heyeshuang/zipf.ipynb

## zipf.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "see https://www.youtube.com/watch?v=fCn8zs912OE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 猴子打字机实验\n",
    "## 方法1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 0 1 0 2 0 0 0 2] ['12', '1', '2', '', '', '2']\n"
     ]
    }
   ],
   "source": [
    "# monkey=np.random.randint(3,size=10)\n",
    "# words=[]\n",
    "# word=\"\"\n",
    "# for key in monkey:\n",
    "#     if key==0:\n",
    "#         words.append(word)\n",
    "#         word=\"\"\n",
    "#     else:\n",
    "#         word+=str(key)\n",
    "# if word!=\"\":\n",
    "#     words.append(word)\n",
    "\n",
    "# print(monkey,words)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 方法2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aP8nTShT1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20a366ec358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[('c', 80593),\n",
       " ('d', 80182),\n",
       " ('a', 80168),\n",
       " ('b', 79756),\n",
       " ('ac', 16166),\n",
       " ('cc', 16112),\n",
       " ('dd', 16112),\n",
       " ('ba', 16084),\n",
       " ('aa', 16058),\n",
       " ('ab', 16029),\n",
       " ('cd', 16011),\n",
       " ('ca', 16001),\n",
       " ('ad', 15970),\n",
       " ('dc', 15960),\n",
       " ('db', 15875),\n",
       " ('bc', 15871),\n",
       " ('bb', 15848),\n",
       " ('bd', 15846),\n",
       " ('da', 15812),\n",
       " ('cb', 15760),\n",
       " ('bcb', 3303),\n",
       " ('baa', 3302),\n",
       " ('bac', 3300),\n",
       " ('acc', 3288),\n",
       " ('bab', 3283),\n",
       " ('acd', 3279),\n",
       " ('aba', 3265),\n",
       " ('bba', 3264),\n",
       " ('ccb', 3255),\n",
       " ('abc', 3249),\n",
       " ('acb', 3246),\n",
       " ('adc', 3238),\n",
       " ('dca', 3237),\n",
       " ('cda', 3236),\n",
       " ('dad', 3234),\n",
       " ('dba', 3234),\n",
       " ('cdd', 3229),\n",
       " ('bdc', 3228),\n",
       " ('dcc', 3226),\n",
       " ('dbb', 3223),\n",
       " ('dac', 3222),\n",
       " ('bad', 3220),\n",
       " ('aad', 3214),\n",
       " ('ccd', 3212),\n",
       " ('ada', 3212),\n",
       " ('ddd', 3211),\n",
       " ('abd', 3209),\n",
       " ('ccc', 3207),\n",
       " ('bbb', 3207),\n",
       " ('aca', 3206),\n",
       " ('cad', 3200),\n",
       " ('abb', 3194),\n",
       " ('aac', 3193),\n",
       " ('dab', 3192),\n",
       " ('bdb', 3191),\n",
       " ('bbd', 3184),\n",
       " ('bcc', 3180),\n",
       " ('daa', 3176),\n",
       " ('aab', 3175),\n",
       " ('dbc', 3174),\n",
       " ('bbc', 3171),\n",
       " ('cbc', 3169),\n",
       " ('cab', 3168),\n",
       " ('cbd', 3166),\n",
       " ('cdb', 3164),\n",
       " ('bdd', 3163),\n",
       " ('dda', 3162),\n",
       " ('add', 3161),\n",
       " ('caa', 3159),\n",
       " ('adb', 3154),\n",
       " ('cbb', 3154),\n",
       " ('bda', 3150),\n",
       " ('ddb', 3148),\n",
       " ('dbd', 3143),\n",
       " ('dcb', 3138),\n",
       " ('cac', 3138),\n",
       " ('ddc', 3134),\n",
       " ('aaa', 3133),\n",
       " ('bcd', 3120),\n",
       " ('dcd', 3119),\n",
       " ('cdc', 3116),\n",
       " ('bca', 3093),\n",
       " ('cca', 3088),\n",
       " ('cba', 3073),\n",
       " ('adda', 707),\n",
       " ('ddbd', 701),\n",
       " ('abcd', 695),\n",
       " ('bdda', 692),\n",
       " ('baca', 688),\n",
       " ('dcbd', 687),\n",
       " ('bcbd', 687),\n",
       " ('dbbb', 686),\n",
       " ('dcab', 683),\n",
       " ('bbcd', 683),\n",
       " ('dccb', 682),\n",
       " ('acbb', 681),\n",
       " ('dacc', 681),\n",
