第二节课.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "coordination_source = \"\"\"\n",
    "{name:'兰州', geoCoord:[103.73, 36.03]},\n",
    "{name:'嘉峪关', geoCoord:[98.17, 39.47]},\n",
    "{name:'西宁', geoCoord:[101.74, 36.56]},\n",
    "{name:'成都', geoCoord:[104.06, 30.67]},\n",
    "{name:'石家庄', geoCoord:[114.48, 38.03]},\n",
    "{name:'拉萨', geoCoord:[102.73, 25.04]},\n",
    "{name:'贵阳', geoCoord:[106.71, 26.57]},\n",
    "{name:'武汉', geoCoord:[114.31, 30.52]},\n",
    "{name:'郑州', geoCoord:[113.65, 34.76]},\n",
    "{name:'济南', geoCoord:[117, 36.65]},\n",
    "{name:'南京', geoCoord:[118.78, 32.04]},\n",
    "{name:'合肥', geoCoord:[117.27, 31.86]},\n",
    "{name:'杭州', geoCoord:[120.19, 30.26]},\n",
    "{name:'南昌', geoCoord:[115.89, 28.68]},\n",
    "{name:'福州', geoCoord:[119.3, 26.08]},\n",
    "{name:'广州', geoCoord:[113.23, 23.16]},\n",
    "{name:'长沙', geoCoord:[113, 28.21]},\n",
    "//{name:'海口', geoCoord:[110.35, 20.02]},\n",
    "{name:'沈阳', geoCoord:[123.38, 41.8]},\n",
    "{name:'长春', geoCoord:[125.35, 43.88]},\n",
    "{name:'哈尔滨', geoCoord:[126.63, 45.75]},\n",
    "{name:'太原', geoCoord:[112.53, 37.87]},\n",
    "{name:'西安', geoCoord:[108.95, 34.27]},\n",
    "//{name:'台湾', geoCoord:[121.30, 25.03]},\n",
    "{name:'北京', geoCoord:[116.46, 39.92]},\n",
    "{name:'上海', geoCoord:[121.48, 31.22]},\n",
    "{name:'重庆', geoCoord:[106.54, 29.59]},\n",
    "{name:'天津', geoCoord:[117.2, 39.13]},\n",
    "{name:'呼和浩特', geoCoord:[111.65, 40.82]},\n",
    "{name:'南宁', geoCoord:[108.33, 22.84]},\n",
    "//{name:'西藏', geoCoord:[91.11, 29.97]},\n",
    "{name:'银川', geoCoord:[106.27, 38.47]},\n",
    "{name:'乌鲁木齐', geoCoord:[87.68, 43.77]},\n",
    "{name:'香港', geoCoord:[114.17, 22.28]},\n",
    "{name:'澳门', geoCoord:[113.54, 22.19]}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import re #引入python的re模块，正则表达式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "l=\"color or colour\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['color', 'colour']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pattern = re.compile(\"colou?r\") #从compile()函数的定义中，可以看出返回的是一个匹配对象，它单独使用就没有任何意义，需要和findall(), search(), match(）搭配使用\n",
    "pattern.findall(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_city_info(city_coordination):\n",
    "    city_location={}\n",
    "    for line in city_coordination.split(\"\\n\"):\n",
    "        if line.startswith(\"//\"):continue\n",
    "        if line.strip()==\"\":continue\n",
    "        \n",
    "        city=re.findall(\"name:'(\\w+)'\",line)[0]\n",
    "        x_y = re.findall(\"Coord:\\[(\\d+.\\d+),\\s(\\d+.\\d+)\\]\",line)[0]\n",
    "        x_y=tuple(map(float,x_y))\n",
    "        city_location[city]=x_y\n",
    "        \n",
    "    return city_location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "city_info=get_city_info(coordination_source)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'兰州': (103.73, 36.03),\n",
       " '嘉峪关': (98.17, 39.47),\n",
       " '西宁': (101.74, 36.56),\n",
       " '成都': (104.06, 30.67),\n",
       " '石家庄': (114.48, 38.03),\n",
       " '拉萨': (102.73, 25.04),\n",
       " '贵阳': (106.71, 26.57),\n",
       " '武汉': (114.31, 30.52),\n",
       " '郑州': (113.65, 34.76),\n",
       " '济南': (117.0, 36.65),\n",
       " '南京': (118.78, 32.04),\n",
       " '合肥': (117.27, 31.86),\n",
       " '杭州': (120.19, 30.26),\n",
       " '南昌': (115.89, 28.68),\n",
       " '福州': (119.3, 26.08),\n",
       " '广州': (113.23, 23.16),\n",
       " '长沙': (113.0, 28.21),\n",
       " '沈阳': (123.38, 41.8),\n",
       " '长春': (125.35, 43.88),\n",
       " '哈尔滨': (126.63, 45.75),\n",
       " '太原': (112.53, 37.87),\n",
       " '西安': (108.95, 34.27),\n",
       " '北京': (116.46, 39.92),\n",
       " '上海': (121.48, 31.22),\n",
       " '重庆': (106.54, 29.59),\n",
       " '天津': (117.2, 39.13),\n",
       " '呼和浩特': (111.65, 40.82),\n",
       " '南宁': (108.33, 22.84),\n",
       " '银川': (106.27, 38.47),\n",
       " '乌鲁木齐': (87.68, 43.77),\n",
       " '香港': (114.17, 22.28),\n",
       " '澳门': (113.54, 22.19)}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "city_info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "###Compute distance between cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "def geo_distance(origin, destination):\n",
    "    \"\"\"\n",
    "    Calculate the Haversine distance.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    origin : tuple of float\n",
    "        (lat, long)\n",
    "    destination : tuple of float\n",
    "        (lat, long)\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    distance_in_km : float\n",
    "\n",
    "    Examples\n",
    "    --------\n",
    "    >>> origin = (48.1372, 11.5756)  # Munich\n",
    "    >>> destination = (52.5186, 13.4083)  # Berlin\n",
    "    >>> round(distance(origin, destination), 1)\n",
    "    504.2\n",
    "    \"\"\"\n",
    "    lat1, lon1 = origin\n",
    "    lat2, lon2 = destination\n",
    "    radius = 6371  # km\n",
    "\n",
    "    dlat = math.radians(lat2 - lat1)\n",
    "    dlon = math.radians(lon2 - lon1)\n",
