---
title: Heaps of fun with shortest paths - Day 17 - Advent of Code 2023
slug: heaps-of-fun-with-shortest-paths-day-17-advent-of-code-2023
published_at: 2023-12-17 21:00:19 +0000
updated_at: 2026-03-04 20:12:54 +0000
summary: 
description: In this episode you'll learn how to solve day 17's \"Clumsy Crucible\" puzzle. We walk through implementing a shortest path algorithm to find the route through a grid-based map with the lowest \"heat loss\".  Using a greedy approach to explore minimum heat paths first Implementing a visited set to avoid exploring already visited states Switching from arrays to a heap data structure for faster state exploration Adding directional state to track movement rules (max 3, later 4-10 blocks)  We'll start with a simple test case to incrementally build a basic solution, then extend it to handle the full puzzle input.   Advent of Code: https://adventofcode.com/ My Solutions: https://gist.github.com/cjavdev/d15a2a4ffed6c840c2fb28a093e9f927/ Playlist https://www.youtube.com/playlist?list=PLS6F722u-R6KYlGyUv65EFpGKl2Esmurr  #adventofcode  #ruby
tags: [cjav_dev, Learn to code, Beginner ruby, Advent of code, Advent of code 2023, Advent of code ruby, Aoc ruby, Aoc 2023, Vim, Advent of code vim, Advent of code explainer, Advent of code challenge, Code challenge, Advent of code tutorial, Web development tutorial, shortest path ruby, heaps ruby, heap data structure]
views: 239
author: CJ Avilla
url: https://www.cjav.dev/videos/heaps-of-fun-with-shortest-paths-day-17-advent-of-code-2023
youtube_url: https://www.youtube.com/watch?v=XssRxCsI0-g
youtube_id: XssRxCsI0-g
embed_url: https://www.youtube.com/embed/XssRxCsI0-g
thumbnail_url: https://i.ytimg.com/vi/XssRxCsI0-g/hqdefault.jpg
type: video
---

# Heaps of fun with shortest paths - Day 17 - Advent of Code 2023

*Published: December 17, 2023*
*Views: 239*

## Watch

[Watch on YouTube](https://www.youtube.com/watch?v=XssRxCsI0-g)

[![Heaps of fun with shortest paths - Day 17 - Advent of Code 2023](https://i.ytimg.com/vi/XssRxCsI0-g/hqdefault.jpg)](https://www.youtube.com/watch?v=XssRxCsI0-g)

## Description

In this episode you'll learn how to solve day 17's "Clumsy Crucible" puzzle. We walk through implementing a shortest path algorithm to find the route through a grid-based map with the lowest "heat loss".

Using a greedy approach to explore minimum heat paths first
Implementing a visited set to avoid exploring already visited states
Switching from arrays to a heap data structure for faster state exploration
Adding directional state to track movement rules (max 3, later 4-10 blocks)

We'll start with a simple test case to incrementally build a basic solution, then extend it to handle the full puzzle input. 

Advent of Code: https://adventofcode.com/
My Solutions: https://gist.github.com/cjavdev/d15a2a4ffed6c840c2fb28a093e9f927/
Playlist https://www.youtube.com/playlist?list=PLS6F722u-R6KYlGyUv65EFpGKl2Esmurr

