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<title>2021/day13.nim</title>
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<span><a href="..">🏡</a></span>
<span><code>2021/day13.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 13: Transparent Origami</h2>
<p>Last days I got lazy and forgot to blogpost after solving the puzzle.
Today I will <em>write the blogpost while I solve the puzzle</em>.</p>
<h3>Part 1</h3>
<p>Let's first understand how to fold, we will implement parse stuff later.</p>
<p>To fold a dot $(x, y)$ along $y=7$, the $x$ coordinate will not change
while the $y$ coordinate will change only if bigger than $7$
and it will be below $7$ by the same amount that it was above $7$:</p>
<p>$$7 - (y - 7) = 2*7 - y$$.</p>
<p>Below I will make a single <code>foldAlong</code> that will work both for $x$ and $y$</p>
<pre><code class="nim hljs"><span class="hljs-keyword">type</span> <span class="hljs-type">Dot</span> = <span class="hljs-keyword">tuple</span>[x, y: <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">func</span> foldAlong(d: <span class="hljs-type">Dot</span>, y = <span class="hljs-number">0</span>, x = <span class="hljs-number">0</span>): <span class="hljs-type">Dot</span> =
<span class="hljs-keyword">if</span> y > <span class="hljs-number">0</span> <span class="hljs-keyword">and</span> d.y > y:
(d.x, <span class="hljs-number">2</span>*y - d.y)
<span class="hljs-keyword">elif</span> x > <span class="hljs-number">0</span> <span class="hljs-keyword">and</span> d.x > x:
(<span class="hljs-number">2</span>*x - d.x, d.y)
<span class="hljs-keyword">else</span>:
d
<span class="hljs-keyword">echo</span> foldAlong(d=(<span class="hljs-number">2</span>, <span class="hljs-number">14</span>), y=<span class="hljs-number">7</span>)</code></pre>
<pre><samp>(x: 2, y: 0)
</samp></pre>
<p>And now we fold a sequence of point, making sure at the end that we
remove duplicates. I could use <code>deduplicate</code> from <code>std / sequtils</code>
but since it does not do anything fancy, I implement it inside here</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> foldAlong(dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>], y = <span class="hljs-number">0</span>, x = <span class="hljs-number">0</span>): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>] =
<span class="hljs-keyword">var</span> e: <span class="hljs-type">Dot</span>
<span class="hljs-keyword">for</span> d <span class="hljs-keyword">in</span> dots:
e = foldAlong(d, y = y, x = x)
<span class="hljs-keyword">if</span> e <span class="hljs-keyword">not_in</span> <span class="hljs-literal">result</span>:
<span class="hljs-literal">result</span>.add e
<span class="hljs-keyword">echo</span> foldAlong(dots = @[(<span class="hljs-number">3</span>, <span class="hljs-number">0</span>), (<span class="hljs-number">5</span>, <span class="hljs-number">0</span>)], x = <span class="hljs-number">4</span>)</code></pre>
<pre><samp>@[(x: 3, y: 0)]
</samp></pre>
<p>Now it make sense to parse stuff. When the input is made of two parts
I prefer to use copy and paste and split the parts manually.