    "    a = (math.sin(dlat / 2) * math.sin(dlat / 2) +\n",
    "         math.cos(math.radians(lat1)) * math.cos(math.radians(lat2)) *\n",
    "         math.sin(dlon / 2) * math.sin(dlon / 2))\n",
    "    c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))\n",
    "    d = radius * c\n",
    "\n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "#重新进行封装\n",
    "def get_city_distance(city1,city2):\n",
    "    return geo_distance(city_info[city1],city_info[city2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "727.52769688981"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_city_distance(\"上海\",\"北京\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "###Draw the graoh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx #NetworkX 主要用于创造、操作复杂网络，以及学习复杂网络的结构、动力学及其功能。用于分析网络结构，建立网络模型，设计新的网络算法，绘制网络等等\n",
    "import matplotlib.pyplot as plt #Matplotlib 是一个 Python 的 2D绘图库，它以各种硬拷贝格式和跨平台的交互式环境生成出版质量级别的图形\n",
    "\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei']\n",
    "plt.rcParams['axes.unicode_minus'] = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['兰州', '嘉峪关', '西宁', '成都', '石家庄', '拉萨', '贵阳', '武汉', '郑州', '济南', '南京', '合肥', '杭州', '南昌', '福州', '广州', '长沙', '沈阳', '长春', '哈尔滨', '太原', '西安', '北京', '上海', '重庆', '天津', '呼和浩特', '南宁', '银川', '乌鲁木齐', '香港', '澳门'])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "city_info.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "city_graph=nx.Graph() #创建一个没有节点和边的空图\n",
    "city_graph.add_nodes_from(list(city_info.keys()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#画图\n",
    "nx.draw(city_graph,city_info,with_labels=True,node_size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "threshold=700"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_conection(city_info):\n",
    "    cities_connection=defaultdict(list)\n",
    "    cities = list(city_info.keys())\n",
    "    \n",
    "    for c1 in cities:\n",
    "        for c2 in cities:\n",
    "            if c1==c2:\n",
    "                continue\n",
    "            \n",
    "            if get_city_distance(c1,c2) < threshold:\n",
    "                cities_connection[c1].append(c2)\n",
    "    return cities_connection #注意 此处的return位置不同，得到的结果也不同，要返回所有的return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "cities_connection = build_conection(city_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(list,\n",
       "            {'兰州': ['嘉峪关', '西宁', '成都', '拉萨', '贵阳', '西安', '重庆', '南宁', '银川'],\n",
       "             '嘉峪关': ['兰州', '西宁', '成都', '拉萨'],\n",
       "             '西宁': ['兰州', '嘉峪关', '成都', '拉萨', '贵阳', '重庆', '银川'],\n",
       "             '成都': ['兰州', '嘉峪关', '西宁', '拉萨', '贵阳', '西安', '重庆', '南宁', '银川'],\n",
       "             '石家庄': ['武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '南昌',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '北京',\n",
       "              '天津',\n",
       "              '呼和浩特'],\n",
       "             '拉萨': ['兰州', '嘉峪关', '西宁', '成都', '贵阳', '重庆', '南宁', '银川'],\n",
       "             '贵阳': ['兰州', '西宁', '成都', '拉萨', '西安', '重庆', '南宁', '银川'],\n",
       "             '武汉': ['石家庄',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '福州',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '北京',\n",
       "              '天津',\n",
       "              '呼和浩特',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '郑州': ['石家庄',\n",
       "              '武汉',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '南昌',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '北京',\n",
       "              '天津',\n",
       "              '呼和浩特',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '济南': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '福州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '北京',\n",
       "              '上海',\n",
       "              '天津',\n",
       "              '呼和浩特'],\n",
       "             '南京': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '福州',\n",
       "              '长沙',\n",
       "              '北京',\n",
       "              '上海',\n",
       "              '天津'],\n",
       "             '合肥': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '福州',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '北京',\n",
       "              '上海',\n",
       "              '天津',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '杭州': ['武汉', '济南', '南京', '合肥', '南昌', '福州', '北京', '上海', '天津'],\n",
       "             '南昌': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '福州',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '北京',\n",
       "              '上海',\n",
       "              '天津',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '福州': ['武汉',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '广州',\n",
       "              '上海',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '广州': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '合肥',\n",
       "              '南昌',\n",
       "              '福州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '南宁',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '长沙': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '南昌',\n",
