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<!DOCTYPE html>
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<title>2021/day06.nim</title>
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<span><a href="..">🏡</a></span>
<span><code>2021/day06.nim</code></span>
<span><a href="https://github.com/pietroppeter/adventofnim"><svg aria-hidden="true" width="1.2em" height="1.2em" style="vertical-align: middle; fill: #fff" preserveAspectRatio="xMidYMid meet" viewBox="0 0 16 16"><path fill-rule="evenodd" d="M8 0C3.58 0 0 3.58 0 8c0 3.54 2.29 6.53 5.47 7.59.4.07.55-.17.55-.38 0-.19-.01-.82-.01-1.49-2.01.37-2.53-.49-2.69-.94-.09-.23-.48-.94-.82-1.13-.28-.15-.68-.52-.01-.53.63-.01 1.08.58 1.23.82.72 1.21 1.87.87 2.33.66.07-.52.28-.87.51-1.07-1.78-.2-3.64-.89-3.64-3.95 0-.87.31-1.59.82-2.15-.08-.2-.36-1.02.08-2.12 0 0 .67-.21 2.2.82.64-.18 1.32-.27 2-.27.68 0 1.36.09 2 .27 1.53-1.04 2.2-.82 2.2-.82.44 1.1.16 1.92.08 2.12.51.56.82 1.27.82 2.15 0 3.07-1.87 3.75-3.65 3.95.29.25.54.73.54 1.48 0 1.07-.01 1.93-.01 2.2 0 .21.15.46.55.38A8.013 8.013 0 0016 8c0-4.42-3.58-8-8-8z"></path></svg></a></span>
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<h2>Day 6: <a href="https://adventofcode.com/2021/day/6">Lanternfish</a> 🎣🔆</h2>
<p>Today is the classical case of: "simple (brute force) approach
will work for part1 but it will not work for part2. Also it
is the kind of the day where I tend to try and derive mathematical
properties on some functions and get lost along the way
(like <a href="../2020/day10hints.html">last year</a>).</p>
<p>This year these days I have some catch up to do
(still have to post day 4 and 5, lots of viz missing)
so I will go with the first stuff that comes to mind,
the end result is not great so you might want to skip
to the end where I give links to better solutions by advent-of-nim-mers.</p>
<h3>Part 1</h3>
<p>If you are still here, well,
I grew fond of the include trick that I used in <a href="day02.html">day02</a>
that I am using it even when there is totally uncalled for.
I just have to modify slightly the input: <code>let puzzleInput = @[<input>]</code>
and actually I do not even need to give it a nim extension, you can include
a file with any extension:</p>
<pre><code class="nim hljs"><span class="hljs-keyword">include</span> <span class="hljs-string">"2021/input06.txt"</span>
<span class="hljs-keyword">echo</span> puzzleInput.len
<span class="hljs-keyword">echo</span> puzzleInput[<span class="hljs-number">0</span> ..< <span class="hljs-number">10</span>], <span class="hljs-string">" ... "</span>, puzzleInput[^<span class="hljs-number">10</span> .. ^<span class="hljs-number">1</span>]</code></pre>
<pre><samp>300
@[4, 3, 3, 5, 4, 1, 2, 1, 3, 1] ... @[1, 1, 1, 1, 2, 1, 1, 1, 2, 1]
</samp></pre>
<p>We are giving a list of numbers (all between 1 and 5) and
they represent "ages" of fishes that evolve with following rules:</p>
<ul>
<li>age decrease by 1 every time step</li>
<li>after reaching 0 a fish cycles back to age 6 and spawns a new fish of age 8 (added at the end of the list)
the question for part 1 is:</li>
</ul>
<blockquote>
<p><em>How many lanternfish would there be after 80 days?</em></p>
</blockquote>
<p>First observation is the fact that there is no interaction between fishes,
so I can concentrate on the evolution of a single fish.
