python_lesson4_data_structures2/lesson4_part2_graph_algo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "<img src=\"../img/python_theme.png\">\n",
    "# MLClass. \"Прикладной анализ данных\"\n",
    "# Модуль \"Инструментарий Data Science\"\n",
    "<img src=\"../img/mlclass_logo.jpg\" height=\"240\" width=\"240\">\n",
    "\n",
    "## Автор материала: Юрий Кашницкий, ФКН НИУ ВШЭ\n",
    "</center>\n",
    "Материал распространяется на условиях лицензии <a href=\"https://opensource.org/licenses/MS-RL\">Ms-RL</a>. Можно использовать в любых целях, кроме коммерческих, но с обязательным упоминанием автора материала."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Урок 4. Структуры данных II"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Часть 2. Классические алгоритмы на графах"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Python 2 and 3 compatibility\n",
    "# pip install future\n",
    "from __future__ import (absolute_import, division,\n",
    "                        print_function, unicode_literals)\n",
    "from builtins import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Кратчайший путь в графе"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Заданы n вершин графа (узлов сети) $v_1, v_2, \\ldots, v_n$ и положительные целые длины дуг $d_{ij} = d(v_i, v_j)$\n",
    "между ними. Нужно для всех $k \\in \\{2, \\ldots, n\\}$ найти минимальную длину пути из $v_1$ в $v_k$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для начала посмотрим, как мы сами могли бы реализовать класс \"Неориентированный граф\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class UndirectedGraph:\n",
    "    def __init__(self):\n",
    "        self.nodes = set()\n",
    "        self.edges = {}\n",
    "        self.distances = {}\n",
    "\n",
    "    def add_node(self, value):\n",
    "        self.nodes.add(value)\n",
    "        self.edges[value] = []\n",
    "        \n",
    "    def add_edge(self, from_node, to_node, distance):\n",
    "        self.edges[from_node].append(to_node)\n",
    "        self.edges[to_node].append(from_node)\n",
    "        self.distances[(from_node, to_node)] = distance\n",
    "        self.distances[(to_node, from_node)] = distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Алгоритм Дейкстры основывается на том простом факте, что что если у нас есть кратчайший путь от **v** до **w**, проходящий через вершину **y**, назовем его $(v \\rightarrow w)^{*}$, то его первая часть от **v** до **y**,\n",
    "$(v \\rightarrow y)^{*}$ тоже будет кратчайшим путем."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../img/dijkstra.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Задачи с подобными свойствами, когда оптимальное решение можно легко получить из оптимальных решений подзадач, обычно хорошо решаются так называемыми \"жадными алгоритмами\". Алгоритм Дейкстры - как раз один их примеров. Его сложность при использовании min-кучи - $O(|E| + |V|log|V|)$, где |E|, |V| - число дуг и вершин соответственно"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Описание алгоритма Дейкстры на <a href=\"http://habrahabr.ru/post/111361/\">Хабрахабре</a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def dijsktra(graph, initial):\n",
    "    visited = {initial: 0}\n",
    "    path = {}\n",
    "\n",
    "    nodes = graph.nodes\n",
    "\n",
    "    while nodes: \n",
    "        min_node = None\n",
    "        for node in nodes:\n",
    "            if node in visited:\n",
    "                if min_node is None:\n",
    "                    min_node = node\n",
    "                elif visited[node] < visited[min_node]:\n",
    "                    min_node = node\n",
    "\n",
    "        if min_node is None:\n",
    "            break\n",
    "\n",
    "        nodes.remove(min_node)\n",
    "        current_weight = visited[min_node]\n",
    "\n",
    "        for edge in G.edges[min_node]:\n",
    "            weight = current_weight + graph.distances[(min_node, edge)]\n",
    "            if edge not in visited or weight < visited[edge]:\n",
    "                visited[edge] = weight\n",
    "                path[edge] = min_node\n",
    "\n",