The first instruction I can also parse manually.</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> parse(text: <span class="hljs-built_in">string</span>): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>] =
<span class="hljs-keyword">for</span> line <span class="hljs-keyword">in</span> text.splitLines:
<span class="hljs-keyword">let</span> l = line.strip.split(<span class="hljs-string">','</span>)
<span class="hljs-literal">result</span>.add (parseInt(l[<span class="hljs-number">0</span>]), parseInt(l[<span class="hljs-number">1</span>]))
<span class="hljs-keyword">let</span> testInput = <span class="hljs-string">"""
6,10
0,14
9,10
0,3
10,4
4,11
6,0
6,12
4,1
0,13
10,12
3,4
3,0
8,4
1,10
2,14
8,10
9,0"""</span>
<span class="hljs-keyword">let</span> testDots = parse testInput
dump testDots.len
<span class="hljs-keyword">echo</span> testDots[<span class="hljs-number">0</span> ..< <span class="hljs-number">3</span>], <span class="hljs-string">" ... "</span>, testDots[^<span class="hljs-number">3</span> .. ^<span class="hljs-number">1</span>]
dump foldAlong(testDots, y=<span class="hljs-number">7</span>).len</code></pre>
<pre><samp>testDots.len = 18
@[(x: 6, y: 10), (x: 0, y: 14), (x: 9, y: 10)] ... @[(x: 2, y: 14), (x: 8, y: 10), (x: 9, y: 0)]
foldAlong(testDots, y = 7).len = 17
</samp></pre>
<p>Test input ok, let's proceed for puzzle input</p>
<pre><code class="nim hljs"><span class="hljs-keyword">let</span>
puzzleInput = readFile(<span class="hljs-string">"2021/input13.txt"</span>)
puzzleDots = parse puzzleInput
dump puzzleDots.len
<span class="hljs-keyword">echo</span> puzzleDots[<span class="hljs-number">0</span> ..< <span class="hljs-number">3</span>], <span class="hljs-string">" ... "</span>, puzzleDots[^<span class="hljs-number">3</span> .. ^<span class="hljs-number">1</span>]
dump foldAlong(puzzleDots, x=<span class="hljs-number">655</span>).len</code></pre>
<pre><samp>puzzleDots.len = 1020
@[(x: 1233, y: 302), (x: 454, y: 539), (x: 1051, y: 301)] ... @[(x: 641, y: 536), (x: 152, y: 142), (x: 376, y: 373)]
foldAlong(puzzleDots, x = 655).len = 850
</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>As expected, part 2 will ask me to complete folding and visualize the code.</p>
<p>Since the folding instructions are not many, a manual fix and a template will do:</p>
<pre><code class="nim hljs"><span class="hljs-keyword">var</span> dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>]
<span class="hljs-keyword">template</span> fold_along(x=<span class="hljs-number">0</span>, y=<span class="hljs-number">0</span>) =
dots = foldAlong(dots, y, x)
<span class="hljs-keyword">template</span> foldTest =
dots = testDots
fold_along(y=<span class="hljs-number">7</span>)
fold_along(x=<span class="hljs-number">5</span>)
<span class="hljs-keyword">template</span> foldPuzzle =
dots = puzzleDots
fold_along(x=<span class="hljs-number">655</span>)
fold_along(y=<span class="hljs-number">447</span>)
fold_along(x=<span class="hljs-number">327</span>)
fold_along(y=<span class="hljs-number">223</span>)
fold_along(x=<span class="hljs-number">163</span>)
fold_along(y=<span class="hljs-number">111</span>)
fold_along(x=<span class="hljs-number">81</span>)
fold_along(y=<span class="hljs-number">55</span>)
fold_along(x=<span class="hljs-number">40</span>)
fold_along(y=<span class="hljs-number">27</span>)
fold_along(y=<span class="hljs-number">13</span>)
fold_along(y=<span class="hljs-number">6</span>)
foldTest
<span class="hljs-keyword">echo</span> dots.len
<span class="hljs-keyword">echo</span> dots</code></pre>
<pre><samp>16
@[(x: 4, y: 4), (x: 0, y: 0), (x: 1, y: 4), (x: 0, y: 3), (x: 0, y: 4), (x: 4, y: 3), (x: 4, y: 0), (x: 4, y: 2), (x: 4, y: 1), (x: 0, y: 1), (x: 0, y: 2), (x: 3, y: 4), (x: 3, y: 0), (x: 2, y: 4), (x: 2, y: 0), (x: 1, y: 0)]
</samp></pre>
<p>to visualize we will first sort to have smallest y first (same y will start with smallest x).