#adventofcode  #ruby

## Transcript

what's up welcome back in this episode you'll see how to solve day 17 for the Advent of code for 2023 this one is called clumsy Crucible and we've got to go through a map and figure out the shortest path with a couple of different twists the elves are trying to get lava from some lava waterfall into their like machine parts factory or whatever and the goal is to go from the top left to the bottom right in these crucibles without losing too much heat and so each of these different blocks represents the amount of heat that we'll lose if we go into and visit that block so if for instance we go here we're going to lose four heat if we go here we lose one heat the idea is to get from this top left corner to the bottom right with the minimum loss of heat so this is like a weighted search I guess we're doing like a shortest path where uh we have weights where we're trying to minimize how much we're spending in terms of heat loss as we go through each one so let's grab our example input and start missing around here so let's go into uh main. RB and we're going to say our input is equal to this example input these are like the each City Block so we'll say blocks is equal to input. spit on new line and then we're going to map over that and for each line we want to map the line chars map toi and this should give us our our blocks so let's run Ruby main. RB and we get back this this nice list of all of our different blocks okay so what I want to do is create a method called find and the whole job of find will be to find the shortest path through this list so we'll start with just like the shortest path given the Heats I think it's actually a little easier easier to work with something smaller something that's really really predictable and also will give us like some interesting data to work with Okay so the shortest path through this would be to just follow the ones right we want to go across the top and down and we want to avoid the nines if we can let's just start out implementing shortest path and then the twist that is involved in the instructions is that the crucible that the elves are moving is a little bit difficult to navigate and it can move at most three blocks in a single Direction before it has to turn 90° either left or right so later on we'll have to limit how far we can go in a single Direction but for now let's just try to figure out the shortest path by following these ones so this is just going to kind of like limit the scope of what we're trying to solve here so we'll make a method called find and this is going to take in some blocks and our goal with find is to return something here so let's actually write maybe we'll write a little test and I'm not sure how far we'll get with these tests it finds the like shortest path or whatever the the shortest yeah so we're not going to count the value for the the heat loss for the first one since we start in that tile then we want one 2 3 4 five six to be our value when we go through this list so we want this to be six and yeah so then we'll just say blocks is this thing should we just do that yeah maybe we should just do one one one one yeah thank you co-pilot okay so we want that to be equal to six so let's run Ruby main. RB and we've got some load error can't load rspec auto run gem install rspec ah I forgot I just upgraded to Ruby 330 because we have a release candidate that will be ready to rock for I think Christmas Day it comes out for the next version of Ruby is coming out it usually it comes out on Christmas okay so we are let's see can we run this Ruby main. RB all right so now we have a failing test great so we got nil this is where things get a little tricky right we want to like keep track of all of the states that we're in because we can only go in certain directions we need to keep track of the states that we're in and what the current heat is at that point and that will let us know yeah and then we need to like increment the heat as we're going out along the edges of this and so we're going to kind of like take a little bit of a greedy approach where we want to try to follow the the minimum path so we're if we're at one we'll take one and add that to this one so this will be this like location will end up being worth two and this location will end up being worth 10 and then we're going to like take the best of those two worlds and try to go down that path so instead of going down the path with 10 we'll go down the path with one but we do need to still consider the path uh with 10 just in case so what we want to do is we want to keep track of a few different things so we want to start with some states and our states could be some like list of things so we're going to start off and this will be our heat we want eventually we want to like optimize based on the heat so we're going to keep that as our most significant like element here and then we're going to in order to be greedy about this we're going to sort these states and take the smallest one first and explore that so we want our heat in the beginning and then we can have our like XY coordinate we also need to know our Direction so DX and Dy we're starting the top left and then there's two different states that we can start at we can either go to the right or we can go down from the beginning so we can go to the right or we can go down so that's going to be like our DX and Dy so we're all always going to have left up or down for our directions that we can potentially go and then what we want to do is like iterate until the list of states is empty and we're going to pop off the best state and take a look at it as our current so we'll say current is States dot so we need this to be sorted and we need to remove so by doing sort bang here we're sorting in place and then we're removing an element from the array so let's take a look at that real quick so if we have some array of 1 2 3 4 1 five 61 something okay so if we do a. sort that gives us back a new array but if if we look at a this is still unsorted so a is still unsorted so if we do like a. sort. shift this will pop one off of the new temporarily sorted array a. sort doob ID is that and a doob ID is this so they're two different things so if we do a. sort bang doob ID we should get the same object ID as if we had a so by doing bang we're sorting in place and we get back the same array so now if we do a do sort well let's let's get a new one so a is this list now if we do a. sort bang. shift now we have a sorted list and when we called shift it popped the the one off of the front so we would have had three ones right and so yeah so we need to use sort bang to sort in place so that when we shift we're removing a state from this list if we don't use the bang then States will never be ENT okay so that's going to be our