    "    return visited, path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({1: 0, 2: 4, 3: 6, 4: 14, 5: 7, 6: 6, 7: 11},\n",
       " {2: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 3})"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = UndirectedGraph()\n",
    "\n",
    "for node in range(1,8):\n",
    "    G.add_node(node)\n",
    "\n",
    "for edge in [(1,7,15),(1,3,6),(1,5,7),\n",
    "            (1,6,6),(1,2,4),(2,4,10),\n",
    "            (3,5,10),(3,7,5),(3,6,5),\n",
    "            (4,7,3),(4,5,15),(5,6,5)]:\n",
    "    G.add_edge(*edge)\n",
    "    \n",
    "# print(G.edges)\n",
    "# print(G.distances)\n",
    "    \n",
    "dijsktra(G, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['source']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAHfCAYAAACS3lTXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLKYlSZKkiiymJUmSpIospiVJkqSK/h++k6LgwTikmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10793e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%pylab inline\n",
    "figsize(12, 8)\n",
    "\n",
    "import networkx as nx\n",
    "\n",
    "G=nx.Graph()\n",
    "G.add_nodes_from(range(1,8))\n",
    "G.add_weighted_edges_from([(1,7,15),(1,3,6),(1,5,7),\n",
    "                           (1,6,6),(1,2,4),(2,4,10),\n",
    "                           (3,5,10),(3,7,5),(3,6,5),\n",
    "                           (4,7,3),(4,5,15),(5,6,5)])\n",
    "\n",
    "pos = nx.spring_layout(G) # positions for all nodes\n",
    "\n",
    "# nodes and node labels\n",
    "nx.draw_networkx_nodes(G,pos,node_size=700)\n",
    "nx.draw_networkx_labels(G,pos,font_size=20,font_family='sans-serif')\n",
    "\n",
    "# edges\n",
    "edges = [(u,v) for (u,v,d) in G.edges(data=True)]\n",
    "nx.draw_networkx_edges(G, pos, edgelist=edges, font_size=16)\n",
    "\n",
    "# edge labels\n",
    "edge_labels=dict([((u,v,),d['weight'])\n",
    "             for u,v,d in G.edges(data=True)])\n",
    "nx.draw_networkx_edge_labels(G,pos,edge_labels=edge_labels)\n",
    "\n",
    "show() # matplotlib.pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"http://code.activestate.com/recipes/577892-dijkstra-shortest-path-implementation/\">Реализация</a> с помощью кучи "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import heapq\n",
    "\n",
    "def dijkstra(adj, costs, s, t):\n",
    "    ''' Return predecessors and min distance if there exists a shortest path \n",
    "        from s to t; Otherwise, return None '''\n",
    "    Q = []     # priority queue of items; note item is mutable.\n",
    "    d = {s: 0} # vertex -> minimal distance\n",
    "    Qd = {}    # vertex -> [d[v], parent_v, v]\n",
    "    p = {}     # predecessor\n",
    "    visited_set = set([s])\n",
    "\n",
    "    for v in adj.get(s, []):\n",
    "        d[v] = costs[s, v]\n",
    "        item = [d[v], s, v]\n",
    "        heapq.heappush(Q, item)\n",
    "        Qd[v] = item\n",
    "\n",
    "    while Q:\n",
    "#         print(Q)\n",
    "        cost, parent, u = heapq.heappop(Q)\n",
    "        if u not in visited_set:\n",
    "#             print('visit:', u)\n",
    "            p[u]= parent\n",
    "            visited_set.add(u)\n",
    "            if u == t:\n",
    "                return p, d[u]\n",
    "            for v in adj.get(u, []):\n",
    "                if d.get(v):\n",
    "                    if d[v] > costs[u, v] + d[u]:\n",
    "                        d[v] =  costs[u, v] + d[u]\n",
    "                        Qd[v][0] = d[v]    # decrease key\n",
    "                        Qd[v][1] = u       # update predecessor\n",
    "                        heapq._siftdown(Q, 0, Q.index(Qd[v]))\n",
    "                else:\n",
    "                    d[v] = costs[u, v] + d[u]\n",
    "                    item = [d[v], u, v]\n",
    "                    heapq.heappush(Q, item)\n",
    "                    Qd[v] = item\n",
    "\n",
    "    return None\n",
    "\n",
    "def make_undirected(cost):\n",
    "    ucost = {}\n",
    "    for k, w in cost.items():\n",
    "        ucost[k] = w\n",
    "        ucost[(k[1],k[0])] = w\n",