Note that sorting could also be a performance hack: we could remove the if check in foldAlong
and deduplicate by checking <code>!=</code> with previous (as <code>deduplicate</code> in <code>sequtils</code> does).</p>
<p>I remember that sorting requires a compare function that gives me a int but I can
never remember if positive means first bigger than second (spoiler: yes) or the other way around
(this probably should an info that belongs to
<a href="https://nim-lang.org/docs/algorithm.html#%2A%2Cint%2CSortOrder">sorting docs</a>, you can find it
in <a href="https://nim-lang.org/docs/system.html#cmp%2CT%2CT">system.cmp docs</a>, should make a PR)</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> cmpAlongY(d, e: <span class="hljs-type">Dot</span>): <span class="hljs-built_in">int</span> =
<span class="hljs-literal">result</span> = (d.y - e.y)
<span class="hljs-keyword">if</span> <span class="hljs-literal">result</span> == <span class="hljs-number">0</span>:
<span class="hljs-literal">result</span> = (d.x - e.x)
dump cmpAlongY((<span class="hljs-number">4</span>, <span class="hljs-number">10</span>), (<span class="hljs-number">6</span>, <span class="hljs-number">8</span>))
dump cmpAlongY((<span class="hljs-number">4</span>, <span class="hljs-number">8</span>), (<span class="hljs-number">6</span>, <span class="hljs-number">8</span>))
<span class="hljs-keyword">func</span> sortedAlongY(dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>]): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>] =
sorted(dots, cmpAlongY)
dump testDots.sortedAlongY[<span class="hljs-number">0</span> .. <span class="hljs-number">5</span>]</code></pre>
<pre><samp>cmpAlongY((4, 10), (6, 8)) = 2
cmpAlongY((4, 8), (6, 8)) = -2
testDots.sortedAlongY[0 .. 5] = @[(x: 3, y: 0), (x: 6, y: 0), (x: 9, y: 0), (x: 4, y: 1), (x: 0, y: 3), (x: 3, y: 4)]
</samp></pre>
<p>and finally it is showtime!</p>
<p>The following <code>show</code> function will work correctly only
if input is sorted along Y axis and yMax and xMax get the whole area</p>
<pre><code class="nim hljs"><span class="hljs-keyword">func</span> show(dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>], yMax=<span class="hljs-number">7</span>, xMax=<span class="hljs-number">50</span>): <span class="hljs-built_in">string</span> =
<span class="hljs-keyword">var</span> i = <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> y <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. yMax:
<span class="hljs-keyword">for</span> x <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. xMax:
<span class="hljs-keyword">if</span> i < dots.len <span class="hljs-keyword">and</span> dots[i] == (x, y):
<span class="hljs-literal">result</span>.add <span class="hljs-string">'#'</span>
inc i
<span class="hljs-keyword">else</span>:
<span class="hljs-literal">result</span>.add <span class="hljs-string">'.'</span>
<span class="hljs-literal">result</span>.add <span class="hljs-string">'\n'</span>
<span class="hljs-comment"># dots currently is results of folding testDots</span>
<span class="hljs-keyword">echo</span> show(dots.sortedAlongY)</code></pre>
<pre><samp>#####..............................................
#...#..............................................
#...#..............................................
#...#..............................................
#####..............................................
...................................................
...................................................
...................................................
</samp></pre>
<p>looks good, let's go with the puzzle:</p>
<pre><code class="nim hljs">foldPuzzle
<span class="hljs-keyword">echo</span> show(dots.sortedAlongY) <span class="hljs-comment">#AHGCPGAU</span></code></pre>
<pre><samp>.##..#..#..##...##..###...##...##..#..#............
#..#.#..#.#..#.#..#.#..#.#..#.#..#.#..#............
#..#.####.#....#....#..#.#....#..#.#..#............
####.#..#.#.##.#....###..#.##.####.#..#............
#..#.#..#.#..#.#..#.#....#..#.#..#.#..#............
#..#.#..#..###..##..#.....###.#..#..##.............
...................................................
...................................................
</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>
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<pre><code class="nim hljs"><span class="hljs-keyword">import</span> animu, nimib
nbInit(theme=useAdventOfNim)
nb.useLatex
nbText: <span class="hljs-string">"""## Day 13: Transparent Origami
Last days I got lazy and forgot to blogpost after solving the puzzle.
Today I will _write the blogpost while I solve the puzzle_.
### Part 1
Let's first understand how to fold, we will implement parse stuff later.
To fold a dot $(x, y)$ along $y=7$, the $x$ coordinate will not change
while the $y$ coordinate will change only if bigger than $7$
and it will be below $7$ by the same amount that it was above $7$:
$$7 - (y - 7) = 2*7 - y$$.
