bfs_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Breadth First Search in Python\n",
    "\n",
    "A quick example using NetworkX to implement a basic graph algorithm.\n",
    "\n",
    "Allen B. Downey\n",
    "\n",
    "[MIT License](https://opensource.org/licenses/MIT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# this line makes the code compatible with Python 2 and 3\n",
    "from __future__ import print_function, division\n",
    "\n",
    "# this line makes Jupyter show figures in the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "\n",
    "def bfs(G, start):\n",
    "    \"\"\"A simple version of BFS that just computes distances.\n",
    "    \n",
    "    G: Graph\n",
    "    start: int start node\n",
    "    \n",
    "    returns: map from node to distance\n",
    "    \"\"\"\n",
    "    dist = {start: 0}\n",
    "    queue = deque([start])\n",
    "    while queue:\n",
    "        node = queue.popleft()         \n",
    "        for child in G.neighbors(node):\n",
    "            if child not in dist:                    \n",
    "                dist[child] = dist[node] + 1\n",
    "                queue.append(child)\n",
    "    return dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from networkx import DiGraph\n",
    "\n",
    "def bfs(G, start):\n",
    "    \"\"\"A simple version of BFS that computes distances and\n",
    "        paths back to start.\n",
    "    \n",
    "    G: Graph\n",
    "    start: int start node\n",
    "    \n",
    "    returns: (map from node to distance,\n",
    "        DiGraph containing paths from each node back to start)\n",
    "    \"\"\"\n",
    "    dist = {start: 0}\n",
    "    tree = DiGraph()\n",
    "    queue = deque([start])\n",
    "    while queue:\n",
    "        node = queue.popleft()         \n",
    "        for child in G.neighbors(node):\n",
    "            if child not in dist:                    \n",
    "                dist[child] = dist[node] + 1\n",
    "                tree.add_edge(child, node) \n",
    "                queue.append(child)\n",
    "    return dist, tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy.random import random\n",
    "\n",
    "def flip(p):\n",
    "    return random() < p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def random_pairs(nodes, p):\n",
    "    \"\"\"Generate random pairs of nodes.\"\"\"\n",
    "    for i, u in enumerate(nodes):\n",
    "        for j, v in enumerate(nodes):\n",
    "            if i<j and flip(p):\n",
    "                yield u, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "\n",
    "def make_random_graph(n, p):\n",
    "    \"\"\"Generate a random graph.\n",
    "    \n",
    "    n: number of nodes\n",
    "    p: probability of an edge between any pair of nodes\n",
    "    \n",
    "    returns: Graph\n",
    "    \"\"\"\n",
    "    G = nx.Graph()\n",
    "    nodes = range(n)\n",
    "    G.add_nodes_from(nodes)\n",
    "    G.add_edges_from(random_pairs(nodes, p))\n",
    "    return G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_graph = make_random_graph(10, 0.3)\n",
    "len(random_graph.edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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o5hjgiAgAUFRUhLNnzyquXYuLi4ONjY1KWPPx8an2vm8bNmzAwYMHsW/fPhEq/2dVQe7k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\nERHJDAMcERERkcwwwBERERHJzP8DtfR3yU8ZndMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7909ece90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "COLORS = sns.color_palette()\n",
    "\n",
    "nx.draw_circular(random_graph, \n",
    "                 node_color=COLORS[2], \n",
    "                 node_size=1000, \n",
    "                 with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0, 1: 3, 2: 3, 3: 1, 4: 3, 5: 2, 6: 2, 7: 1, 8: 2, 9: 1}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist, tree = bfs(random_graph, 0)\n",
    "dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9ysHN2dkZQUFBT4TMqigHuS+//BKffPIJgxxVC+c10gcGOBLNsd17cHnPXjhmZqGxtc2z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\ndgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff78dcc1a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_circular(tree, \n",
    "                 node_color=COLORS[2], \n",
    "                 node_size=1000, \n",
    "                 with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fft(ys):\n",
    "    N = len(ys)\n",
    "    if N == 1:\n",
    "        return ys\n",
    "    \n",
    "    He = fft(ys[::2])\n",
    "    Ho = fft(ys[1::2])\n",
    "    \n",
    "    ns = np.arange(N)\n",
    "    W = np.exp(-1j * PI2 * ns / N)\n",
    "    \n",
    "    return np.tile(He, 2) + W * np.tile(Ho, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}