The algorithmic complexity of snow shoveling

Another storm, another clearing of the driveway.  I don’t mind it all that much, at least this early in the season, since snow brightens everything.    It’d be entirely fine if you didn’t have to drive on filthy slush.   I’ve seen Russian kids going to school on snowy paths with 18″ skis strapped to their boots, and envied them.

But the trouble with shoveling is that every time an inch of snow falls it has to be lifted above the N inches that are already there.   Shoveling gets harder and harder as the piles accumulate.  I remember that the Blizzard of ’78 was particularly bad because there had already been a 22″ snowfall a few days before, so when another 26″ fell there was no place to put the stuff.

In computer science terms this would be called an O (N^2) problem, because the work increases as the square of N, not just as N.  It’s like sorting a list by comparing every element to every other element – as the size N of the list increases, the time increases as N^2.

So what to do?  There are a couple of approaches:

  • O (1) – Do nothing.  Wait for it to melt.  The Washington DC approach.
  • O (N) – Do the same thing no matter how much snow there is.  This is the snow blower principle – just throw it all up high enough and it’ll get over whatever piles are already there.
  • O (N log N) – As the piles get higher, make them wider.  That is, move the snow farther away from where you’re shoveling.  This is the principle of the mighty Wovel, which my brother gave me for Christmas one year:
  • a snow shovel with a huge wheel in the middle

    Wovel in action, though not by me

    You push down on it to raise the shovel, and then jerk it back to add to a pile.  The nice thing is that you can transport the snow easily to a new pile when one gets too tall.   It can’t lift things more than about two feet, though, which isn’t all that high.

  • O (N^2) – Get depressed as winter proceeds.

As you can tell, my mind wanders when I’m doing this.

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One Response to The algorithmic complexity of snow shoveling

  1. There was one approach that was oddly not considered. It is an O(epsilon) process that does not use nuclear weapons. You will feel ecstatic. This is the flame thrower approach. Okay. Okay. So some neighbors may complain or even call 9-1-1. But if you do it quickly enough, before the neighbors can get photographic evidence of you using this method, you can live in glee that you did it your way. You can return the snow to the cold hell from which it came in seconds with a flaming barrage of ignited gasoline, and get back inside your house before the commercials are over. You’ll never have to miss a piece of Ren and Stimpy again. What greater joy in life is there than that?

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