       "              '广州',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '北京',\n",
       "              '天津',\n",
       "              '呼和浩特',\n",
       "              '南宁',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '沈阳': ['长春', '哈尔滨', '上海'],\n",
       "             '长春': ['沈阳', '哈尔滨'],\n",
       "             '哈尔滨': ['沈阳', '长春'],\n",
       "             '太原': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '合肥',\n",
       "              '南昌',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '西安',\n",
       "              '北京',\n",
       "              '天津',\n",
       "              '呼和浩特',\n",
       "              '银川',\n",
       "              '澳门'],\n",
       "             '西安': ['兰州',\n",
       "              '成都',\n",
       "              '石家庄',\n",
       "              '贵阳',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '重庆',\n",
       "              '呼和浩特',\n",
       "              '南宁',\n",
       "              '银川'],\n",
       "             '北京': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '天津',\n",
       "              '呼和浩特'],\n",
       "             '上海': ['济南', '南京', '合肥', '杭州', '南昌', '福州', '沈阳', '天津'],\n",
       "             '重庆': ['兰州', '西宁', '成都', '拉萨', '贵阳', '西安', '呼和浩特', '南宁', '银川'],\n",
       "             '天津': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '南京',\n",
       "              '合肥',\n",
       "              '杭州',\n",
       "              '南昌',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '北京',\n",
       "              '上海',\n",
       "              '呼和浩特'],\n",
       "             '呼和浩特': ['石家庄',\n",
       "              '武汉',\n",
       "              '郑州',\n",
       "              '济南',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '北京',\n",
       "              '重庆',\n",
       "              '天津',\n",
       "              '银川'],\n",
       "             '南宁': ['兰州',\n",
       "              '成都',\n",
       "              '拉萨',\n",
       "              '贵阳',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '西安',\n",
       "              '重庆',\n",
       "              '银川',\n",
       "              '香港',\n",
       "              '澳门'],\n",
       "             '银川': ['兰州',\n",
       "              '西宁',\n",
       "              '成都',\n",
       "              '拉萨',\n",
       "              '贵阳',\n",
       "              '太原',\n",
       "              '西安',\n",
       "              '重庆',\n",
       "              '呼和浩特',\n",
       "              '南宁'],\n",
       "             '香港': ['武汉', '郑州', '合肥', '南昌', '福州', '广州', '长沙', '南宁', '澳门'],\n",
       "             '澳门': ['武汉',\n",
       "              '郑州',\n",
       "              '合肥',\n",
       "              '南昌',\n",
       "              '福州',\n",
       "              '广州',\n",
       "              '长沙',\n",
       "              '太原',\n",
       "              '南宁',\n",
       "              '香港']})"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cities_connection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "cities_connection_graph=nx.Graph(cities_connection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(cities_connection_graph,city_info,with_labels=True,node_size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#BFS算法\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bfs(graph,start ,destination):\n",
    "    pathes=[[start]] #paths是要维护的搜索历史\n",
    "    visited =set()\n",
    "    \n",
    "    while pathes:\n",
    "        path =pathes.pop(0) #每次把第一条路径拿出来探索\n",
    "        froniter =path[-1] #检查path路径最后的点是否有其他点相连\n",
    "        \n",
    "        if froniter in visited:continue #如果最后的点有经历过，就跳过\n",
    "            \n",
    "        successors = graph[froniter] #将图中所有的与这个点相连的点放在successors中\n",
    "        \n",
    "        for city in successors:\n",
    "            if city in path:continue #遍历每个相连点的城市，在检查是否为环\n",
    "                \n",
    "            new_path = path + [city]\n",
    "            \n",
    "            pathes.append(new_path)  #每次有新拓展的路径  就放在之前路径的尾部\n",
    "            \n",
    "            \n",
    "           \n",
    "            \n",
    "            if city==destination:\n",
    "                return new_path #如果是我们需要的路径，如果是就返回\n",
    "        \n",
    "        visited.add(froniter)\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['上海', '合肥', '香港']"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs(cities_connection,\"上海\",\"香港\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['拉萨', '兰州', '西安']"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs(cities_connection,\"拉萨\",\"西安\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dfs(graph,start ,destination):\n",
    "    pathes=[[start]]\n",
    "    visited =set()\n",
    "    \n",
    "    while pathes:\n",
    "        path =pathes.pop(0)\n",
    "        froniter =path[-1]\n",
    "        \n",
    "        if froniter in visited:continue\n",
    "            \n",
    "        successors = graph[froniter]\n",
    "        \n",
    "        for city in successors:\n",
    "            if city in path:continue\n",
