{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def factorial_iterative(n):\n",
    "    product = 1\n",
    "    for i in range(2, n+1):\n",
    "        product *= i\n",
    "    return product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def factorial_recursive(n):\n",
    "    if 1 >= n:\n",
    "        return 1\n",
    "    else:\n",
    "        return n * factorial_recursive(n-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# time measurement for the two \"factorial\" implementations\n",
    "\n",
    "import time\n",
    "import random\n",
    "\n",
    "step = 2\n",
    "nmax = 64\n",
    "repetitions = 100000\n",
    "\n",
    "perf_iter, perf_recu = {}, {}\n",
    "\n",
    "for n in range(0, nmax+1, step):\n",
    "    runtime_iter, runtime_recu = 0.0, 0.0\n",
    "    result_iter, result_recu = 0, 0\n",
    "    \n",
    "    for i in range(repetitions):\n",
    "        start = time.time()\n",
    "        result_iter = factorial_iterative(n)\n",
    "        runtime_iter += time.time() - start\n",
    "        \n",
    "        start = time.time()\n",
    "        result_recu = factorial_recursive(n)\n",
    "        runtime_recu += time.time() - start\n",
    "\n",
    "    perf_iter[n] = runtime_iter/repetitions\n",
    "    perf_recu[n] = runtime_recu/repetitions\n",
    "\n",
    "    print(n, \"%10.5e\" % perf_iter[n], \"%10.5e\" % perf_recu[n], \"%10.5e\" % result_iter, \"%10.5e\"% result_recu, sep=\"\\t\", end=\"\\n\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot the measurement using seaborn\n",
    "\n",
    "import seaborn as sbn\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "keylist_iter = list(perf_iter.keys())\n",
    "vallist_iter = list(perf_iter.values())\n",
    "\n",
    "keylist_recu = list(perf_recu.keys())\n",
    "vallist_recu = list(perf_recu.values())\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(15, 9)\n",
    "plt.xticks(fontsize=18, color=\"#322300\")\n",
    "plt.yticks(fontsize=18, color=\"#322300\")\n",
    "\n",
    "ax.set_xlabel(\"argument value n\", fontsize=24, color=\"#322300\")\n",
    "ax.set_ylabel(\"average runtime in seconds\", fontsize=24, color=\"#322300\")\n",
    "\n",
    "sbn.regplot(x=keylist_iter, y=vallist_iter, color='#147864', \\\n",
    "            order=1, scatter_kws={'s':5})  # green for iterative\n",
    "sbn.regplot(x=keylist_recu, y=vallist_recu, color='#002855', \\\n",
    "            order=1, scatter_kws={'s':5})  # blue for recursive\n",
    "\n",
    "ax.set(xlim=(min(min(keylist_iter), min(keylist_recu)), max(max(keylist_iter), max(keylist_recu))))\n",
    "ax.set(ylim=(min(min(vallist_iter), min(vallist_recu)), max(max(vallist_iter), max(vallist_recu))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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