{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#The-Push-relabel-Algorithm\" data-toc-modified-id=\"The-Push-relabel-Algorithm-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>The Push-relabel Algorithm</a></div><div class=\"lev2 toc-item\"><a href=\"#Initialization\" data-toc-modified-id=\"Initialization-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Initialization</a></div><div class=\"lev2 toc-item\"><a href=\"#Push\" data-toc-modified-id=\"Push-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Push</a></div><div class=\"lev2 toc-item\"><a href=\"#Main-Loop\" data-toc-modified-id=\"Main-Loop-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Main Loop</a></div><div class=\"lev1 toc-item\"><a href=\"#Questions\" data-toc-modified-id=\"Questions-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Questions</a></div><div class=\"lev1 toc-item\"><a href=\"#Summary\" data-toc-modified-id=\"Summary-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Summary</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Push-relabel Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Push-relabel algorithmを実装してみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 前回作った\n",
    "def makeResidualGraph(G):\n",
    "    '''\n",
    "    Input: a graph G\n",
    "    Output: its residual graph Gf\n",
    "    '''\n",
    "    Gf = G.copy()\n",
    "    edgeList = G.edges()\n",
    "    \n",
    "    for edge in edgeList:\n",
    "        # Initialize flow\n",
    "        Gf[edge[0]][edge[1]]['flow'] = 0\n",
    "        \n",
    "        # 逆向きのedgeがないものは追加\n",
    "        if not (edge[1], edge[0]) in edgeList:\n",
    "            Gf.add_edge(edge[1],edge[0])\n",
    "            Gf[edge[1]][edge[0]]['capacity'] = Gf[edge[0]][edge[1]]['flow']\n",
    "            Gf[edge[1]][edge[0]]['flow'] = 0\n",
    "    \n",
    "    return Gf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Initialize(G, s, t):\n",
    "    '''\n",
    "    Inputs:\n",
    "        G: a residual graph\n",
    "            V: vertices\n",
    "                height\n",
    "                excess\n",
    "            E: edges\n",
    "                flow(preflow)\n",
    "                capacity\n",
    "                    NB: flow <= capacity\n",
    "        s: a start point\n",
    "        t: an end point\n",
    "    Output:\n",
    "        None\n",
    "    \n",
    "    Initialize the height and excess of each vertex.\n",
    "    '''\n",
    "    for v in G.nodes():\n",
    "        G.node[v]['excess'] = 0\n",
    "\n",
    "    for v in G.nodes():\n",
    "        # 始点以外の点について\n",
    "        if v != s:\n",
    "            G.node[v]['height'] = 0\n",
    "            # G.node[v]['excess'] = 0\n",
    "            for p in G.neighbors(v):\n",
    "                G[v][p]['flow'] = 0\n",
    "        # 始点について\n",
    "        else:\n",
    "            # 始点の高さをnに\n",
    "            G.node[v]['height'] = G.number_of_nodes() # n\n",
    "            # 始点から出る枝のpreflowをcapacityギリギリに\n",
    "            # このとき、始点に隣接する点のexcessを更新\n",
    "            for p in G.neighbors(v):\n",
    "                G[v][p]['flow'] = G[v][p]['capacity']\n",
    "                # backward edgeのcapacityの更新\n",
    "                G[p][v]['capacity'] = G[v][p]['flow']\n",
    "                G.node[p]['excess'] = G[v][p]['flow']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
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5UJlkRGGggDt16hSjR49m8uTJVK9enYkTJ2ppYcm+X3+FLHqNp/Hzz1C1as7V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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10296e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 例のグラフを作成\n",
    "\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "\n",
    "# Lecture1の例のグラフGを生成\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from([('s','v',{'capacity': 3}),('s','w',{'capacity': 2}),('v','w',{'capacity': 5}),('v','t',{'capacity': 2}),('w','t',{'capacity': 3})])\n",
    "for e in G.edges():\n",
    "    G[e[0]][e[1]]['flow'] = 0\n",
    "\n",
    "# 描画\n",
    "\n",
    "pos={'s':(0,2),'v':(3,4),'w':(3,0),'t':(6,2)}\n",
