\n",
- " \n",
+ " oninput=\"anim371f62c512dc43638cafc61e9bb8bb48.set_frame(parseInt(this.value));\">\n",
" \n",
- " \n",
"
\n",
"![](\"https://pbs.twimg.com/media/GejUQBgWIAAUtDf?format=jpg&name=medium\")
\n",
"\n",
"\n",
- "I'll define `blink` to simulate the effect of a given number of blinks, and `change_stone` to change a single stone, returning a list of wither one or two stones (the two stones computed by `split_stone`):"
+ "I'll define `blink` to simulate the effect of a given number of blinks, and `change_stone` to change a single stone, returning a list of either one or two stones (the two stones computed by `split_stone`):"
]
},
{
"cell_type": "code",
- "execution_count": 1008,
+ "execution_count": 775,
"id": "1513df56-3d6f-42cf-8aec-1bdbeb991d90",
"metadata": {},
"outputs": [],
@@ -1931,24 +1936,24 @@
},
{
"cell_type": "code",
- "execution_count": 1009,
+ "execution_count": 776,
"id": "eff17cd0-a2c7-4d69-bc55-c0ef97917915",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "Puzzle 11.1: .063 seconds, answer 194482 ok"
+ "Puzzle 11.1: .062 seconds, answer 194482 ok"
]
},
- "execution_count": 1009,
+ "execution_count": 776,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"answer(11.1, 194482, lambda:\n",
- " len(blink(stones)))"
+ " len(blink(stones, 25)))"
]
},
{
@@ -1962,12 +1967,13 @@
"- Although the puzzle makes it clear that the stones are in a line, it turns out their position in the line is irrelevant.\n",
"- Because all the even-digit numbers get split in half, it seems like many small numbers will appear multiple times.\n",
"- (In the given example, after 6 blinks the number 2 appears 4 times.)\n",
- "- Therefore, I'll keep a `Counter` of stones rather than a `list` of stones."
+ "- Therefore, I'll keep a `Counter` of stones rather than a `list` of stones.\n",
+ "- (Note my [utility function](AdventUtils.ipynb) `accumulate` takes as input an iterable of (key, count) pairs, and returns a Counter of the total count for each key.)"
]
},
{
"cell_type": "code",
- "execution_count": 1011,
+ "execution_count": 778,
"id": "707b5a97-0296-48df-bdab-e34064cc67c2",
"metadata": {},
"outputs": [],
@@ -1992,7 +1998,7 @@
},
{
"cell_type": "code",
- "execution_count": 1013,
+ "execution_count": 780,
"id": "efdcdbf8-e8ec-4a85-9d09-90a20e08c66a",
"metadata": {},
"outputs": [
@@ -2002,7 +2008,7 @@
"Puzzle 11.1: .002 seconds, answer 194482 ok"
]
},
- "execution_count": 1013,
+ "execution_count": 780,
"metadata": {},
"output_type": "execute_result"
}
@@ -2014,17 +2020,17 @@
},
{
"cell_type": "code",
- "execution_count": 1014,
+ "execution_count": 781,
"id": "657b1f13-ffcc-44c6-84f1-398fa2fcdac7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "Puzzle 11.2: .057 seconds, answer 232454623677743 ok"
+ "Puzzle 11.2: .055 seconds, answer 232454623677743 ok"
]
},
- "execution_count": 1014,
+ "execution_count": 781,
"metadata": {},
"output_type": "execute_result"
}
@@ -2039,7 +2045,7 @@
"id": "ce377749-b3e2-4ca4-b50d-e7c3d2e7201a",
"metadata": {},
"source": [
- "Again, I did pretty well, with no errors, and moving at what I thought was a good pace, but I didn't even crack the top 2000 on the leaderboard. I guess I spent too much time writing docstrings and type hints, and refactoring as I went."
