ChimeClicker.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_max = 10**1\n",
    "cost_0 = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cost_from_level(level, cost_0, previous = None):\n",
    "    if level == 0:\n",
    "        return cost_0\n",
    "    if previous:\n",
    "        return previous + 0.1 * cost_0 * level\n",
    "    return cost_from_level(level-1, cost_0) + 0.1 * cost_0 * level\n",
    "    \n",
    "def cost_stable(level, cost_0):\n",
    "    return cost_0 * (1 + 0.05 * level*(level-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KC4B5wHFNrUGSJEkqdynBY4/BJZdA374wdSp873uwaBFcfTUcdljeFUrbrzmWCv8P8ANg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\ni8EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6f1cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.42108547152e-14\n"
     ]
    }
   ],
   "source": [
    "levels = np.linspace(1, n_max, n_max, dtype = 'i')\n",
    "c1 = [cost_from_level(0, cost_0, 0)]\n",
    "for i in range(1, n_max):\n",
    "    c1.append(cost_from_level(i, cost_0, c1[-1]))\n",
    "c2 = [cost_stable(i, cost_0) for i in levels]\n",
    "diff = [c2[i-1] - c1[i-1] for i in levels]\n",
    "\n",
    "plt.figure(figsize=(16,6))\n",
    "\n",
    "plt.plot(levels, c1, \"b-\")\n",
    "plt.plot(levels, c2, \"r*\")\n",
    "plt.plot(levels, diff, \"r-\")\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(max(diff))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cum_cost_stable(level_to, level_from, cost_0):\n",
    "    n = level_from\n",
    "    m = level_to\n",
    "    return cost_0 * (m - n + 1 + 1/60 * (m*(m+1)*(m+2) - n*n*n + n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dO+ZdnSQVB7e1kSRJakDTp2ch9d57oWXLbLjvU09B9+55VyZJjZ+BVZIkqZZe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7752ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2737367544323206e-13\n"
     ]
    }
   ],
   "source": [
    "levels = np.linspace(1, n_max, n_max, dtype = 'i')\n",
    "cc1 = [cost_0]\n",
    "for i in range(1, n_max):\n",
    "    cc1.append(cc1[-1] + c1[i])\n",
    "\n",
    "cc2 = [cum_cost_stable(i, 0, cost_0) for i in range(n_max)]\n",
    "diff = [i - j for (i,j) in zip(cc1,cc2)]\n",
    "\n",
    "plt.figure(figsize=(16,6))\n",
    "\n",
    "plt.plot(levels, cc1, \"b-\")\n",
    "plt.plot(levels, cc2, \"r*\")\n",
    "plt.plot(levels, diff, \"r-\")\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(max(diff))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}