travel distance. (If they are parked slanted and the parking lot is full, you would have to zigzag every other aisle of cars, since every other aisle switches direction of traffic. On the “good” aisles you can take the same diagonal passing between cars on each side. On the “bad” aisles, you need to walk away from the store on the first side, but then can turn to walk towards the store in the middle to take a diagonal between cars on the other side.) So it depends on: 1. Length of aisle of cars. 2. Length from aisle to entrance. 3. Width of 1 and 2. 4. Number of “good” aisles. 5. Number of “bad” aisles. 6. Angle of parking space slant. 7. Length and width of cars you are sometimes zigzagging around. I suspect in many cases you can take a single square’s diagonal with zigzags to save time over the L shape (with slight rectangle diagonal savings). ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [April 26, 2018, 3:39pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/27 "2018-04-26T15:39:44Z")
[Here](https://github.com/subh83/DOSL) is an example library (there are many different libraries out there, and various algorithms like Dijkstra’s algorithm, the Fast Marching Method, etc.) that can do some path planning, in case anyone wants to experiment with different layouts and obstacles on the computer. ---
**Author:** ![PastTense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pasttense/32/14550_2.png) [@PastTense](https://boards.straightdope.com/u/PastTense)\ **Post date:** [April 26, 2018, 6:40pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/28 "2018-04-26T18:40:04Z")
None of you have even considered an issue some of us have: that it is not uncommon to forget exactly where we have parked our cars. All of this diagonal travel most of you recommend makes remembering the exact location more and more difficult–so any time we save on the initial trip is more than lost on the return trip. Thus Snfaulkner is correct: “Down one row until you can’t, then over to the exit.” ---
**Author:** ![Randolph](https://avatars.discourse-cdn.com/v4/letter/r/e5b9ba/32.png) [@Randolph](https://boards.straightdope.com/u/Randolph)\ **Post date:** [April 26, 2018, 6:59pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/29 "2018-04-26T18:59:41Z")
> [@septimus](#): > > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . [COLOR=“Black”] \* . .[/color] ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . [COLOR=“Black”] \* . .[/color] ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . [COLOR=“Black”] \* . .[/color] ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . [COLOR=“Black”] \* . .[/color] ௵ ௵ > ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ . . . . ௵ ௵ Maybe you can ride one of the elephants up and over? Once they hatch, I mean. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [April 26, 2018, 9:16pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/30 "2018-04-26T21:16:04Z")
> [@MrDibble](#): > > The asterisks _are_ on the optimal path, but your sub-paths _aren’t_ all subsets of that path, but will still be a shorter distance than pure rectilinear motion - is how I read it. For instance, in that example, I’d make my path out to be one steeper diagonals and one shallower one, and then a second set of same: Then I believe we have a debate, because I am of the belief that if you change your “pitch,” which you’re calling steep and shallow, then you cannot be on the optimal path. All your pitches should be equal, unless you’re going to hit the center of a bumper. ---
**Author:** ![Tim\_T-Bonham.net](https://avatars.discourse-cdn.com/v4/letter/t/46a35a/32.png) [@Tim\_T-Bonham.net](https://boards.straightdope.com/u/Tim_T-Bonham.net)\ **Post date:** [April 26, 2018, 10:11pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/31 "2018-04-26T22:11:33Z")
> [@CookingWithGas](#): > > How can people get out of their cars if there isn’t even enough room to walk between them? Well, duh! Many (most?) cars have only a single occupant – the driver. So you can park as close as you want on the passenger side. Sometimes that makes it hard for the person parked next to you to get back into their car, but many parkers don’t seem to care. ---
**Author:** ![Jim\_Peebles](https://avatars.discourse-cdn.com/v4/letter/j/5f9b8f/32.png) [@Jim\_Peebles](https://boards.straightdope.com/u/Jim_Peebles)\ **Post date:** [April 27, 2018, 2:14am UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/32 "2018-04-27T02:14:13Z")
Septimus’ superb diagram had me so confused I didn’t even want to address it. But then I realized the problem was line wrap on my phone. If I hold my phone horizontal there is more room for each line, and the diagram is shown as intended, and I agree for that parking lot. ---
**Author:** ![JKellyMap](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jkellymap/32/15880_2.png) [@JKellyMap](https://boards.straightdope.com/u/JKellyMap)\ **Post date:** [April 27, 2018, 5:21am UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/33 "2018-04-27T05:21:49Z")
My Tamil-speaking mother-in-law says there’s no need to curse fifty times! ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [April 28, 2018, 10:32am UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/34 "2018-04-28T10:32:46Z")
> [@Chessic\_Sense](#): > > Then I believe we have a debate, because I am of the belief that if you change your “pitch,” which you’re calling steep and shallow, then you cannot be on the optimal path. All your pitches should be equal, unless you’re going to hit the center of a bumper. A single pitch would be the \*ideal \*path, but the need to move rectilinearly between cars means that the most optimal \*possible \*paths are \*not \*the ideal. Unless you had square cars, maybe? Like I said, I think if you dogleged between cars, you might have a more even pitch and be closer to ideal. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [April 28, 2018, 12:01pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/35 "2018-04-28T12:01:12Z")
Unless you can take a picture of the car park at the time you park and then spend time calculating the optimal path, you could never beat the mark1 eyeball/brain combo. This is because there will always be a few empty spaces which you can use as shortcuts. Maybe someone could make an app for it, using an overhead CCTV feed, but it would have to constantly update as people empty and fill spaces on your path. There would also be a high risk of being mowed down by someone looking for a space while you are looking at your screen. I won’t even mention the complication of a herringbone layout 🙂 ---
**Author:** ![nachtmusick](https://avatars.discourse-cdn.com/v4/letter/n/ac91a4/32.png) [@nachtmusick](https://boards.straightdope.com/u/nachtmusick)\ **Post date:** [April 28, 2018, 3:33pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/36 "2018-04-28T15:33:33Z")
My thought-experiment is to first imagine you park in one corner of an empty parking lot with your destination at the far corner. The shortest path to your destination is obviously a straight line diagonally across the lot. Now imagine that 20 percent of the spots are filled with cars. It’s still readily apparent that the shortest path is the straightest diagonal, even though you would have to sidestep a few cars. Now imagine slowly adding cars until the lot is filled. At what point, and for what reason, would the most diagonal path not still be the shortest possible route? This assumes that one can always pass unobstructed between any two parallel vehicles, which of course is far from true in the real world. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [April 29, 2018, 12:33pm UTC](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751/37 "2018-04-29T12:33:13Z")
> [@PastTense](#): > > None of you have even considered an issue some of us have: that it is not uncommon to forget exactly where we have parked our cars. All of this diagonal travel most of you recommend makes remembering the exact location more and more difficult–so any time we save on the initial trip is more than lost on the return trip. Thus Snfaulkner is correct: “Down one row until you can’t, then over to the exit.” It was considered 9 posts before yours. See post #19. [Previous page](https://boards.straightdope.com/t/optimal-walking-route-across-a-full-parking-lot/812751.md?page=1)