+ "Again, I did pretty well, with no errors, and moving at what I thought was a good pace, but I didn't even crack the top 2000 on the leaderboard. "
]
},
{
@@ -2049,12 +2055,12 @@
"source": [
"# [Day 12](https://adventofcode.com/2024/day/12): Garden Groups\n",
"\n",
- "Today's input is yet another 2D map. This one depicts different garden plots on a farm, each plot planted with a crop, indicated by a letter (maybe \"I\" is iceberg lettuce and \"U\" is udo, and so on):"
+ "Today's input is yet another 2D map. This one depicts different garden plots on a farm, each plot planted with a crop, indicated by a letter (maybe \"I\" is iceberg lettuce and \"O\" is okra, and so on):"
]
},
{
"cell_type": "code",
- "execution_count": 1017,
+ "execution_count": 784,
"id": "8161ee7e-76e3-499a-abf8-a607991c9602",
"metadata": {},
"outputs": [
@@ -2093,7 +2099,7 @@
},
{
"cell_type": "code",
- "execution_count": 1019,
+ "execution_count": 786,
"id": "79f91f38-e325-44f2-9e53-b64ce12d9d35",
"metadata": {},
"outputs": [],
@@ -2117,12 +2123,12 @@
"id": "9524ee15-c378-4cd4-a79b-14fb99b17cb3",
"metadata": {},
"source": [
- "To find all the regions I'll start at a point and do a [flood fill](https://en.wikipedia.org/wiki/Flood_fill) to neighboring points with the same region letter, keeping track of points that have already been found so as to not duplicate them. The function `regions` iterates over all points to make sure it finds every region, and `flood_fill` recursively expands to all points that neighbor `p` and have the same crop (letter). This function mutates the set `already_found` as it goes (and also mutates the `region` it is building up)."
+ "To find all the regions I'll start at a point and do a [flood fill](https://en.wikipedia.org/wiki/Flood_fill) to neighboring points with the same region letter, keeping track of points that have already been found so as to not duplicate them. The function `regions` iterates over all points to make sure it finds every region, and `flood_fill` recursively expands to all points that neighbor `p` and have the same crop (letter). `flood_fill` mutates the set `already_found` as it goes (and also mutates the `region` it is building up)."
]
},
{
"cell_type": "code",
- "execution_count": 1021,
+ "execution_count": 788,
"id": "1fbabbfb-50c8-4197-8517-e7cee9582765",
"metadata": {},
"outputs": [],
@@ -2146,7 +2152,7 @@
},
{
"cell_type": "code",
- "execution_count": 1022,
+ "execution_count": 789,
"id": "cdaf655b-d12c-4973-b19b-3132e5e691c6",
"metadata": {},
"outputs": [
@@ -2156,7 +2162,7 @@
"Puzzle 12.1: .031 seconds, answer 1402544 ok"
]
},
- "execution_count": 1022,
+ "execution_count": 789,
"metadata": {},
"output_type": "execute_result"
}
@@ -2173,9 +2179,9 @@
"source": [
"### Part 2: What is the new total price of fencing all regions on your map, with the bulk discount?\n",
"\n",
- "In Part 2 we get a **bulk discount** on the fencing; we only need to pay for the number of straight line sides on the perimeter, not the total length of the perimeter. For example, a 10 x 10 square has perimeter 40, but has only 4 sides; that's a 90% discount!\n",
+ "In Part 2 we get a **bulk discount** on the fencing; we only need to pay for the number of straight line sides on the perimeter, not the total length of the perimeter. For example, a 10 x 10 square has perimeter 40, but has only 4 sides. That's a 90% discount!\n",
"\n",
- "It took me a while to figure out a good approach for this. At first I was reminded of the Convex Hull problem, for which I have [a notebook](https://github.com/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb). But that's not really appropriate here; our regions could be non-convex, and the set of points in a region are not the same as the vertexes of a polygon (e.g., a region with one point has 4 sides, not 0).\n",
