{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use [memoization](https://en.wikipedia.org/wiki/Memoization) to cache results for odd numbers. We don't cache even numbers since there's a separate loop that divides even numbers by 2 until we have an odd number. By storing only half of the numbers we also halve the amount of memory needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "837799"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cache = {}\n",
    "def total_stopping_time(n):\n",
    "    t = n\n",
    "    c = 0\n",
    "    while True:\n",
    "        while t % 2 == 0:\n",
    "            t //= 2\n",
    "            c += 1\n",
    "        if t == 1:\n",
    "            break\n",
    "        if cache.get(t):\n",
    "            c += cache.get(t)\n",
    "            break\n",
    "        t = (3*t + 1)\n",
    "        c += 1\n",
    "        \n",
    "    if n % 2 != 0:\n",
    "        cache[n] = c\n",
    "    return c\n",
    "\n",
    "max_n = 0\n",
    "max_length = 0\n",
    "for n in range(1, 1_000_000):\n",
    "    length = total_stopping_time(n)\n",
    "    if length > max_length:\n",
    "        max_length = length\n",
    "        max_n = n\n",
    "max_n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
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  "title": "Longest Collatz sequence"
 },
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