add problem 79

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
+}

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