current state now we can destructure current into heat XY DX and Dy if we want and then we want to also keep track of which ones which states we visited my my kids do this they're like oh I've been now I've been to Virginia and now I've been to Nevada and Oregon and whatever so we're going to see which states we visited and this will be set. new and so we need to require set I think and then we'll say something like if we've visited uh this state and in this case the state is going to be everything in current except the heat so XY DX and Dy why so if we've visited that state and we're headed in a certain direction then we know we have already visited it otherwise we want to add that into our list of visited okay that we don't want to include the heat there because otherwise every time you visit the state there's a different heat there right like when you go to Nevada if you go in the summer it's hot it's very hot if you go in the winter it's very very cold so uh we don't want to include the heat there this time around okay so what do we got now okay so now the next step is so this is basically just find the current state and then check if we've already been there we need to know if we went to the right or if we went down what would our new X and Y be so let's get a a new X and a new y as DX and Dy okay we want to check and see if it's inside the grid if it's not then we're going to run into issues and I always use X and Y backwards uh so our blocks our block sizes are a little wonky but okay so this is make sure the new X and New Y are on the grid now we can get our heat or like a a new heat right and our new heat would be the current heat so this is our current heat which would be one plus what is the heat at that new X or New Y so when we're looking at this first first state we pop off this first state and we're looking we haven't visited yet now we just visited this first state and now we have our new X and our new y our new X and our new Y is going to be in this first case because we're going to the right our new heat would be one yeah our new heat is going to be one because our existing heat starts at zero 0 plus one so our new heat is going to be one now what we want to do is check to see check if we've reached the end okay okay so if we've reached the end in this case that just means that we're at like the bottom right corner if NX is equal to Locks do minus1 and NY is equal to locks. length yeah first. length. one then we want to return that new heat that means that we're done we found we found something puts we like found it yes okay all right so now we need to add the new potential States so if we didn't find it we're not at the bottom right corner now we need to keep exploring the potential directions we can go is left right up and down so let's make a a list of directions we can go so we can go right we can go down we can go left and we can go up okay so these are all the different directions we can go now we want to say dur do each do direction we can destructure this into DDX and ddy I don't know or yeah this is going to be because we now we have we already have a DX in here so we already have the direction we're changing for the current state so this is the direction that we would be changing for the next state here what we want to do is we want to check like yeah don't go back the way we came that's good if DDX plus DX and d y + Dy is equal to Z so if if we're going to the right and our so if our direction is right that would be 01 and then if we tried to go back to the left we would get 0 negative 1 0 + 0 would be 0 and then 1+ negative 1 would be Zer so then we would end up with zero this would tell us that we were we're like going back the way that we just came from so we want to skip over that state um and then I guess like for each Direction really we want to add in some states here so we want to add our new heat which was calculated based on expanding around in the directions near us and we also want to add our new X and New Y and we want to add the direction that we're going so this is like the new direction that we're going as we're going through each of these directions and that should I think I don't know maybe that should get us something like passing test maybe let's see hey oh my gosh no way all right that's wild okay we found it all right cool now we want to throw the wrench into the mix back to the back to the instructions here we can move at most three blocks in a single Direction because we're keeping track of the direction we're going we also need to pass forward how many times we've already stepped in that direction yeah one of the hardest parts of these kind of of trick questions is to figure out what you need to pass forward and so in this case at each state we also need to know how many blocks uh how many blocks we're passing forwards blocks in dur I don't know blocks in that direction so here we'll say okay so if we were able to go maximum I guess Max Ender because this yeah so this is this would be like Max the maximum number of blocks that we can go in that direction for this example example when we run it with one it should continue to work and be the number six because or no I guess we want this to be like 10 or something if you can go 10 blocks in any direction then it should be able to like navigate through this just fine for all of our states we need to add in the concept of how many times we've gone in that direction and for our starting States we'll say that we've gone one in that direction this looks crazy right like these a bunch of zeros and ones but hopefully this makes sense so we have our heat we have our DX we have our Dy and then we have our like numb in or like count inder or something yeah count in yeah that's how many we've gone in that direction so now when we destructure current we're going to get count in that direction and I think we still Yeah we actually do we need that for visited I don't know we'll have to come back and experiment to see if that's actually required for visited we need to figure out whether or not we should add the state and if we're changing directions then we need to reset the count in the directions back to one if we're going in the same direction we need to increase it if going the same direction increase num in we call it count Hender okay so if those are the same that means we're going the same direction then then uh like a new count in dur is going to be count in dur plus one otherwise the new cender is equal to one I know this is hopefully this is easy to follow but okay so now we have this other state in here and our test should theoretically still be passing okay great now we can write another test here and it finds the shortest path without limitation or okay and then it finds the shortest path with Max 2 in dur or something