+ "It took me a while to figure out a good approach for this. At first I was reminded of the Convex Hull problem, for which I have [a notebook](https://github.com/norvig/pytudes/blob/main/ipynb/Convex%20Hull.ipynb). But that's not really appropriate here; our regions could be non-convex, and the set of sides in a region are not the same as the vertexes of a polygon (e.g., a region with one point has 4 sides, not 0).\n",
"\n",
"A better idea is to start with the perimeter length and subtract one for every case in which a points has an edge in one direction (e.g., an edge to the North) and also has a neighbor with the same edge. To be precise, I'll look for four cases:\n",
"- A point with an edge to the North whose neighbor to the East also has an edge to the North\n",
@@ -2183,7 +2189,7 @@
"- A point with an edge to the South whose neighbor to the West also has an edge to the South\n",
"- A point with an edge to the West whose neighbor to the North also has an edge to the West\n",
"\n",
- "Here are two diagrams of two regions with \"`X`\" and \"`W`\" crops with a \"`-`\" marking each place where a perimeter piece would be subtracted.\n",
+ "Here are two diagrams of two regions with two kinds of crop, \"`X`\" and \"`W`\", with a \"`-`\" marking each place where a perimeter piece would be subtracted.\n",
"\n",
" .X-... .-------..\n",
" -X-.X- .WWWWWWWW-\n",
@@ -2191,12 +2197,12 @@
" ..XXX. -WWWWWWWW.\n",
" ...--. ..-------.\n",
"\n",
- "I'll parameterize `fence_price` to take a `region_price` parameter, and show that the change is backwards compatible to Part 1:"
+ "I'll refactor `fence_price` to take a `region_price` parameter, and show that the change is backwards compatible to Part 1:"
]
},
{
"cell_type": "code",
- "execution_count": 1024,
+ "execution_count": 791,
"id": "38c30e15-3a33-40c2-b734-163a15af7a8a",
"metadata": {},
"outputs": [],
@@ -2219,7 +2225,7 @@
},
{
"cell_type": "code",
- "execution_count": 1025,
+ "execution_count": 792,
"id": "72175812-dcd0-4f1b-9efa-0dceeeafa609",
"metadata": {},
"outputs": [
@@ -2229,7 +2235,7 @@
"Puzzle 12.1: .030 seconds, answer 1402544 ok"
]
},
- "execution_count": 1025,
+ "execution_count": 792,
"metadata": {},
"output_type": "execute_result"
}
@@ -2241,17 +2247,17 @@
},
{
"cell_type": "code",
- "execution_count": 1026,
+ "execution_count": 793,
"id": "9defcd35-91bc-41d4-a16f-bb7a4ede75e7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "Puzzle 12.2: .043 seconds, answer 862486 ok"
+ "Puzzle 12.2: .042 seconds, answer 862486 ok"
]
},
- "execution_count": 1026,
+ "execution_count": 793,
"metadata": {},
"output_type": "execute_result"
}
@@ -2275,7 +2281,7 @@
},
{
"cell_type": "code",
- "execution_count": 1028,
+ "execution_count": 795,
"id": "e78f45c0-c420-4661-aad2-14e122b4473b",
"metadata": {},
"outputs": [
@@ -2334,12 +2340,12 @@
"- Calculate how many presses of the **B** button would be required to get to the prize's X location.\n",
"- If the number of presses is an integer, and would also arrive at the prize's Y location, then yield that solution.\n",
"- Out of these solutions, the cheapest solution is the one that needs the fewest tokens.\n",
- "- (If there are no solutions, `cheapest_solution` will return 0, whcih is convenient for adding the results up.)"
+ "- (If there are no solutions, `cheapest_solution` will return 0, whcih is convenient for adding the results up, but is worrisome because it doesn't distinguish between an impossible-to-reach prize and a prize at the origin. On this puzzle, that's ok, but it is still worrisome.)"