    "    return ucost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimal cost from 1 to 7: 11\n",
      "shortest path from 1 to 7: [1, 3, 7]\n"
     ]
    }
   ],
   "source": [
    "# adjacent list\n",
    "adj = { 1: [2, 3, 5, 7],\n",
    "        2: [1, 4],\n",
    "        3: [1, 5, 6,7],\n",
    "        4: [2, 5, 7],\n",
    "        5: [1, 3, 4, 6],\n",
    "        6: [3, 5],\n",
    "        7: [1, 3, 4]}\n",
    "    \n",
    "# edge costs\n",
    "edges = {(1, 2): 4, (4, 7): 3, (1, 3): 6, (4, 5): 15,\n",
    "        (1, 5): 7, (1, 6): 6, (3, 6): 5, (1, 7): 15, \n",
    "        (5, 6): 5, (3, 7): 5, (2, 4): 10, (3, 5): 10}\n",
    "\n",
    "edge_cost = make_undirected(edges)\n",
    "\n",
    "source, target = 1, 7\n",
    "predecessors, min_cost = dijkstra(adj, edge_cost, source, target)\n",
    "c = target\n",
    "path = [c]\n",
    "print('Minimal cost from {0} to {1}: {2}'.format(source, target, min_cost))\n",
    "while predecessors.get(c):\n",
    "    path.insert(0, predecessors[c])\n",
    "    c = predecessors[c]\n",
    "\n",
    "print('shortest path from {0} to {1}: {2}'.format(source, target, path))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Нахождение кратчайших путей с помощью методов библиотеки Networkx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function single_source_dijkstra in module networkx.algorithms.shortest_paths.weighted:\n",
      "\n",
      "single_source_dijkstra(G, source, target=None, cutoff=None, weight='weight')\n",
      "    Compute shortest paths and lengths in a weighted graph G.\n",
      "    \n",
      "    Uses Dijkstra's algorithm for shortest paths.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    G : NetworkX graph\n",
      "    \n",
      "    source : node label\n",
      "       Starting node for path\n",
      "    \n",
      "    target : node label, optional\n",
      "       Ending node for path\n",
      "    \n",
      "    cutoff : integer or float, optional\n",
      "       Depth to stop the search. Only paths of length <= cutoff are returned.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    distance,path : dictionaries\n",
      "       Returns a tuple of two dictionaries keyed by node.\n",
      "       The first dictionary stores distance from the source.\n",
      "       The second stores the path from the source to that node.\n",
      "    \n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> G=nx.path_graph(5)\n",
      "    >>> length,path=nx.single_source_dijkstra(G,0)\n",
      "    >>> print(length[4])\n",
      "    4\n",
      "    >>> print(length)\n",
      "    {0: 0, 1: 1, 2: 2, 3: 3, 4: 4}\n",
      "    >>> path[4]\n",
      "    [0, 1, 2, 3, 4]\n",
      "    \n",
      "    Notes\n",
      "    ---------\n",
      "    Edge weight attributes must be numerical.\n",
      "    Distances are calculated as sums of weighted edges traversed.\n",
      "    \n",
      "    Based on the Python cookbook recipe (119466) at\n",
      "    http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/119466\n",
      "    \n",
      "    This algorithm is not guaranteed to work if edge weights\n",
      "    are negative or are floating point numbers\n",
      "    (overflows and roundoff errors can cause problems).\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    single_source_dijkstra_path()\n",
      "    single_source_dijkstra_path_length()\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(nx.single_source_dijkstra)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({1: 0, 2: 4, 3: 6, 4: 14, 5: 7, 6: 6, 7: 11},\n",
       " {1: [1],\n",
       "  2: [1, 2],\n",
       "  3: [1, 3],\n",
       "  4: [1, 2, 4],\n",
       "  5: [1, 5],\n",
       "  6: [1, 6],\n",
       "  7: [1, 3, 7]})"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.single_source_dijkstra(G, source=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 4]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.dijkstra_path(G,1,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Реализация алгоритма Беллмана-Форда. Его сложность $O(|V||E|)$ (хуже, чем у алгоритма Дейкстры), зато можно работать с отрицательными весами."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function bellman_ford in module networkx.algorithms.shortest_paths.weighted:\n",