I started thinking about properites of a couple of functions $f, F$:</p>
<ol>
<li>
<p>$f(a, s, t)$: number of generated fish at time $t from a fish of age a at time s</p>
</li>
<li>
<p>$f(a, s, t) = f(a, 0, t - s)$: I should not really care about $s$.</p>
</li>
<li>
<p>$f(a + b, s, t) = f(a, s, t - b)$</p>
</li>
<li>
<p>$F(a_1, ..., a_N, t)$: tot number of gen fish at time $t$ from fishes of "ages" $a_1, ... a_N$ at time 0
(I need to compute $F(\mathrm{input}, 80)$)</p>
</li>
<li>
<p>$F(a_1, ..., a_N, t) = f(a1, 0, t) + ... + f(aN, 0, t)$
(this is the observation above that fish evolutions are independent)</p>
</li>
<li>
<p>if $b_1, ... b_5$ are numbers of fishes with ages equal to $1, ..., 5$, then
$F(a_1, ..., a_N, t) = b_1 \cdot f(1, 0, t) + ... + b_5 \cdot f(5, 0, t)$</p>
</li>
<li>
<p>using rule 3 above I only need to compute $f(1, 0, t - i)$ for $i \in 1 .. 5$</p>
</li>
</ol>
<p>In practice I need only to compute the evolution of <code>@[1]</code>.
The basic function that ticks evolution at every time step:</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> tick(school: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>]): <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>] =
<span class="hljs-literal">result</span> = newSeqWith(len=school.len): -<span class="hljs-number">1</span>
<span class="hljs-keyword">for</span> i, a <span class="hljs-keyword">in</span> school:
<span class="hljs-keyword">if</span> a == <span class="hljs-number">0</span>:
<span class="hljs-literal">result</span>[i] = <span class="hljs-number">6</span>
<span class="hljs-literal">result</span>.add <span class="hljs-number">8</span>
<span class="hljs-keyword">else</span>:
<span class="hljs-literal">result</span>[i] = a - <span class="hljs-number">1</span></code></pre>
<p>and now solution for part 1</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> part1(input: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>], targetTime=<span class="hljs-number">80</span>): (<span class="hljs-built_in">int</span>, <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>]) =
<span class="hljs-keyword">var</span>
counts: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
values: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">for</span> a <span class="hljs-keyword">in</span> input:
<span class="hljs-keyword">assert</span> a <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>
inc counts[a]
<span class="hljs-keyword">var</span> school = @[<span class="hljs-number">1</span>]
<span class="hljs-keyword">for</span> t <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. targetTime:
school = tick school
<span class="hljs-keyword">if</span> t >= targetTime - <span class="hljs-number">4</span>:
<span class="hljs-keyword">let</span> i = targetTime - t + <span class="hljs-number">1</span>
<span class="hljs-keyword">assert</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>
values[i] = school.len
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
<span class="hljs-literal">result</span>[<span class="hljs-number">0</span>] += counts[i]*values[i]
<span class="hljs-literal">result</span>[<span class="hljs-number">1</span>] = school
<span class="hljs-keyword">let</span> testInput = @[<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">1</span>, <span class="hljs-number">2</span>]
doAssert part1(testInput)[<span class="hljs-number">0</span>] == <span class="hljs-number">5934</span>
dump part1(puzzleInput)[<span class="hljs-number">0</span>]</code></pre>
<pre><samp>part1(puzzleInput)[0] = 387413
</samp></pre>
<blockquote>
<p>That's the right answer! You are <em class="star">one gold star</em> closer to saving your vacation.</p>
</blockquote>
<h3>Part 2</h3>
<p>And indeed we are asked to do the compute the same function
but over a horizon of 256 days. I tried expecting no result
and indeed the above approach does not give me an answer in
a reasonable time not even for test input.</p>
<p>Now the approach of counts in part1 was very promising
and I could have gotten a simple solution out of it
(see below of examples) but somehow I decided seeing 256
that I would chunk the problem in 16 chunks of duration 16
(making things more complicated than they should be).</p>
<p>So I set myself to compute:</p>
<ul>
