diff --git a/notebooks/problem0079.ipynb b/notebooks/problem0079.ipynb new file mode 100644 index 0000000..56e6209 --- /dev/null +++ b/notebooks/problem0079.ipynb @@ -0,0 +1,87 @@ +{ + "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())" + ] + } + ], + "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 +} diff --git a/notebooks/txt/0079_keylog.txt b/notebooks/txt/0079_keylog.txt new file mode 100644 index 0000000..41f1567 --- /dev/null +++ b/notebooks/txt/0079_keylog.txt @@ -0,0 +1,50 @@ +319 +680 +180 +690 +129 +620 +762 +689 +762 +318 +368 +710 +720 +710 +629 +168 +160 +689 +716 +731 +736 +729 +316 +729 +729 +710 +769 +290 +719 +680 +318 +389 +162 +289 +162 +718 +729 +319 +790 +680 +890 +362 +319 +760 +316 +729 +380 +319 +728 +716