Readme.md

Hex Ed

There are multiple ways to arrive at the same destination. For example:

n + s = 0       ne + nw = n
   _ _             _ _ 
 /     \         /     \         
/  ^    \       /  ^  ^ \ _ _    
\  | |  /       \  |   \/     \  
 \ _ _ /         \ _ _ /\      \ 
 / | | \         / |   \/      / 
/    v  \       /      /\ _ _ /  
\       /       \     / /        
 \ _ _ /         \ _ _ /                 

Opposites cancel each other out, and if we take two steps separated by 120°, we could instead take one step in the direction that is „in between” them. Following those optimizations, we arrive at a normalized path that cannot be reduced further (in terms of the number of steps).

Part II

The dumb solution was to iterate over its path, extending it one step at a time. But this is like a quadratic complexity, I guess? It was slow, it took like a minute to calculate. Each next iteration had to redo all the steps of the previous one, and add one on top.

The smart solution is to turn the counter into an iterator. It calculates the whole path in one go, but it optimizes after each step and yields partial results along the way. It does that in a flash.

Visualization

It’s 1:15 am, and I guess I have nothing better to do than to vusialize the kid’s distance on a graph:

      ^
 1501 │
      │                                                                         ▓▓▓▓▓▓▓
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 1296 │                                                                       ▓▓▓▓▓▓▓▓▓▓▓▓
      │                                                                      ▓▓▓▓▓▓▓▓▓▓▓▓▓▓
      │                                                          ▓▓▓▓▓▓     ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
 1091 │                                                       ▓▓▓▓▓▓▓▓▓▓  ▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
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