Spiral Memory

Advent of Code 2017 Day 3

Part 1

1. Spiraling out of - then into? - control!
2. Studying the DNA of this spiral and solving the puzzle

Spiraling out of - then into? - control!

• I don't recall any prior spiral-related puzzles
• This seems like a fun pattern-identification puzzle
• Although, I need to see a much larger slice of the spiral to start analyzing how it grows

Studying the DNA of this spiral and solving the puzzle

This animation shows my analysis and discovery of the answer happening in real-time:

This was a manual process with a scavenger hunting algorithm:

Start with num as 1 and n as 0
Trying offsets between 1 and 8
Do as long as num is less than or equal to my puzzle input
  Increment num by the sum of offset and (the product of 8 and n)
  Increment n by 1
  Print the current states of num and n

• An offset of 7 got me closest to - and slightly greater than - my puzzle input
• Thankfully, this offset corresponded to a number in the spiral directly below 1
• From there, I subtracted enough from that number to arrive at my puzzle input
• That number was the amount of steps left
• So, the sum of the amount of steps down - n in my algorithm - and the amount of steps left was my answer!

Part 2

1. Yikes, I may have to build a spiral
2. Solving Part 1 again, but algorithmically
3. Solving Part 2 with a slightly more complex algorithm

Yikes, I may have to build a spiral

• Solving this part manually will require a lot of careful arithmetic
• No, thanks
• I'd rather challenge myself to build the spiral from Part 1, hoping that - if I can - it will lend itself to solving Part 2

Solving Part 1 again, but algorithmically

When re-analyzing the spiral:

• The number of times moving right, up, left, down increased in a repeatable pattern: each amount increments by 2
• I could build a dictionary where the keys are the incrementing numbers, and the values are the coordinates in the spiral
• Then go as many cycles as it took to fill the dictionary with the key I needed to know: my puzzle input
• Lastly, return the sum of the absolute values of the coordinates related to my desired key

This is how my algorithm works:

Solving Part 2 with a slightly more complex algorithm

• In the setup, I create a variable, match that starts empty
• The added complexity comes from checking the eight adjacent cells each time a new cell in the spiral is added

I iterate through each adjacent cell coordinate:

If there is an adjacent cell, update its coordinate with that value
If there is no adjacent cell, update its coordinate with 0

Then, the condition:

If, after determining the value to populate a cell, it is greater than my puzzle input AND my match variable is empty
  Update match to the value of the cell

My algorithm goes a little over...but not by any significant amount.

The more important thing is it stores one and only match: the correct answer!

I did it!!

• I solved both parts!
• I solved Part 1 twice: one naive way, and another algorithmic way!
• I made a couple GIFs that animate my analysis and algorithmic thinking in real-time!
• I surpassed my personal best star score! I now have 42 stars...with two opportunities left to increase that to 46!

This spiral puzzle was a wonderful, thought-provoking puzzle that had me mystified at first...digging for patterns.

I'll admit, I wasn't expecting something this difficult for me in the earliest five days.

On to my penultimate puzzle of 2017!