like that and so then we have to change this to two Okay so the number is actually going to be different right because we can't just skate across this top row and down this column now we need to say if we've gone one two now we have to turn so now we plus so we're going to have 1 2 + 9 is 11 12 13 14 I think that might be right 14 it might be more than 14 let's see okay expected 14 but we got six okay so this means that we are not actually limiting it so we're counting it we're sure we counting it but we're not restricting it so we need to we need to like skip over yeah so if the new count in that direction is bigger than Max count then we need to skip over it okay so if the new count in that direction so let's say that we're going to the right and we're passing forward this new count to the right if that new count is bigger than in our test case two then we should not include it in the list of possible States the possible next States all right great so now we have another passing test that's fantastic okay I think we might be ready to test the example input so let's comment this out for a second and what we want to do is say uh P find blocks and in the ex in the example here it says three and we should get back 102 as our answer so let's run this and see what we get a got back six that's because we haven't we left in our other input here take that out okay found it and it is 102 so that matches what our example was fantastic okay so let's now drop in our real input okay get your puzzle input get your puzzle input and here we go 102 still because we didn't actually use our puzzle input and here okay we need to say yeah so we're going to say input is data. read so we'll just read all the data in and run it and it's hanging okay so now we need to have a discussion about data structures okay so the couple couple of things here right works for the example input fantastic when we do uh sort bangang this is expensive when we do shift bang this is also expensive I think in Ruby shift let's see Big O for shift Ruby really it depends on how shift is implemented under the hood and whether or not it is reallocating a bunch of memory and then moving stuff around I don't actually know the answer but I just assume that shift is expensive but I know for sure that sort is expensive Big O notation for sort bang in Ruby I think yeah so under the hood it's using um quick sort which is n log n and so every single time every single for every single state that we go through we're doing n login operations to sort it and then we're doing a shift which might also potentially be expensive let's maybe assume this isn't expensive this is n log n time the number of states which is really really really expensive so I actually ran this with the same implementation we have now and it took 15 minutes and 38 seconds so long time but there is another data structure that we can use that is basically perfect for this use case so anytime that we want to pull off like the minimum one we can use a heap so a heap is a special kind of data structure that you can pretend that it always stays sorted it it's not necessarily true but it has a really efficient way of resorting when when items are added so it by staying like mostly in a sorted State when when you pull stuff off it will give you the minimum pretty efficiently we want to change States from an array I'm going to leave in the array implementation just so you can see this one is like slow and then current is states. pop and here we're going to use a heap we're going to say heap. new and Heap is something that you can get from a gem RB Heap RB Heap gem so head over to RB Heap uh RB Heap here Florian's RB Heap implementation so you can initialize it with a like a method to call on pairs of objects when it's comparing the sort you can also pass it a block here as the comparison function so that when you yeah this will be executed when it needs to do its re heaping thing okay so here it tells us that pop is Ol log n and Peak is constant time when we pop it removes it from the Heap returns it and then does its heapify thing and then if we Peak we're just looking at the top one so this will be faster much faster so we'll get n log in but if we try to run it like this so Ruby main. RB then we get an error here undefined method less than for instance of array so before we go too far let's let's go back to our the example input just so that we're working with a smaller uh smaller case here okay so we need need to figure out how to pass a block to Heap so that it can compare our States because our states aren't just numbers it needs to know how to compare those so let's actually let's let's let's play around with Heap for a second require RB Heap and if we make a new Heap and we can say Heap we'll push in one and then Heap push in four and then we'll push in two and eight and three whatever so we've got a heap and it has a bunch of values in it right and you can see the internal instance variable for a heap looks sorted but it's not necessarily sorted also there is a reference to the proc that's going to be called when it does its comparison and the default proc is somewhere in this file so that's cool so if we do H.P then we get back one and one should no longer be in the Heap so if we look at H again you won't see one in the Heap here and interestingly like like the last time that we saw this Heap three was at the very end right and it was like huh Heap doesn't look like it's actually sorted because we have one and then we have two and then another two and then an eight but you would think that three and four would be on the other side so the internal representation looks like a Rish but really it's being stored as like a tree and every time that we pop something off it gets re heaped or reified so in this case like right after we did h. poop this caused an operation which moved the three from back here until between the two and the eight so now this is like more heaped so if we do h. pop again we get back two then a two then a three now what would you expect the next value to be okay we just popped off 223 that was 22 3 is it going to be an eight or is it going to be a four four what do you think it should give us the four because when we reified by calling pop pop pop this Hippy Hippy Hippy and at at one of these different points the four got moved in front of the eight surely so if we look at H now we have the four in front of the eight so if we do h. pop we're going to see the four the other thing is if we let's put some more back onto it well let's put on 10 and H we'll put on one again and one again and one again and one again and one again as you are shifting stuff on you can see it like moving around what's interesting is you can also put negative numbers and if we do h. Peak this will tell us what the