Below I will make a single `foldAlong` that will work both for $x$ and $y$
"""</span>
nbCode:
<span class="hljs-keyword">type</span> <span class="hljs-type">Dot</span> = <span class="hljs-keyword">tuple</span>[x, y: <span class="hljs-built_in">int</span>]
<span class="hljs-keyword">func</span> foldAlong(d: <span class="hljs-type">Dot</span>, y = <span class="hljs-number">0</span>, x = <span class="hljs-number">0</span>): <span class="hljs-type">Dot</span> =
<span class="hljs-keyword">if</span> y > <span class="hljs-number">0</span> <span class="hljs-keyword">and</span> d.y > y:
(d.x, <span class="hljs-number">2</span>*y - d.y)
<span class="hljs-keyword">elif</span> x > <span class="hljs-number">0</span> <span class="hljs-keyword">and</span> d.x > x:
(<span class="hljs-number">2</span>*x - d.x, d.y)
<span class="hljs-keyword">else</span>:
d
<span class="hljs-keyword">echo</span> foldAlong(d=(<span class="hljs-number">2</span>, <span class="hljs-number">14</span>), y=<span class="hljs-number">7</span>)
nbText: <span class="hljs-string">"""
And now we fold a sequence of point, making sure at the end that we
remove duplicates. I could use `deduplicate` from `std / sequtils`
but since it does not do anything fancy, I implement it inside here
"""</span>
nbCode:
<span class="hljs-keyword">func</span> foldAlong(dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>], y = <span class="hljs-number">0</span>, x = <span class="hljs-number">0</span>): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>] =
<span class="hljs-keyword">var</span> e: <span class="hljs-type">Dot</span>
<span class="hljs-keyword">for</span> d <span class="hljs-keyword">in</span> dots:
e = foldAlong(d, y = y, x = x)
<span class="hljs-keyword">if</span> e <span class="hljs-keyword">not_in</span> <span class="hljs-literal">result</span>:
<span class="hljs-literal">result</span>.add e
<span class="hljs-keyword">echo</span> foldAlong(dots = @[(<span class="hljs-number">3</span>, <span class="hljs-number">0</span>), (<span class="hljs-number">5</span>, <span class="hljs-number">0</span>)], x = <span class="hljs-number">4</span>)
nbText: <span class="hljs-string">"""
Now it make sense to parse stuff. When the input is made of two parts
I prefer to use copy and paste and split the parts manually.
The first instruction I can also parse manually.
"""</span>
nbCode:
<span class="hljs-keyword">func</span> parse(text: <span class="hljs-built_in">string</span>): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>] =
<span class="hljs-keyword">for</span> line <span class="hljs-keyword">in</span> text.splitLines:
<span class="hljs-keyword">let</span> l = line.strip.split(<span class="hljs-string">','</span>)
<span class="hljs-literal">result</span>.add (parseInt(l[<span class="hljs-number">0</span>]), parseInt(l[<span class="hljs-number">1</span>]))
<span class="hljs-keyword">let</span> testInput = <span class="hljs-string">"""
6,10
0,14
9,10
0,3
10,4
4,11
6,0
6,12
4,1
0,13
10,12
3,4
3,0
8,4
1,10
2,14
8,10
9,0"""</span>
<span class="hljs-keyword">let</span> testDots = parse testInput
dump testDots.len
<span class="hljs-keyword">echo</span> testDots[<span class="hljs-number">0</span> ..< <span class="hljs-number">3</span>], <span class="hljs-string">" ... "</span>, testDots[^<span class="hljs-number">3</span> .. ^<span class="hljs-number">1</span>]
dump foldAlong(testDots, y=<span class="hljs-number">7</span>).len
nbText: <span class="hljs-string">"Test input ok, let's proceed for puzzle input"</span>
nbCode:
<span class="hljs-keyword">let</span>
puzzleInput = readFile(<span class="hljs-string">"2021/input13.txt"</span>)
puzzleDots = parse puzzleInput
dump puzzleDots.len
<span class="hljs-keyword">echo</span> puzzleDots[<span class="hljs-number">0</span> ..< <span class="hljs-number">3</span>], <span class="hljs-string">" ... "</span>, puzzleDots[^<span class="hljs-number">3</span> .. ^<span class="hljs-number">1</span>]
dump foldAlong(puzzleDots, x=<span class="hljs-number">655</span>).len
gotTheStar
nbText: <span class="hljs-string">"""### Part 2
As expected, part 2 will ask me to complete folding and visualize the code.