<li>$g(i, t) = [g_0(i, t), ... g_8(i, t)]$</li>
<li>where $g(i, t)$ is a multi valued function that tells me
how many fishes of age $j$ I will have at time $t$
starting from a single fish of age $i$ ($g_j(i, t)$)</li>
</ul>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> g(chunkTime: <span class="hljs-built_in">int</span>): <span class="hljs-built_in">array</span>[<span class="hljs-number">9</span>, <span class="hljs-built_in">array</span>[<span class="hljs-number">9</span>, <span class="hljs-built_in">int</span>]] =
<span class="hljs-keyword">var</span>
school: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>]
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
school = @[i]
<span class="hljs-keyword">for</span> t <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. chunkTime:
school = tick school
<span class="hljs-keyword">for</span> j <span class="hljs-keyword">in</span> school:
inc <span class="hljs-literal">result</span>[i][j]
<span class="hljs-keyword">let</span> chunk = g(<span class="hljs-number">16</span>)
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
<span class="hljs-keyword">echo</span> <span class="hljs-string">"i: "</span>, i, <span class="hljs-string">"; results: "</span>, chunk[i]</code></pre>
<pre><samp>i: 0; results: [2, 0, 1, 0, 0, 1, 0, 1, 0]
i: 1; results: [0, 2, 0, 1, 0, 0, 1, 0, 1]
i: 2; results: [1, 0, 2, 0, 1, 0, 0, 0, 0]
i: 3; results: [0, 1, 0, 2, 0, 1, 0, 0, 0]
i: 4; results: [0, 0, 1, 0, 2, 0, 1, 0, 0]
i: 5; results: [0, 0, 0, 1, 0, 2, 0, 1, 0]
i: 6; results: [0, 0, 0, 0, 1, 0, 2, 0, 1]
i: 7; results: [1, 0, 0, 0, 0, 1, 0, 1, 0]
i: 8; results: [0, 1, 0, 0, 0, 0, 1, 0, 1]
</samp></pre>
<p>and here is the function that puts together the chunks:</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> part2(input: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>], chunk=<span class="hljs-number">16</span>, times=<span class="hljs-number">16</span>): <span class="hljs-built_in">int</span> =
<span class="hljs-keyword">var</span>
counts: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
countsNext: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> input:
<span class="hljs-keyword">assert</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>
inc counts[i]
<span class="hljs-keyword">let</span> chunkCounts = g(chunk)
<span class="hljs-keyword">for</span> k <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. times:
countsNext = [<span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>]
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
<span class="hljs-keyword">for</span> j <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
countsNext[j] += counts[i]*chunkCounts[i][j]
counts = countsNext
<span class="hljs-literal">result</span> = sum(counts)
dump part2(testInput)
dump part2(puzzleInput)</code></pre>
<pre><samp>part2(testInput) = 26984457539
part2(puzzleInput) = 1738377086345
</samp></pre>
<blockquote>
<p>That's the right answer! You are <em class="star">one gold star</em> closer to saving your vacation.</p>
</blockquote>
<h3>Highlights</h3>
<ul>
<li>see how simple could have been the solution if I went with the count approach
looking at <a href="https://github.com/PMunch/aoc2021/blob/master/day06/part2.nim">pmunch solution for part 2</a>.
Do not forget that he also <a href="https://www.youtube.com/playlist?list=PL9Yd0XwsGAqyd_lKcHm3f_nlE8vMdacV0">streams</a> his way about the solutions
which is a great way to see how someone reasons starting from scratch!</li>
<li>another approach for this would have been a recursive, memoized approach
like the one beautifully and concisely expressed by <a href="https://github.com/MichalMarsalek/Advent-of-code/blob/master/2021/Nim/day6.nim">MichalMarsalek</a></li>
<li>Michal got <a href="https://xkcd.com/356/">nerd sniped</a> by this and did a <a href="https://www.reddit.com/r/adventofcode/comments/ra3f5i/2021_day_6_part_3_day_googol/">part 3</a> and a <a href="https://www.reddit.com/r/adventofcode/comments/ra88up/2021_day_6_part_4_day_googolplex/">part 4</a>
with increasingly higher target times that requires more sophisticated behaviours
and even involve a nice little cryptographic primitive called the <a href="https://en.wikipedia.org/wiki/Linear-feedback_shift_register">LSFR</a> (Linear-feedback shift register).
