11

2017, Day 11: Hex Ed

Crossing the bridge, you've barely reached the other side of the stream when a program comes up to you, clearly in distress. "It's my child process," she says, "he's gotten lost in an infinite grid!"

Fortunately for her, you have plenty of experience with infinite grids.

Unfortunately for you, it's a hex grid.

Part 1

The hexagons ("hexes") in this grid are aligned such that adjacent hexes can be found to the north, northeast, southeast, south, southwest, and northwest:

  \ n  /
nw +--+ ne
  /    \
-+      +-
  \    /
sw +--+ se
  / s  \

You have the path the child process took. Starting where he started, you need to determine the fewest number of steps required to reach him. (A "step" means to move from the hex you are in to any adjacent hex.)

For example:

• ne,ne,ne is 3 steps away.
• ne,ne,sw,sw is 0 steps away (back where you started).
• ne,ne,s,s is 2 steps away (se,se).
• se,sw,se,sw,sw is 3 steps away (s,s,sw).

Your puzzle answer was 722.

Part 2

How many steps away is the furthest he ever got from his starting position?

Your puzzle answer was 1551.

Solution Notes

Not an outstanding puzzle at all; the hardest part is getting the hex coordinate logic right. Like in many puzzles like this, I (mis-)used complex numbers as lightweight wrappers for 2D coordinates.

• Part 1, Python: 167 bytes, <100 ms
• Part 2, Python: 194 bytes, <100 ms