Since the folding instructions are not many, a manual fix and a template will do:
"""</span>
nbCode:
<span class="hljs-keyword">var</span> dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>]
<span class="hljs-keyword">template</span> fold_along(x=<span class="hljs-number">0</span>, y=<span class="hljs-number">0</span>) =
dots = foldAlong(dots, y, x)
<span class="hljs-keyword">template</span> foldTest =
dots = testDots
fold_along(y=<span class="hljs-number">7</span>)
fold_along(x=<span class="hljs-number">5</span>)
<span class="hljs-keyword">template</span> foldPuzzle =
dots = puzzleDots
fold_along(x=<span class="hljs-number">655</span>)
fold_along(y=<span class="hljs-number">447</span>)
fold_along(x=<span class="hljs-number">327</span>)
fold_along(y=<span class="hljs-number">223</span>)
fold_along(x=<span class="hljs-number">163</span>)
fold_along(y=<span class="hljs-number">111</span>)
fold_along(x=<span class="hljs-number">81</span>)
fold_along(y=<span class="hljs-number">55</span>)
fold_along(x=<span class="hljs-number">40</span>)
fold_along(y=<span class="hljs-number">27</span>)
fold_along(y=<span class="hljs-number">13</span>)
fold_along(y=<span class="hljs-number">6</span>)
foldTest
<span class="hljs-keyword">echo</span> dots.len
<span class="hljs-keyword">echo</span> dots
nbText: <span class="hljs-string">"""
to visualize we will first sort to have smallest y first (same y will start with smallest x).
Note that sorting could also be a performance hack: we could remove the if check in foldAlong
and deduplicate by checking `!=` with previous (as `deduplicate` in `sequtils` does).
I remember that sorting requires a compare function that gives me a int but I can
never remember if positive means first bigger than second (spoiler: yes) or the other way around
(this probably should an info that belongs to
[sorting docs](https://nim-lang.org/docs/algorithm.html#%2A%2Cint%2CSortOrder), you can find it
in [system.cmp docs](https://nim-lang.org/docs/system.html#cmp%2CT%2CT), should make a PR)
"""</span>
nbCode:
<span class="hljs-keyword">func</span> cmpAlongY(d, e: <span class="hljs-type">Dot</span>): <span class="hljs-built_in">int</span> =
<span class="hljs-literal">result</span> = (d.y - e.y)
<span class="hljs-keyword">if</span> <span class="hljs-literal">result</span> == <span class="hljs-number">0</span>:
<span class="hljs-literal">result</span> = (d.x - e.x)
dump cmpAlongY((<span class="hljs-number">4</span>, <span class="hljs-number">10</span>), (<span class="hljs-number">6</span>, <span class="hljs-number">8</span>))
dump cmpAlongY((<span class="hljs-number">4</span>, <span class="hljs-number">8</span>), (<span class="hljs-number">6</span>, <span class="hljs-number">8</span>))
<span class="hljs-keyword">func</span> sortedAlongY(dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>]): <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>] =
sorted(dots, cmpAlongY)
dump testDots.sortedAlongY[<span class="hljs-number">0</span> .. <span class="hljs-number">5</span>]
nbText: <span class="hljs-string">"""and finally it is showtime!
The following `show` function will work correctly only
if input is sorted along Y axis and yMax and xMax get the whole area
"""</span>
nbCode:
<span class="hljs-keyword">func</span> show(dots: <span class="hljs-built_in">seq</span>[<span class="hljs-type">Dot</span>], yMax=<span class="hljs-number">7</span>, xMax=<span class="hljs-number">50</span>): <span class="hljs-built_in">string</span> =
<span class="hljs-keyword">var</span> i = <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> y <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. yMax:
<span class="hljs-keyword">for</span> x <span class="hljs-keyword">in</span> <span class="hljs-number">0</span> .. xMax:
<span class="hljs-keyword">if</span> i < dots.len <span class="hljs-keyword">and</span> dots[i] == (x, y):
<span class="hljs-literal">result</span>.add <span class="hljs-string">'#'</span>
inc i
<span class="hljs-keyword">else</span>:
<span class="hljs-literal">result</span>.add <span class="hljs-string">'.'</span>
<span class="hljs-literal">result</span>.add <span class="hljs-string">'\n'</span>
<span class="hljs-comment"># dots currently is results of folding testDots</span>
<span class="hljs-keyword">echo</span> show(dots.sortedAlongY)
nbText: <span class="hljs-string">"looks good, let's go with the puzzle:"</span>
nbCode:
foldPuzzle
<span class="hljs-keyword">echo</span> show(dots.sortedAlongY) <span class="hljs-comment">#AHGCPGAU</span>
gotTheStar
nbSave
</code></pre>
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