front one is but it won't actually remove it so if we look at H again it's still there so h. Peak is a way of looking at the front without popping it off okay all right so we're going to create a new Heap and this time we want to pass in a block that will compare array values so that the contents of our Heap the elements of our Heap can be arrays so let's just like start actually by looking at array of 1 2 3 and an array of 1 1 one is a less than b oh we get the same error right we can't have a less than but oddly you can do like a rocket ship B which tells you that a is bigger than b right we looked at this comparison operator a few episodes back so if you want to look at rocket ship stuff you can go look at the comparison so if a rocket ship B is one and and B rocket ship a is -1 that means that b is less than a what we can do is we can use this information as part of heap. new when we pass in this block of a so when we compare A and B this block is our comparator and we want to say if a rocket ship B is like equal to1 then it's like correctly sorted in the right order so now if we say h and we push on 1 2 3 and then we push on one one one and then if we push on one 2 one and just for fun we'll put some tens in here okay and we can also do some negative numbers all right so H h. Peak gives us back the minimum array correctly so we're expecting these to be in order based on their first element if their first element matches we want to look at the second element so if we do H do pop and now we have yeah so h. pop should give us 111 that's like the next smallest and then 112 and 121 we want to get back one to one right because that is smaller in our representation this means the array is smaller and we want to investigate this state next because that means that we have um yeah potentially a smaller path so h. pop again and we get one two one so that's correct so we we would end up like exploring all of those different states in the order that we want so we need to pass this a comparator and our comparator is going to be a rocket ship B is equal to1 and by doing that when we call Pop here it should be pretty fast so yeah look at this it's still hanging that's because it's only been running for a few minutes so let's run it again over here it'll be a race it'll be a race okay boom found 102 now we want to run it against our real input all right cross your fingers hey look at that okay so we got back one one0 which is our puzzle answer for part one okay so that's that is the answer for part one and it ran in a reasonable amount of time right 5 Seconds not too shabby not too shabby at all oh hey real quick a Shameless plug buildand learn. deev this is a podcast where me and my buddy Colin hang out and we talk about software development and also just things that were building and we're learning so if that kind of stuff interests you head over to building. Dev you can listen on any of the podcast players that you're used to so yeah let's get back into ad the code cheers on to part two so the crucibles of lava aren't large enough so now we're going to use ultra crucibles and the ultra Crucible introduces a new restriction where it needs to move a minimum of four blocks and then a maximum of 10 consecutive blocks so before our Max was three but now we're going to have a Max of 10 and a new constraint here is a minimum of four so we are still passing forward our count in Direction I think we can just modify we can modify this restriction here so if the new count is greater than Max in the direction um or or the new count in dur is less than the Min iner and then I guess we have to take in a mininder let's see Min Ander Max [Music] Ander so for the example use case it was one and three and if we run that again we still get the same answer that's good all right so now we want to run this against uh four as our minimum and 10 as our maximum I'm going to stop printing out the blocks too just so that we can see oh let's also run it against the example because then we can compare all right we got nil that's not good all right so we have our input we're our minimum is four and our maximum is 10 oh I guess it's going to be below the minimum yeah it's going to be below the minimum in the beginning no matter what right because we've only gone one we do need to collect up the first few States I think this condition we only want to check this condition if we're changing direction like if we're making a turn that's when we want to check if this is different so we need to kind of like combine um whether uh yeah okay so does here we have um we'll say turn is true and turn is false and here we can say if turn and that then we want to skip it okay so we're expecting 94 we're looking looking for 94 here okay so okay so if if we're making a turn so let's say okay so we are making a turn but every time we turn we're resetting the new count back to one so I don't think we want to yeah we don't want to check against new count we want to check against the count for the current state right so let's pull that out and take a look here 94 that is the example okay so now let's run it against uh our input all right 1294 is that the Answer 1 1294 that is the answer for part two oh my goodness okay that's that's pretty cool all right so we've got this working and yeah I think this makes a little bit of sense again yeah if you're you're using just like the default arrays and such you might be needing to do something very fancy to keep this fast enough in any language really so that it can go through and process these as expected now what I'm not sure about if is if visited actually needs to have the count in that direction if we pull that out I don't I'm not sure if that matters let's also run this against the example input here okay yeah it does matter because yeah it's a different it's technically a different state then right if we're if we encounter that same tile but with a different number of counts of that direction Okay so we've got our 94 back is there anything else that we could trim off here I am not sure I guess if we are doing a turn this is where we could check to see if the count is less than Min endure next and then we don't have to keep these variables around um I guess I count in if count in that direction is not that then we could do that early okay that works and yeah okay yeah I'm pretty happy with this solution I learned a lot about heaps yeah it's been a long time since I've messed around with heaps so uh it was fun to pull out RB Heap this library that was already written for us to play around with how do we keep a basically like priority cue so that we can work through this in or thanks so much for watching really appreciate your time and attention and we'll see in the next one cheers

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