]
},
{
"cell_type": "code",
- "execution_count": 1030,
+ "execution_count": 797,
"id": "c2c4bbc9-42cd-483d-8da2-97cf051e93fe",
"metadata": {},
"outputs": [],
@@ -2358,22 +2364,22 @@
"\n",
"def cheapest_solution(claw: Claw) -> int: \n",
" \"\"\"The minimum cost out of every possible solution to this claw machine.\"\"\"\n",
- " return min((3 * A + 1 * B for (A, B) in solve_claw(claw)), default=0)"
+ " return min((3 * A + B for (A, B) in solve_claw(claw)), default=0)"
]
},
{
"cell_type": "code",
- "execution_count": 1031,
+ "execution_count": 798,
"id": "f5638ed4-1e59-4b9f-b1fc-427d2eb0d036",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "Puzzle 13.1: .011 seconds, answer 29598 ok"
+ "Puzzle 13.1: .010 seconds, answer 29598 ok"
]
},
- "execution_count": 1031,
+ "execution_count": 798,
"metadata": {},
"output_type": "execute_result"
}
@@ -2410,7 +2416,7 @@
},
{
"cell_type": "code",
- "execution_count": 1033,
+ "execution_count": 800,
"id": "df8da2ae-52f9-409b-a54f-ad7d21b32e45",
"metadata": {},
"outputs": [
@@ -2420,7 +2426,7 @@
"Counter({0: 168, 1: 152})"
]
},
- "execution_count": 1033,
+ "execution_count": 800,
"metadata": {},
"output_type": "execute_result"
}
@@ -2434,7 +2440,9 @@
"id": "f0f97d47-5741-4c6e-ae96-5b3161ee2e56",
"metadata": {},
"source": [
- "So, what is the intersection point of two lines? You could [look it up](https://www.wolframalpha.com/input?i=solve+for+a%2C+b%3A+p+*+a+%2B+q+*+b+%3D+r++and+++s+*+a+%2B+t+*+b+%3D+u) or work it out by hand. Given the two equations over the two variables *a* and *b*:\n",
+ "This says that 168 claw machines have no solution and 152 have exactly one. None of them have more than one solution.\n",
+ "\n",
+ "So, what is the intersection point of two lines? You could [look it up](https://www.wolframalpha.com/input?i=solve+for+a%2C+b%3A+p+*+a+%2B+q+*+b+%3D+r++and+++s+*+a+%2B+t+*+b+%3D+u) or work it out by hand, or [call a function](https://numpy.org/doc/2.1/reference/generated/numpy.linalg.solve.html). Given the two equations over the two variables *a* and *b*:\n",
"\n",
" p * a + q * b = r\n",
" s * a + t * b = u\n",
@@ -2449,7 +2457,7 @@
},
{
"cell_type": "code",
- "execution_count": 1035,
+ "execution_count": 802,
"id": "6bbd0934-d962-4c93-940b-810651e9e568",
"metadata": {},
"outputs": [],
@@ -2473,7 +2481,7 @@
},
{
"cell_type": "code",
- "execution_count": 1037,
+ "execution_count": 804,
"id": "dd38ba4c-44ba-426b-b1c8-0e10adbdd642",
"metadata": {},
"outputs": [],
@@ -2485,7 +2493,7 @@
},
{
"cell_type": "code",
- "execution_count": 1038,
+ "execution_count": 805,
"id": "9f578b3e-6b6d-4eb0-9228-c98122a84747",
"metadata": {},
"outputs": [
@@ -2495,7 +2503,7 @@
"Puzzle 13.2: .000 seconds, answer 93217456941970 ok"
]
},
- "execution_count": 1038,
+ "execution_count": 805,
"metadata": {},
"output_type": "execute_result"
}
@@ -2510,12 +2518,12 @@
"id": "db917eed-07e5-4409-a92d-b26534a1fcd4",
"metadata": {},
"source": [
- "The refactored `solve_claw` is compatible with Part 1, and should be a bit faster:"
+ "The refactored `solve_claw` is compatible with Part 1, and should be faster:"
]
},
{
"cell_type": "code",
- "execution_count": 1040,
+ "execution_count": 807,
"id": "609ed4ce-548c-4af4-8e09-c621aca0124e",
"metadata": {},
"outputs": [
@@ -2525,7 +2533,7 @@
"Puzzle 13.1: .000 seconds, answer 29598 ok"
]
},
- "execution_count": 1040,
+ "execution_count": 807,
"metadata": {},
"output_type": "execute_result"
}
@@ -2535,6 +2543,14 @@
" sum(map(cheapest_solution, claws)))"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "741bd221-cda4-432b-8ad2-b8c6950c7dc3",
+ "metadata": {},
+ "source": [
+ "I could have recognized in Part 1 that we have a system of two linear equations in two unknowns, and gone straight to the Part 2 solution. But I have no regrets; I took the hint that trial-and-test for 100 trials was a good idea, and I saved the complicated algebra for when I really needed it in Part 2. Having two independent implementations give the answer incrreases my confidence in both of them."