      "\n",
      "bellman_ford(G, source, weight='weight')\n",
      "    Compute shortest path lengths and predecessors on shortest paths\n",
      "    in weighted graphs.\n",
      "    \n",
      "    The algorithm has a running time of O(mn) where n is the number of\n",
      "    nodes and m is the number of edges.  It is slower than Dijkstra but\n",
      "    can handle negative edge weights.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    G : NetworkX graph\n",
      "       The algorithm works for all types of graphs, including directed\n",
      "       graphs and multigraphs.\n",
      "    \n",
      "    source: node label\n",
      "       Starting node for path\n",
      "    \n",
      "    weight: string, optional (default='weight')\n",
      "       Edge data key corresponding to the edge weight\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    pred, dist : dictionaries\n",
      "       Returns two dictionaries keyed by node to predecessor in the\n",
      "       path and to the distance from the source respectively.\n",
      "    \n",
      "    Raises\n",
      "    ------\n",
      "    NetworkXUnbounded\n",
      "       If the (di)graph contains a negative cost (di)cycle, the\n",
      "       algorithm raises an exception to indicate the presence of the\n",
      "       negative cost (di)cycle.  Note: any negative weight edge in an\n",
      "       undirected graph is a negative cost cycle.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> import networkx as nx\n",
      "    >>> G = nx.path_graph(5, create_using = nx.DiGraph())\n",
      "    >>> pred, dist = nx.bellman_ford(G, 0)\n",
      "    >>> sorted(pred.items())\n",
      "    [(0, None), (1, 0), (2, 1), (3, 2), (4, 3)]\n",
      "    >>> sorted(dist.items())\n",
      "    [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)]\n",
      "    \n",
      "    >>> from nose.tools import assert_raises\n",
      "    >>> G = nx.cycle_graph(5, create_using = nx.DiGraph())\n",
      "    >>> G[1][2]['weight'] = -7\n",
      "    >>> assert_raises(nx.NetworkXUnbounded, nx.bellman_ford, G, 0)\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    Edge weight attributes must be numerical.\n",
      "    Distances are calculated as sums of weighted edges traversed.\n",
      "    \n",
      "    The dictionaries returned only have keys for nodes reachable from\n",
      "    the source.\n",
      "    \n",
      "    In the case where the (di)graph is not connected, if a component\n",
      "    not containing the source contains a negative cost (di)cycle, it\n",
      "    will not be detected.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(nx.bellman_ford)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: None, 2: 1, 3: 1, 4: 2, 5: 1, 6: 1, 7: 3}\n",
      "{1: 0, 2: 4, 3: 6, 4: 14, 5: 7, 6: 6, 7: 11}\n"
     ]
    }
   ],
   "source": [
    "pred, dist = nx.bellman_ford(G, 1)\n",
    "print(pred)\n",
    "print(dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача коммивояжера"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Заданы неориентированный граф из n вершин-городов, и $d_{ij} = d(v_i, v_j)$ — положительные целые расстояния между городами.\n",
    "Чему равна наименьшая возможная длина гамильтонова цикла (кольцевого маршрута, проходя-\n",
    "щего по одному разу через все города)?\n",
    "То есть нужно найти $$min \\sum_{i=1}^{n-1}d_{p_i,p_{i+1}} + d_{p_n,p_1},$$ \n",
    "где минимум берется по всем перестановкам p чисел $1, \\ldots, n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import permutations\n",
    "\n",
    "INFINITY = pow(10, 20)\n",
    "\n",
    "def TSP_BruteForce(G, init_node_index):\n",
    "    def get_path_length(path):\n",
    "        path_length = 0\n",
    "        for i, v1 in enumerate(path):\n",
    "            v2 = path[ (i+1) % len(path)]\n",
    "            if not G.has_edge(v1, v2):\n",
    "                return INFINITY\n",
    "            path_length += G[v1][v2][\"weight\"]\n",
    "        return path_length\n",
    "    \n",