    "                \n",
    "            new_path = path + [city] #dfs与bfs的区别：将新增的点放在维护list的前面\n",
    "            \n",
    "            pathes.append(new_path)\n",
    "            \n",
    "            \n",
    "            pathes = [new_path] + pathes\n",
    "            \n",
    "            if city==destination:\n",
    "                return new_path\n",
    "        \n",
    "        visited.add(froniter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['拉萨', '银川', '南宁', '澳门', '香港', '长沙', '北京']"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfs(cities_connection,\"拉萨\",\"北京\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['拉萨', '重庆', '呼和浩特', '北京']"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs(cities_connection,\"拉萨\",\"北京\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['拉萨', '银川', '西安']"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfs(cities_connection,\"拉萨\",\"西安\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['拉萨', '兰州', '西安']"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs(cities_connection,\"拉萨\",\"西安\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bfs_2(graph,start,destination,search_strategy):\n",
    "    pathes=[[start]]\n",
    "    \n",
    "    #visite=set()\n",
    "    \n",
    "    while pathes:\n",
    "        path=pathes.pop(0)\n",
    "        froniter=path[-1]\n",
    "        \n",
    "                \n",
    "        #if froniter in visite : continue\n",
    "        \n",
    "        successors=  graph[froniter]\n",
    "        \n",
    "        for city in successors:\n",
    "            if city in path :continue\n",
    "                \n",
    "            new_path = path+[city]\n",
    "                \n",
    "            pathes.append(new_path)\n",
    "                \n",
    "        pathes = search_strategy(pathes) # 一条路经过G  不是最短的\n",
    "            \n",
    "        if pathes and pathes[0][-1] == destination: #这条路，经过重排之后是最短的，并且最后一点是终点\n",
    "            return pathes[0]                      # 经过重排 path=[]\n",
    "     #   visite.add(froniter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "#排序函数\n",
    "def sort_by_distance(pathes):\n",
    "    def get_distance_of_path(path):\n",
    "        distance = 0\n",
    "        for i,_ in enumerate(path[:-1]):\n",
    "                distance +=get_city_distance(path[i],path[i+1])\n",
    "            \n",
    "        return distance\n",
    "    return sorted(pathes,key = get_distance_of_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_diatance_of_path(path):\n",
    "    distance =0\n",
    "    for i,_ in enumerate(path[:-1]):\n",
    "        distance += get_city_distance(path[i],path[i+1])\n",
    "    \n",
    "    return distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "752.66259009181"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_diatance_of_path([\"北京\",\"济南\",\"上海\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "732.5085345714293"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_diatance_of_path([\"北京\",\"天津\",\"上海\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['北京', '天津', '上海']"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs_2(cities_connection,\"北京\",\"上海\",search_strategy=sort_by_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['北京', '济南', '上海']"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs(cities_connection,\"北京\",\"上海\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "752.66259009181"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_diatance_of_path([\"北京\",\"济南\",\"上海\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "梯度下降\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston #sklearn.datasets模块主要提供了一些导入、在线下载及本地生成数据集的方法\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = load_boston()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,\n",
       "         4.9800e+00],\n",
       "        [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,\n",
       "         9.1400e+00],\n",
       "        [2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,\n",
       "         4.0300e+00],\n",
       "        ...,\n",
       "        [6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n",
       "         5.6400e+00],\n",
       "        [1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,\n",
       "         6.4800e+00],\n",
       "        [4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n",
       "         7.8800e+00]]),\n",
       " 'target': array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n",
       "        18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n",
       "        15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n",
       "        13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n",
       "        21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n",
       "        35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n",
       "        19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n",
       "        20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n",