It will take me a moment to absorb all that!</li>
<li>a <a href="https://www.reddit.com/r/adventofcode/comments/ra7gl8/2021_day_6_number_of_lanternfish_of_each_age_per/">nice animation</a> of the count of fishes by age on a log axis;
you can kind of see the exponential growth since it seems to grow linearly
on the log axis.</li>
<li>love the <a href="https://www.reddit.com/r/adventofcode/comments/rall1t/2021_day_6_the_lanternfish_solved_it_for_me/">ascii fish</a> as cursor writing the solution and what's the name of
the thing where you change indentation of code to make it look like
sort of image (in this case a tree branching down)?</li>
</ul>
<h3>Visualization</h3>
<p>I do not really know when I will have time do that (if ever), but I would
love to try and make a little <a href="https://github.com/ftsf/nico">nico</a> game with lanternfishes popping
around and your submarine trying to evoke whales to kill them...</p>
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<pre><code class="nim hljs"><span class="hljs-keyword">import</span> animu, nimib
nbInit(theme=useAdventOfNim)
nb.useLatex
<span class="hljs-comment">#[
todo: add in nimib a `nbHeader "## Day 6: Lanternfish 🎣🔆"
that creats a header with link name day-6-lanternfish
and could add a headers section in context with...
well I am just picking a different api for the toc example of the cheatsheet...
]#</span>
nbText: <span class="hljs-string">"""## Day 6: [Lanternfish] 🎣🔆
[Lanternfish]: https://adventofcode.com/2021/day/6
Today is the classical case of: "simple (brute force) approach
will work for part1 but it will not work for part2. Also it
is the kind of the day where I tend to try and derive mathematical
properties on some functions and get lost along the way
(like [last year](../2020/day10hints.html)).
This year these days I have some catch up to do
(still have to post day 4 and 5, lots of viz missing)
so I will go with the first stuff that comes to mind,
the end result is not great so you might want to skip
to the end where I give links to better solutions by advent-of-nim-mers.
### Part 1
If you are still here, well,
I grew fond of the include trick that I used in [day02](day02.html)
that I am using it even when there is totally uncalled for.
I just have to modify slightly the input: `let puzzleInput = @[<input>]`
and actually I do not even need to give it a nim extension, you can include
a file with any extension:
"""</span>
nbCode:
<span class="hljs-keyword">include</span> <span class="hljs-string">"2021/input06.txt"</span>
<span class="hljs-keyword">echo</span> puzzleInput.len
<span class="hljs-keyword">echo</span> puzzleInput[<span class="hljs-number">0</span> ..< <span class="hljs-number">10</span>], <span class="hljs-string">" ... "</span>, puzzleInput[^<span class="hljs-number">10</span> .. ^<span class="hljs-number">1</span>]
nbText: <span class="hljs-string">"""
We are giving a list of numbers (all between 1 and 5) and
they represent "ages" of fishes that evolve with following rules:
- age decrease by 1 every time step
- after reaching 0 a fish cycles back to age 6 and spawns a new fish of age 8 (added at the end of the list)
the question for part 1 is:
> _How many lanternfish would there be after 80 days?_
First observation is the fact that there is no interaction between fishes,
so I can concentrate on the evolution of a single fish.
I started thinking about properites of a couple of functions $f, F$:
1. $f(a, s, t)$: number of generated fish at time $t from a fish of age a at time s
2. $f(a, s, t) = f(a, 0, t - s)$: I should not really care about $s$.