    "    def node_permutations(G, init_node_index):\n",
    "        nodes = G.nodes()\n",
    "        init_node = nodes[init_node_index]\n",
    "        nodes.remove(init_node)\n",
    "        return [[init_node] + list(a_tuple) \n",
    "                 for a_tuple in permutations(nodes)]\n",
    "    \n",
    "    min_path = min_path_length = None\n",
    "    # перебор всех перестановок с фиксированным первым узлом\n",
    "    for path in node_permutations(G, init_node_index):\n",
    "        path_length = get_path_length(path)\n",
    "        if not min_path or min_path_length > path_length:\n",
    "            min_path, min_path_length = path, path_length\n",
    "    return min_path, min_path_length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['source', 'dist']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAs0AAAHfCAYAAACrueWMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niDj4fzoR4OVGdWYkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10779b6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%pylab inline\n",
    "figsize(12, 8)\n",
    "\n",
    "import networkx as nx\n",
    "\n",
    "G=nx.Graph()\n",
    "G.add_nodes_from(range(1,8))\n",
    "G.add_weighted_edges_from([(1,7,15),(1,3,6),(1,5,7),\n",
    "                           (1,6,6),(1,2,4),(2,4,10),\n",
    "                           (3,5,10),(3,7,5),(3,6,5),\n",
    "                           (4,7,3),(4,5,15),(5,6,5)])\n",
    "\n",
    "pos = nx.spring_layout(G) # positions for all nodes\n",
    "\n",
    "# nodes and node labels\n",
    "nx.draw_networkx_nodes(G,pos,node_size=700)\n",
    "nx.draw_networkx_labels(G,pos,font_size=20,font_family='sans-serif')\n",
    "\n",
    "# edges\n",
    "edges = [(u,v) for (u,v,d) in G.edges(data=True)]\n",
    "nx.draw_networkx_edges(G, pos, edgelist=edges, font_size=16)\n",
    "\n",
    "# edge labels\n",
    "edge_labels=dict([((u,v,),d['weight'])\n",
    "             for u,v,d in G.edges(data=True)])\n",
    "nx.draw_networkx_edge_labels(G,pos,edge_labels=edge_labels)\n",
    "\n",
    "show() # matplotlib.pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Гамильтонов цикл с минимальной суммой весов ребер"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Оптимальный маршрут: [1, 2, 4, 7, 3, 6, 5]. Его стоимость = 39'"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"Оптимальный маршрут: {0}. Его стоимость = {1}\".format(*TSP_BruteForce(G, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Поиск в глубину\n",
    "Поиск в глубину (англ. Depth-first search, DFS) — один из методов обхода графа. Стратегия поиска в глубину, как и следует из названия, состоит в том, чтобы идти \"вглубь\" графа, насколько это возможно. Алгоритм поиска описывается рекурсивно: перебираем все исходящие из рассматриваемой вершины рёбра. Если ребро ведёт в вершину, которая не была рассмотрена ранее, то запускаем алгоритм от этой нерассмотренной вершины, а после возвращаемся и продолжаем перебирать рёбра. Возврат происходит в том случае, если в рассматриваемой вершине не осталось рёбер, которые ведут в нерассмотренную вершину. Если после завершения алгоритма не все вершины были рассмотрены, то необходимо запустить алгоритм от одной из нерассмотренных вершин."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Рассмотрим на примере следующего неориентированного невзвешенного графа"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAs0AAAHfCAYAAACrueWMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104b90fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%pylab inline\n",
    "figsize(12, 8)\n",
    "\n",
    "import networkx as nx\n",
    "\n",
    "G=nx.Graph()\n",
    "G.add_nodes_from(['A', 'B', 'C', 'D', 'E', 'F'])\n",
    "G.add_edges_from([('A','B'),('A','C'),('B','D'),\n",
    "                    ('B','E'),('C','F'), ('E','F')])\n",
    "\n",
    "pos = nx.spring_layout(G) # positions for all nodes\n",
    "\n",
    "# nodes and node labels\n",
    "nx.draw_networkx_nodes(G, pos, node_size=700)\n",
    "nx.draw_networkx_labels(G,pos,font_size=20,font_family='sans-serif')\n",
    "\n",
    "nx.draw_networkx_edges(G, pos, edgelist=G.edges(), font_size=16)\n",
    "\n",