       "        23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,\n",
       "        33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,\n",
       "        21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n",
       "        20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n",
       "        23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n",
       "        15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n",
       "        17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n",
       "        25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n",
       "        23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n",
       "        32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,\n",
       "        34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,\n",
       "        20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n",
       "        26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n",
       "        31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n",
       "        22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n",
       "        42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n",
       "        36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n",
       "        32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n",
       "        20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,\n",
       "        20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,\n",
       "        22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n",
       "        21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n",
       "        19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n",
       "        32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n",
       "        18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n",
       "        16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n",
       "        13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3,  8.8,\n",
       "         7.2, 10.5,  7.4, 10.2, 11.5, 15.1, 23.2,  9.7, 13.8, 12.7, 13.1,\n",
       "        12.5,  8.5,  5. ,  6.3,  5.6,  7.2, 12.1,  8.3,  8.5,  5. , 11.9,\n",
       "        27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3,  7. ,  7.2,  7.5, 10.4,\n",
       "         8.8,  8.4, 16.7, 14.2, 20.8, 13.4, 11.7,  8.3, 10.2, 10.9, 11. ,\n",
       "         9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4,  9.6,  8.7,  8.4, 12.8,\n",
       "        10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n",
       "        15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n",
       "        19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n",
       "        29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n",
       "        20.6, 21.2, 19.1, 20.6, 15.2,  7. ,  8.1, 13.6, 20.1, 21.8, 24.5,\n",
       "        23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9]),\n",
       " 'feature_names': array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "        'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7'),\n",
       " 'DESCR': \".. _boston_dataset:\\n\\nBoston house prices dataset\\n---------------------------\\n\\n**Data Set Characteristics:**  \\n\\n    :Number of Instances: 506 \\n\\n    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\\n\\n    :Attribute Information (in order):\\n        - CRIM     per capita crime rate by town\\n        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\\n        - INDUS    proportion of non-retail business acres per town\\n        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\\n        - NOX      nitric oxides concentration (parts per 10 million)\\n        - RM       average number of rooms per dwelling\\n        - AGE      proportion of owner-occupied units built prior to 1940\\n        - DIS      weighted distances to five Boston employment centres\\n        - RAD      index of accessibility to radial highways\\n        - TAX      full-value property-tax rate per $10,000\\n        - PTRATIO  pupil-teacher ratio by town\\n        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\\n        - LSTAT    % lower status of the population\\n        - MEDV     Median value of owner-occupied homes in $1000's\\n\\n    :Missing Attribute Values: None\\n\\n    :Creator: Harrison, D. and Rubinfeld, D.L.\\n\\nThis is a copy of UCI ML housing dataset.\\nhttps://archive.ics.uci.edu/ml/machine-learning-databases/housing/\\n\\n\\nThis dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\\n\\nThe Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\\nprices and the demand for clean air', J. Environ. Economics & Management,\\nvol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\\n...', Wiley, 1980.   N.B. Various transformations are used in the table on\\npages 244-261 of the latter.\\n\\nThe Boston house-price data has been used in many machine learning papers that address regression\\nproblems.   \\n     \\n.. topic:: References\\n\\n   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\\n   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\\n\",\n",
