Add implementation of Conway say-and-tell sequence

Author: gjbex

source_code/conway_say_and_tell.ipynb

@@ -0,0 +1,204 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0738d385-d3ac-4240-a9c8-404501ec320e",
+   "metadata": {},
+   "source": [
+    "# Requirements"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "id": "90e02852-f5a9-4f2b-ade4-6381350e59c1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import re"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dbba3d84-6d7b-47dc-b3f7-f9e3a934bcbf",
+   "metadata": {},
+   "source": [
+    "# Problem"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11156389-33b0-4c13-aab6-b6eb5ea6f2ac",
+   "metadata": {},
+   "source": [
+    "The aim is to generate Conway's look-and-say sequence:\n",
+    "\n",
+    "  * 1\n",
+    "  * 11\n",
+    "  * 21\n",
+    "  * 1211\n",
+    "  * 111221\n",
+    "  * 312211\n",
+    "  * 13112221\n",
+    "  * 1113213211\n",
+    "  * 31131211131221\n",
+    "  * ...\n",
+    "\n",
+    "The sequence is generated by looking at the string, determining the length of sequences of identical characters, and replacing those by the count and the character."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13fc6c45-2eab-4f99-a0e1-c0399b2c27af",
+   "metadata": {},
+   "source": [
+    "# Implementation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "55166a40-75a1-4542-8d24-4a3151142b81",
+   "metadata": {},
+   "source": [
+    "It is easy to split a string into slices that consist of one or more of the same characters using regular expressions. The first part of the expression matches a digit and stores the match for future use (`(\\d)`).  The second part matches zero or more occurences of the digit that was just matched, and stores it as well (`(\\1*)`).  The resultting sequence of tuples contain a digit, followed by the remainder of the sequence, so the next string in Conway's look-and-say sequence is easy to construct."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "0036b458-9e3a-47f5-aefb-0dd0bb0c6a79",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def look_say(sequence):\n",
+    "    new_sequance = ''\n",
+    "    for match in re.findall(r'(\\d)(\\1*)', sequence):\n",
+    "        new_sequance += f'{str(1 + len(match[1]))}{match[0]}'\n",
+    "    return new_sequance"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8805d91c-2e6c-4bc5-b1e0-e5fb8574b138",
+   "metadata": {},
+   "source": [
+    "For convenience, a generator  is defined to generate the sequence up to any number of elements."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "2d957a66-2464-4fbd-bf89-47944d01828b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def look_and_say_sequence():\n",
+    "    s = '1'\n",
+    "    yield s\n",
+    "    while True:\n",
+    "        s = look_say(s)\n",
+    "        yield s"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "id": "b1033bcb-d1e4-4f66-970e-759516325233",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1\n",
+      "11\n",
+      "21\n",
+      "1211\n",
+      "111221\n",
+      "312211\n",
+      "13112221\n",
+      "1113213211\n",
+      "31131211131221\n",
+      "13211311123113112211\n"
+     ]
+    }
+   ],
+   "source": [
+    "seq = look_and_say_sequence()\n",
+    "for _ in range(10):\n",
+    "    print(next(seq))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "03ee3ba4-3e64-4017-a701-827c5499cef8",
+   "metadata": {},
+   "source": [
+    "We can check how many digits the sequence has for the first 200 elements in the sequence."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "33d9f2f0-50ad-4592-8318-1e80e51941ab",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "nr_elements = 50"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "835dab2b-f877-4673-9f90-221eefc91b29",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "lengths = []\n",
+    "seq = look_and_say_sequence()\n",
+    "for _ in rangenr_elements):\n",
+    "    lengths.append(len(next(seq)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3d812c68-27e7-4a55-a89f-3a117ccab9df",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.plot(list(range(1, 201)), lengths)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1e22377c-d2d7-4abd-8b94-259956416be1",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}