98 lines
2.9 KiB
Plaintext
98 lines
2.9 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d84ea0fd",
|
|
"metadata": {},
|
|
"source": [
|
|
"# [Passcode Derivation](https://projecteuler.net/problem=79)\n",
|
|
"\n",
|
|
"Gotta read the data first."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "56df44fb",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"with open(\"txt/0079_keylog.txt\") as f:\n",
|
|
" keylog = {tuple(int(c) for c in line.strip()) for line in f}"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "043f31a9",
|
|
"metadata": {},
|
|
"source": [
|
|
"If we assume that no characters are repeated in the passcode, then each entry in the keylog gives a [partial ordering](https://en.wikipedia.org/wiki/Partially_ordered_set) of the characters in the passcode. In math jargon, we are then looking for a [linear extension](https://en.wikipedia.org/wiki/Linear_extension) of the partial ordering. This can be found with a [topological sorting](https://en.wikipedia.org/wiki/Topological_sorting) algorithm.\n",
|
|
"\n",
|
|
"(If characters *are* repeated, we would instead have a [preordering](https://en.wikipedia.org/wiki/Preorder), and a topological sort wouldn't work. Fortunately for us, our assumption turns out to be correct.)\n",
|
|
"\n",
|
|
"Conveniently, and somewhat interestingly, Python has [graphlib](https://docs.python.org/3/library/graphlib.html) in its standard library, which (as of the time of writing) *only* implements topological sorting - but that's all we need for this problem, so I guess don't look a gift horse in the mouth."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "4e742b06",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(7, 3, 1, 6, 2, 8, 9, 0)"
|
|
]
|
|
},
|
|
"execution_count": 2,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"from graphlib import TopologicalSorter\n",
|
|
"\n",
|
|
"ts = TopologicalSorter()\n",
|
|
"for attempt in keylog:\n",
|
|
" for (idx, d) in enumerate(attempt):\n",
|
|
" predecessors = attempt[:idx]\n",
|
|
" ts.add(d, *predecessors)\n",
|
|
"\n",
|
|
"tuple(ts.static_order())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "242e35e6",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Copyright (C) 2025 filifa\n",
|
|
"\n",
|
|
"This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "SageMath 9.5",
|
|
"language": "sage",
|
|
"name": "sagemath"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|