    "show() # matplotlib.pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dfs(graph, start, visited=None):\n",
    "    if visited is None:\n",
    "        visited = set()\n",
    "    visited.add(start)\n",
    "    # adjacent to start - graph.adj[start].keys()\n",
    "    for next in set(graph.adj[start].keys()) - visited:\n",
    "        dfs(graph, next, visited)\n",
    "    return visited"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'B', 'C', 'D', 'E', 'F'}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfs(G, 'C')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dfs_paths(graph, start, goal, path=None):\n",
    "    if path is None:\n",
    "        path = [start]\n",
    "    if start == goal:\n",
    "        yield path\n",
    "    for next in set(graph.adj[start].keys()) - set(path):\n",
    "        yield from dfs_paths(graph, next, goal, path + [next])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['C', 'F'], ['C', 'A', 'B', 'E', 'F']]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(dfs_paths(G, 'C', 'F'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Поиск в ширину\n",
    "Поиск в ширину (англ. breadth-first search, BFS) — метод обхода графа и поиска пути в графе.\n",
    "Поиск в ширину работает путём последовательного просмотра отдельных уровней графа, начиная с узла-источника $u$.\n",
    "\n",
    "Рассмотрим все рёбра $(u,v)$, выходящие из узла $u$. Если очередной узел $v$ является целевым узлом, то поиск завершается; в противном случае узел $v$ добавляется в очередь. После того, как будут проверены все рёбра, выходящие из узла $u$, из очереди извлекается следующий узел $u$, и процесс повторяется."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bfs_paths(graph, start, goal):\n",
    "    queue = [(start, [start])]\n",
    "    while queue:\n",
    "        (vertex, path) = queue.pop(0)\n",
    "        for next in set(graph.adj[vertex].keys()) - set(path):\n",
    "            if next == goal:\n",
    "                yield path + [next]\n",
    "            else:\n",
    "                queue.append((next, path + [next]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['A', 'C', 'F'], ['A', 'B', 'E', 'F']]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(bfs_paths(G, 'A', 'F'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ссылки\n",
    "- Описание алгоритмов <a href=\"https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%94%D0%B5%D0%B9%D0%BA%D1%81%D1%82%D1%80%D1%8B\">Дейкстры</a>, <a href=\"https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%A4%D0%BB%D0%BE%D0%B9%D0%B4%D0%B0_%E2%80%94_%D0%A3%D0%BE%D1%80%D1%88%D0%B5%D0%BB%D0%BB%D0%B0\">Флойда-Уоршелла</a> и <a href=\"https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%91%D0%B5%D0%BB%D0%BB%D0%BC%D0%B0%D0%BD%D0%B0_%E2%80%94_%D0%A4%D0%BE%D1%80%D0%B4%D0%B0\">Беллмана-Форда</a> на Википедии\n",
    "- <a href=\"https://class.coursera.org/algo-003/lecture/57\">Видео</a> с описанием алгоритма Дейкстры на Coursera\n",
    "- Алгоритм Прима - <a href=\"http://neerc.ifmo.ru/wiki/index.php?title=%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%9F%D1%80%D0%B8%D0%BC%D0%B0\">конспект</a> Университета ИТМО\n",
    "- <a href=\"https://yadi.sk/i/cT6ikxLqjVy2r\">Книга</a> \"Эффективные алгоритмы и сложность вычислений\" с примерами на языке Python (Фомин, Кузюрин, 2011)\n",
    "- Про <a href=\"https://ru.wikibooks.org/wiki/%D0%A0%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D0%B8_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC%D0%BE%D0%B2/%D0%9F%D0%BE%D0%B8%D1%81%D0%BA_%D0%B2_%D0%B3%D0%BB%D1%83%D0%B1%D0%B8%D0%BD%D1%83\">поиск в глубину</a> и <a href=\"https://ru.wikibooks.org/wiki/%D0%A0%D0%B5%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D0%B8_%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC%D0%BE%D0%B2/%D0%9F%D0%BE%D0%B8%D1%81%D0%BA_%D0%B2_%D1%88%D0%B8%D1%80%D0%B8%D0%BD%D1%83\">поиск в ширину</a> на Wikibooks\n",
    "- Поиск в глубину на <a href=\"http://habrahabr.ru/post/200074/\">Хабрахабре</a> на примере лабиринта \n",
    "- Поиск в ширину на <a href=\"http://habrahabr.ru/post/200252/\">Хабрахабре</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}