       " ('addd', 680),\n",
       " ('dbcd', 676),\n",
       " ('abad', 676)]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import string,random\n",
    "from collections import Counter\n",
    "s=string.ascii_lowercase+\" \"\n",
    "s=\"abcd \"\n",
    "monkey=''.join(random.choices(s, k=10000000))\n",
    "monkey=[m for m in monkey.split(\" \") if m]\n",
    "c=Counter(monkey)\n",
    "common=c.most_common()[:10000]\n",
    "fre=[value for (key,value) in common]\n",
    "plt.plot(fre)\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.show()\n",
    "c.most_common(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "阶梯形状可能是由于概率相等"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 连接曲别针实验1\n",
    "\n",
    "取100个曲别针位置，随机在每个位置上连接新的曲别针，某个位置曲别针最多，新曲别针连接此位置的概率越高"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "l=100\n",
    "list=np.ones(l)\n",
    "for i in range(100000):\n",
    "    s=sum(list)\n",
    "    p=[j/s for j in list]\n",
    "    k=np.random.choice(l,1, p=p)\n",
    "    list[k]+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wuHfQ67IyhrpuRMQXzq0v5pm/v5R7bryQw72DfPg7T/Pkq+1el5URFPQi4ht5ecabFpby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\nnvooLPYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20a47caee80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sorted(list,reverse=True))\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.show() #指数分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 连接曲别针实验2\n",
    "\n",
    "- 随机将两个串连接起来\n",
    "- 串选中的概率与串中曲别针个数有关"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 方法1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.244961769883503\n"
     ]
    }
   ],
   "source": [
    "tic=timeit.default_timer()\n",
    "l=20000\n",
    "list=[1]*l\n",
    "while len(list)>14000:\n",
    "    s=sum(list)\n",
    "    p=[j/s for j in list]\n",
    "    k1=np.random.choice(len(list),1, p=p)\n",
    "    a1=list.pop(k1[0])\n",
    "    s=sum(list)\n",
    "    p=[j/s for j in list]\n",
    "    k2=np.random.choice(len(list),1, p=p)\n",
    "    a2=list.pop(k2[0])\n",
    "    list.append(a1+a2)\n",
    "toc=timeit.default_timer()\n",
    "print(toc-tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IETNTsm/3Wy5N7S8kp8+fW7gZC+SQWPtrDMn53ELQAzkk1pbzrMXPMQQ9kENi7UnPVse5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e75dbf8160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# print(list)\n",
    "plt.plot(sorted(list,reverse=True))\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 方法2\n",
    "\n",
    "可能有一些不为人知的坑"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.68740146877235\n"
     ]
    }
   ],
   "source": [
    "tic=timeit.default_timer()\n",
    "l=20000\n",
    "list=[1]*l\n",
    "while len(list)>14000:\n",
    "    r=np.random.randint(l)\n",
    "    k1=len(list)-1\n",
    "\n",
    "    for k,v in enumerate(list):\n",
    "        if r<=0:\n",
    "            k1=k-1\n",
    "            break\n",
    "        else:\n",
    "            r-=v\n",
    "    a1=list.pop(k1)\n",
    "    k2=len(list)-1\n",
    "    r=np.random.randint(l)\n",
    "    for k,v in enumerate(list):\n",
    "        if r<=0:\n",
    "            k2=k-1\n",
    "            break\n",
    "        else:\n",
    "            r-=v\n",
    "    a2=list.pop(k2)\n",
    "    list.append(a1+a2)\n",
    "#     print(len(list))\n",
    "toc=timeit.default_timer()\n",
    "print(toc-tic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2e75dabab00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# print(list)\n",
    "plt.plot(sorted(list,reverse=True))\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}