       " 'filename': 'D:\\\\OpenSources\\\\Anaconda3\\\\install\\\\lib\\\\site-packages\\\\sklearn\\\\datasets\\\\data\\\\boston_house_prices.csv'}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x,y = dataset['data'],dataset['target']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,\n",
       "        4.9800e+00],\n",
       "       [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,\n",
       "        9.1400e+00],\n",
       "       [2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,\n",
       "        4.0300e+00],\n",
       "       ...,\n",
       "       [6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n",
       "        5.6400e+00],\n",
       "       [1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,\n",
       "        6.4800e+00],\n",
       "       [4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n",
       "        7.8800e+00]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n",
       "       18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n",
       "       15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n",
       "       13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n",
       "       21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n",
       "       35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n",
       "       19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n",
       "       20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n",
       "       23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,\n",
       "       33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,\n",
       "       21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n",
       "       20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n",
       "       23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n",
       "       15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n",
       "       17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n",
       "       25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n",
       "       23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n",
       "       32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,\n",
       "       34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,\n",
       "       20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n",
       "       26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n",
       "       31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n",
       "       22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n",
       "       42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n",
       "       36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n",
       "       32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n",
       "       20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,\n",
       "       20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,\n",
       "       22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n",
       "       21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n",
       "       19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n",
       "       32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n",
       "       18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n",
       "       16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n",
       "       13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3,  8.8,\n",
       "        7.2, 10.5,  7.4, 10.2, 11.5, 15.1, 23.2,  9.7, 13.8, 12.7, 13.1,\n",
       "       12.5,  8.5,  5. ,  6.3,  5.6,  7.2, 12.1,  8.3,  8.5,  5. , 11.9,\n",
       "       27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3,  7. ,  7.2,  7.5, 10.4,\n",
       "        8.8,  8.4, 16.7, 14.2, 20.8, 13.4, 11.7,  8.3, 10.2, 10.9, 11. ,\n",
       "        9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4,  9.6,  8.7,  8.4, 12.8,\n",
       "       10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n",
       "       15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n",
       "       19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n",
       "       29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n",
       "       20.6, 21.2, 19.1, 20.6, 15.2,  7. ,  8.1, 13.6, 20.1, 21.8, 24.5,\n",
       "       23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape #x的描述"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.7310e-02, 0.0000e+00, 7.0700e+00, 0.0000e+00, 4.6900e-01,\n",
       "       6.4210e+00, 7.8900e+01, 4.9671e+00, 2.0000e+00, 2.4200e+02,\n",
       "       1.7800e+01, 3.9690e+02, 9.1400e+00])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape[1]\n",
    "x[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y.shape #y的描述"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x[1].shape\n",