3. $f(a + b, s, t) = f(a, s, t - b)$
4. $F(a_1, ..., a_N, t)$: tot number of gen fish at time $t$ from fishes of "ages" $a_1, ... a_N$ at time 0
(I need to compute $F(\mathrm{input}, 80)$)
5. $F(a_1, ..., a_N, t) = f(a1, 0, t) + ... + f(aN, 0, t)$
(this is the observation above that fish evolutions are independent)
6. if $b_1, ... b_5$ are numbers of fishes with ages equal to $1, ..., 5$, then
$F(a_1, ..., a_N, t) = b_1 \cdot f(1, 0, t) + ... + b_5 \cdot f(5, 0, t)$
7. using rule 3 above I only need to compute $f(1, 0, t - i)$ for $i \in 1 .. 5$
In practice I need only to compute the evolution of `@[1]`.
The basic function that ticks evolution at every time step:
"""</span>
nbCode:
<span class="hljs-keyword">func</span> tick(school: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>]): <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>] =
<span class="hljs-literal">result</span> = newSeqWith(len=school.len): -<span class="hljs-number">1</span>
<span class="hljs-keyword">for</span> i, a <span class="hljs-keyword">in</span> school:
<span class="hljs-keyword">if</span> a == <span class="hljs-number">0</span>:
<span class="hljs-literal">result</span>[i] = <span class="hljs-number">6</span>
<span class="hljs-literal">result</span>.add <span class="hljs-number">8</span>
<span class="hljs-keyword">else</span>:
<span class="hljs-literal">result</span>[i] = a - <span class="hljs-number">1</span>
nbText: <span class="hljs-string">"and now solution for part 1"</span>
nbCode:
<span class="hljs-keyword">func</span> part1(input: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>], targetTime=<span class="hljs-number">80</span>): (<span class="hljs-built_in">int</span>, <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>]) =
<span class="hljs-keyword">var</span>
counts: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
values: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">for</span> a <span class="hljs-keyword">in</span> input:
<span class="hljs-keyword">assert</span> a <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>
inc counts[a]
<span class="hljs-keyword">var</span> school = @[<span class="hljs-number">1</span>]
<span class="hljs-keyword">for</span> t <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. targetTime:
school = tick school
<span class="hljs-keyword">if</span> t >= targetTime - <span class="hljs-number">4</span>:
<span class="hljs-keyword">let</span> i = targetTime - t + <span class="hljs-number">1</span>
<span class="hljs-keyword">assert</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>
values[i] = school.len
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
<span class="hljs-literal">result</span>[<span class="hljs-number">0</span>] += counts[i]*values[i]
<span class="hljs-literal">result</span>[<span class="hljs-number">1</span>] = school
<span class="hljs-keyword">let</span> testInput = @[<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">3</span>, <span class="hljs-number">1</span>, <span class="hljs-number">2</span>]
doAssert part1(testInput)[<span class="hljs-number">0</span>] == <span class="hljs-number">5934</span>
dump part1(puzzleInput)[<span class="hljs-number">0</span>]
gotTheStar
nbText: <span class="hljs-string">"""### Part 2
And indeed we are asked to do the compute the same function
but over a horizon of 256 days. I tried expecting no result
and indeed the above approach does not give me an answer in
a reasonable time not even for test input.
Now the approach of counts in part1 was very promising
and I could have gotten a simple solution out of it
(see below of examples) but somehow I decided seeing 256
that I would chunk the problem in 16 chunks of duration 16
(making things more complicated than they should be).