+ ]
+ },
{
"cell_type": "markdown",
"id": "2576ce68-3f1e-4887-ab0b-62fa94cbe55a",
@@ -2542,12 +2558,12 @@
"source": [
"# [Day 14](https://adventofcode.com/2024/day/14 ): Restroom Redoubt\n",
"\n",
- "Today's narratives involve robots roaming around a restroom. Each line of the input describes a robot's position and velocity in two dimensions:"
+ "Today's narratives involve multiple robots roaming around a restroom. Each line of the input describes a robot's position and velocity in two dimensions:"
]
},
{
"cell_type": "code",
- "execution_count": 1042,
+ "execution_count": 810,
"id": "1a5f5875-426d-47ea-a35a-405c39ced5dd",
"metadata": {},
"outputs": [
@@ -2598,7 +2614,7 @@
},
{
"cell_type": "code",
- "execution_count": 1044,
+ "execution_count": 812,
"id": "be22ac94-7401-4cf6-ab83-e43775536af7",
"metadata": {},
"outputs": [],
@@ -2620,7 +2636,7 @@
},
{
"cell_type": "code",
- "execution_count": 1045,
+ "execution_count": 813,
"id": "69093001-79aa-463a-b801-51cd5b4de4eb",
"metadata": {},
"outputs": [
@@ -2630,7 +2646,7 @@
"Puzzle 14.1: .000 seconds, answer 216027840 ok"
]
},
- "execution_count": 1045,
+ "execution_count": 813,
"metadata": {},
"output_type": "execute_result"
}
@@ -2649,16 +2665,17 @@
"\n",
"I was so sure Part 2 was going to ask for 10 trillion steps. But I was wrong. \n",
"\n",
- "Instead they ask the very vague question of when a picture emerges. They gave the hint that \"*very rarely, most of the robots should arrange themselves into a picture of a Christmas tree.*\" Since I don't know exactly how to specify a Christmas tree picture, I see two options:\n",
+ "Instead they ask the very vague question of when a picture emerges. They gave the hint that \"*very rarely, most of the robots should arrange themselves into a picture of a Christmas tree.*\" Since I don't know exactly how to specify a Christmas tree picture, I see three options:\n",
"- I could build an animation, and watch as each frame is displayed, stopping when I see something that looks like a tree.\n",
- "- The phrase \"*most of the robots should arrange themselves*\" suggests that most of the robots are in one area. I could check for that. \n",
+ "- The phrase \"*most of the robots should arrange themselves*\" suggests that most of the robots are in one area. I could check for that.\n",
+ "- Generate an image for each time step and send it off to an image recognition service. That would be iffy, and possibly expensive. \n",
"\n",
- "I'll try the animation first. Google and Stack overflow led me to the `matplotlib.animation.FuncAnimation` function:"
+ "I'll try the animation approach first. Google and Stack Overflow led me to the `matplotlib.animation.FuncAnimation` function:"
]
},
{
"cell_type": "code",
- "execution_count": 1047,
+ "execution_count": 815,
"id": "664c686e-0c3d-43b8-970f-88c0bf47dbf6",
"metadata": {},
"outputs": [],
@@ -2675,7 +2692,7 @@
" points = robot_dance(robots, t)\n",
" plt.cla()\n",
" ax.yaxis.set_inverted(True)\n",
- " plt.plot(*T(points), 'o')\n",
+ " plt.plot(*T(points), 'go')\n",
" plt.title(f'{t} seconds')\n",
" return matplotlib.animation.FuncAnimation(fig, animate, frames=times)"
]
@@ -2690,7 +2707,7 @@
},
{
"cell_type": "code",
- "execution_count": 1049,
+ "execution_count": 817,
"id": "87843969-cb37-4fa5-9788-6a1b71c43521",
"metadata": {},
"outputs": [
@@ -2882,42 +2899,42 @@
"\n",
"\n",
"