    "x[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "       'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\".. _boston_dataset:\\n\\nBoston house prices dataset\\n---------------------------\\n\\n**Data Set Characteristics:**  \\n\\n    :Number of Instances: 506 \\n\\n    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\\n\\n    :Attribute Information (in order):\\n        - CRIM     per capita crime rate by town\\n        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\\n        - INDUS    proportion of non-retail business acres per town\\n        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\\n        - NOX      nitric oxides concentration (parts per 10 million)\\n        - RM       average number of rooms per dwelling\\n        - AGE      proportion of owner-occupied units built prior to 1940\\n        - DIS      weighted distances to five Boston employment centres\\n        - RAD      index of accessibility to radial highways\\n        - TAX      full-value property-tax rate per $10,000\\n        - PTRATIO  pupil-teacher ratio by town\\n        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\\n        - LSTAT    % lower status of the population\\n        - MEDV     Median value of owner-occupied homes in $1000's\\n\\n    :Missing Attribute Values: None\\n\\n    :Creator: Harrison, D. and Rubinfeld, D.L.\\n\\nThis is a copy of UCI ML housing dataset.\\nhttps://archive.ics.uci.edu/ml/machine-learning-databases/housing/\\n\\n\\nThis dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\\n\\nThe Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\\nprices and the demand for clean air', J. Environ. Economics & Management,\\nvol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\\n...', Wiley, 1980.   N.B. Various transformations are used in the table on\\npages 244-261 of the latter.\\n\\nThe Boston house-price data has been used in many machine learning papers that address regression\\nproblems.   \\n     \\n.. topic:: References\\n\\n   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\\n   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\\n\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset['DESCR']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_rm=x[:,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_rm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x27f15795e10>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_rm,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y=k*rm+b$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def price(rm ,k,b):\n",
    "    return k*rm+b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$loss = \\frac{1}{n}\\sum{(y_i-\\hat{y_i})}^2$$\n",
    "$$loss = \\frac{1}{n}\\sum{(y_i-(kx_i+b_i))}^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(y,y_hat):\n",
    "    return sum((y_i -y_hat_i)**2 for y_i,y_hat_i in zip(list(y),list(y_hat)))/len(list(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$$ \\frac{\\partial{loss}}{\\partial{k}} = -\\frac{2}{n}\\sum(y_i - \\hat{y_i})x_i$$\n",
    "\n",
    "$$ \\frac{\\partial{loss}}{\\partial{b}} = -\\frac{2}{n}\\sum(y_i - \\hat{y_i})$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def partial_derivative_k(x,y,y_hat):\n",
    "    n=len(y)\n",
    "    gradient =0\n",
    "    for x_i,y_i,y_hat_i in zip(list(x),list(y),list(y_hat)):\n",
    "        gradient += (y_i - y_hat_i) * x_i\n",
    "    return -2/n * gradient\n",
    "\n",
    "def partial_derivative_b(y,y_hat):\n",
    "    n=len(y)\n",
    "    gradient =0\n",
    "    for y_i,y_hat_i in zip(list(y),list(y_hat)):\n",
    "        gradient += (y_i - y_hat_i) \n",
    "    return -2/n *gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0, the loss is 179168.5822412377, parameters k is 76.68522067746369 and b is -38.84113899727919\n",
      "Iteration 1, the loss is 151011.85580318092, parameters k is 71.33243505987005 and b is -39.682268256378904\n",
      "Iteration 2, the loss is 127281.15970982292, parameters k is 66.41833038514794 and b is -40.45443465583952\n",
      "Iteration 3, the loss is 107280.75453487839, parameters k is 61.906954731339454 and b is -41.1632900200576\n",
      "Iteration 4, the loss is 90424.26597421218, parameters k is 57.765302601940895 and b is -41.814022980410876\n",
      "Iteration 5, the loss is 76217.49345278223, parameters k is 53.96307345277735 and b is -42.41139693605771\n",
      "Iteration 6, the loss is 64243.92109216399, parameters k is 50.47245000871129 and b is -42.959784903674404\n",
      "Iteration 7, the loss is 54152.50624744622, parameters k is 47.26789474831699 and b is -43.463201511096116\n",
      "Iteration 8, the loss is 45647.38759633653, parameters k is 44.325963067572516 and b is -43.9253323689317\n",
      "Iteration 9, the loss is 38479.2110409856, parameters k is 41.62513175564692 and b is -44.349561035039514\n",
      "Iteration 10, the loss is 32437.81911426466, parameters k is 39.14564152788603 and b is -44.738993769140386\n",
      "Iteration 11, the loss is 27346.08955762305, parameters k is 36.86935246394475 and b is -45.09648225867608\n",
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      "Iteration 184, the loss is 46.14629664902029, parameters k is 11.361841927355078 and b is -49.0449861795577\n",