So I set myself to compute:
- $g(i, t) = [g_0(i, t), ... g_8(i, t)]$
- where $g(i, t)$ is a multi valued function that tells me
how many fishes of age $j$ I will have at time $t$
starting from a single fish of age $i$ ($g_j(i, t)$)
"""</span>
nbCode:
<span class="hljs-keyword">func</span> g(chunkTime: <span class="hljs-built_in">int</span>): <span class="hljs-built_in">array</span>[<span class="hljs-number">9</span>, <span class="hljs-built_in">array</span>[<span class="hljs-number">9</span>, <span class="hljs-built_in">int</span>]] =
<span class="hljs-keyword">var</span>
school: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>]
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
school = @[i]
<span class="hljs-keyword">for</span> t <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. chunkTime:
school = tick school
<span class="hljs-keyword">for</span> j <span class="hljs-keyword">in</span> school:
inc <span class="hljs-literal">result</span>[i][j]
<span class="hljs-keyword">let</span> chunk = g(<span class="hljs-number">16</span>)
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
<span class="hljs-keyword">echo</span> <span class="hljs-string">"i: "</span>, i, <span class="hljs-string">"; results: "</span>, chunk[i]
nbText: <span class="hljs-string">"and here is the function that puts together the chunks:"</span>
nbCode:
<span class="hljs-keyword">func</span> part2(input: <span class="hljs-built_in">seq</span>[<span class="hljs-built_in">int</span>], chunk=<span class="hljs-number">16</span>, times=<span class="hljs-number">16</span>): <span class="hljs-built_in">int</span> =
<span class="hljs-keyword">var</span>
counts: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
countsNext: <span class="hljs-built_in">array</span>[<span class="hljs-number">0</span> .. <span class="hljs-number">8</span>, <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> input:
<span class="hljs-keyword">assert</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>
inc counts[i]
<span class="hljs-keyword">let</span> chunkCounts = g(chunk)
<span class="hljs-keyword">for</span> k <span class="hljs-keyword">in</span> <span class="hljs-number">1</span> .. times:
countsNext = [<span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>]
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
<span class="hljs-keyword">for</span> j <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. <span class="hljs-number">8</span>:
countsNext[j] += counts[i]*chunkCounts[i][j]
counts = countsNext
<span class="hljs-literal">result</span> = sum(counts)
dump part2(testInput)
dump part2(puzzleInput)
gotTheStar
nbText: <span class="hljs-string">"""### Highlights
- see how simple could have been the solution if I went with the count approach
looking at [pmunch solution for part 2](https://github.com/PMunch/aoc2021/blob/master/day06/part2.nim).
Do not forget that he also [streams](https://www.youtube.com/playlist?list=PL9Yd0XwsGAqyd_lKcHm3f_nlE8vMdacV0) his way about the solutions
which is a great way to see how someone reasons starting from scratch!
- another approach for this would have been a recursive, memoized approach
like the one beautifully and concisely expressed by [MichalMarsalek](https://github.com/MichalMarsalek/Advent-of-code/blob/master/2021/Nim/day6.nim)
- Michal got [nerd sniped] by this and did a [part 3] and a [part 4]
with increasingly higher target times that requires more sophisticated behaviours
and even involve a nice little cryptographic primitive called the [LSFR] (Linear-feedback shift register).
It will take me a moment to absorb all that!
- a [nice animation] of the count of fishes by age on a log axis;
you can kind of see the exponential growth since it seems to grow linearly
on the log axis.
- love the [ascii fish] as cursor writing the solution and what's the name of
the thing where you change indentation of code to make it look like
sort of image (in this case a tree branching down)?
[ascii fish]: https://www.reddit.com/r/adventofcode/comments/rall1t/2021_day_6_the_lanternfish_solved_it_for_me/
[nice animation]: https://www.reddit.com/r/adventofcode/comments/ra7gl8/2021_day_6_number_of_lanternfish_of_each_age_per/
[nerd sniped]: https://xkcd.com/356/
[part 3]: https://www.reddit.com/r/adventofcode/comments/ra3f5i/2021_day_6_part_3_day_googol/
[part 4]: https://www.reddit.com/r/adventofcode/comments/ra88up/2021_day_6_part_4_day_googolplex/
[LSFR]: https://en.wikipedia.org/wiki/Linear-feedback_shift_register
### Visualization
I do not really know when I will have time do that (if ever), but I would
love to try and make a little [nico] game with lanternfishes popping
around and your submarine trying to evoke whales to kill them...
[nico]: https://github.com/ftsf/nico
"""</span>
nbSave</code></pre>
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