      "Iteration 185, the loss is 46.14617421367837, parameters k is 11.361786800990247 and b is -49.04464063951098\n",
      "Iteration 186, the loss is 46.146051784320306, parameters k is 11.36173174037189 and b is -49.04429509764626\n",
      "Iteration 187, the loss is 46.1459293609309, parameters k is 11.361676740218844 and b is -49.04394955479356\n",
      "Iteration 188, the loss is 46.14580694349708, parameters k is 11.361621795682755 and b is -49.04360401171486\n",
      "Iteration 189, the loss is 46.145684532007934, parameters k is 11.361566902312614 and b is -49.04325846910968\n",
      "Iteration 190, the loss is 46.14556212645425, parameters k is 11.361512056022189 and b is -49.042912927620186\n",
      "Iteration 191, the loss is 46.145439726828094, parameters k is 11.36145725306013 and b is -49.0425673878359\n",
      "Iteration 192, the loss is 46.14531733312278, parameters k is 11.36140248998253 and b is -49.04222185029803\n",
      "Iteration 193, the loss is 46.145194945332726, parameters k is 11.361347763627716 and b is -49.04187631550339\n",
      "Iteration 194, the loss is 46.1450725634531, parameters k is 11.361293071093131 and b is -49.04153078390807\n",
      "Iteration 195, the loss is 46.14495018747977, parameters k is 11.361238409714092 and b is -49.041185255930785\n",
      "Iteration 196, the loss is 46.144827817409215, parameters k is 11.361183777044296 and b is -49.040839731955884\n",
      "Iteration 197, the loss is 46.14470545323849, parameters k is 11.361129170837923 and b is -49.04049421233622\n",
      "Iteration 198, the loss is 46.14458309496496, parameters k is 11.361074589033208 and b is -49.040148697395715\n",
      "Iteration 199, the loss is 46.14446074258647, parameters k is 11.361020029737352 and b is -49.039803187431716\n"
     ]
    }
   ],
   "source": [
    "#initialized parameters\n",
    "\n",
    "k = random.random() * 200 - 100  # -100 100\n",
    "b = random.random() * 200 - 100  # -100 100\n",
    "\n",
    "learning_rate = 1e-3\n",
    "\n",
    "iteration_num = 200 \n",
    "losses = []\n",
    "for i in range(iteration_num):\n",
    "    \n",
    "    price_use_current_parameters = [price(r, k, b) for r in X_rm]  # \\hat{y}\n",
    "    \n",
    "    current_loss = loss(y, price_use_current_parameters)\n",
    "    losses.append(current_loss)\n",
    "    print(\"Iteration {}, the loss is {}, parameters k is {} and b is {}\".format(i,current_loss,k,b))\n",
    "    \n",
    "    k_gradient = partial_derivative_k(X_rm, y, price_use_current_parameters)\n",
    "    b_gradient = partial_derivative_b(y, price_use_current_parameters)\n",
    "    \n",
    "    k = k + (-1 * k_gradient) * learning_rate\n",
    "    b = b + (-1 * b_gradient) * learning_rate\n",
    "best_k = k\n",
    "best_b = b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x27f16aac0f0>]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list(range(iteration_num)),losses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x27f16b19588>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "price_use_best_parameters = [price(r, best_k, best_b) for r in X_rm]\n",
    "\n",
    "plt.scatter(X_rm,y)\n",
    "plt.scatter(X_rm,price_use_current_parameters)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   \n",
    "   \n",
    "# 问答作业\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "What conditions are required to make the BFS return the optimal solution ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "是BFS返回最优的解，需要一个队列，将其是节点放入队列的尾部，在队列不为空的情况下取出并删除队列首节点并处理，再将该节点相邻的未处理的节点加入到队列的尾部"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Is there a way to make DFS find the optimal solution ? (You may need to read some material about iterative DFS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "有方法\n",
    "迭代加深搜索算法：\n",
    "    就是仿广度优先搜索的深度优先搜索，既能满足深度优先搜索的线性存储要求，又能保证发现一个最小深度的目标结点。迭代加深搜索并不比广度优先搜索慢很多，但是空间复杂度却与深度优先搜索相同，比广度优先搜索小很多。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "In what conditions BFS is a better choice than DFS and vice versa ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在搜索路径上：BFS是用来搜索最短径路的解是比较合适的,DFS适合搜索全部的解。\n",
    "\n",
    "因为BFS搜索过程中遇到的解一定是离根最近的，所以遇到一个解，一定就是最优解，此时算法可以终止。因为DFS搜索到的解不一定是离根最近的，只有全局搜索完毕，才能从所有解中找出离根的最近的解\n",
    "\n",
    "在空间上：DFS不需要保存搜索过程中的状态，而BFS在搜索过程中需要保存搜索过的状态，而且一般情况需要一个队列来记录"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " When can we use machine learning ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "机器学习要发现的是资料中存在的模式，机器学习中目标函数非常重要.当模式相对复杂,人们无法直接定义规则的时候才比较适合使用机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "What is the gradient of a function ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "表示某一函数在该点处的方向导数沿着该方向取得最大值，即函数在该点处沿着该方向变化最快，变化率最大"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "How can we find the maximum value of a function using the information of gradient ?¶"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "利用梯度下降法得到函数的极小值的方法，在将原函数原函数取负值，求极小值最后在去相反数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 编程题没时间做\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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