    "edge_labels = {(i, j): (w['capacity'], str((w['flow'])) ) for i, j, w in G.edges(data=True)}\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_color='r')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw(G, pos)\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initializeがきちんと動くか確認してみる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Gf = makeResidualGraph(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Initialize(Gf, 's', 't')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gf.node['s']['height']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gf.node['v']['height']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gf.node['t']['height']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['s', 't', 'v', 'w']"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gf.nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gf['w']['s']['capacity']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the excess of the node w: 2\n",
      "the excess of the node t: 0\n",
      "the excess of the node v: 3\n"
     ]
    }
   ],
   "source": [
    "nodelist = Gf.nodes()\n",
    "nodelist.remove('s')\n",
    "for p in nodelist:\n",
    "    print( 'the excess of the node ' + p +': ' + str(Gf.node[p]['excess']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上手く動いているみたいだ。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Push"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "code_folding": [
     1
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def Push(G, v, w, forwardEdges):\n",
    "    '''\n",
    "    G: a graph(a residual graph)\n",
    "    v, w: vertices of G such that h(v) = h(w) + 1\n",
    "    forwardEdges: a list of the edges of the original graph\n",
    "    \n",
    "    augment the flow of (v,w)\n",
    "    '''\n",
    "\n",
    "    # 更新量diffを計算\n",
    "    residualCapacity = G[v][w]['capacity'] - G[v][w]['flow']\n",
    "    diff = np.min([G.node[v]['excess'], residualCapacity])\n",
    "\n",
    "    # (v,w), (w,v)を更新, p.3を参考に\n",
    "    if (v,w) in forwardEdges:\n",
    "        G[v][w]['flow'] += diff\n",
    "        G[w][v]['capacity'] += diff\n",
    "        G.node[v]['excess'] -= diff\n",
    "        G.node[w]['excess'] += diff\n",
    "    else:\n",
    "        G[w][v]['flow'] -= diff\n",
    "        G[v][w]['capacity'] -= diff\n",
    "        G.node[w]['excess'] += diff\n",
    "        G.node[v]['excess'] -= diff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Main Loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def loopCondition(G, s, t):\n",
    "    # ここではO(n)の時間をかけてcheckしているが、データ構造を工夫するとO(1)の時間でcheckすることが可能らしい\n",
    "    nodelist = G.nodes()\n",
    "    nodelist.remove(s)\n",
    "    nodelist.remove(t)\n",
    "\n",
    "    for v in nodelist:\n",
    "        if(G.node[v]['excess'] > 0):\n",
    "            return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def PushRelabel(G, s, t):\n",
    "    '''\n",
    "    Inputs:\n",
    "        G: a graph\n",
    "        s: a starting point\n",
    "        t: an end point\n",
    "    Output:\n",
    "        the graph G with its maximum flow\n",
    "    '''\n",
    "\n",
    "    # Forward Edges を記録\n",
    "    forwardEdges = G.edges()\n",
    "\n",
    "    # s,tを除いたnodeのlistを作る\n",
    "    nodeList = G.nodes()\n",
    "    nodeList.remove(s)\n",
    "    nodeList.remove(t)\n",
    "\n",
    "    # residual graph の作成\n",
    "    Gf = makeResidualGraph(G)\n",
    "\n",
    "    # Initialization\n",
    "    Initialize(Gf, s, t)\n",
    "\n",
    "    # Main Loop\n",
    "    while(loopCondition(Gf, s, t)):\n",
    "        # 高さが最も高く、かつexcess > 0の点vを探す\n",
    "        height = -100 # 適当に負の値を設定\n",
    "        for p in nodeList:\n",
    "            if(Gf.node[p]['excess'] > 0 and Gf.node[p]['height'] > height):\n",
    "                v = p\n",
    "                height = Gf.node[p]['height']\n",
    "\n",
    "        # h(v) = h(w) + 1 を満たす点wを探す\n",
    "        # vのneighborsの中から探す(そうじゃないとkey eroorに)\n",
    "        w = None\n",
    "        for p in Gf.neighbors(v):\n",
    "            if(Gf.node[v]['height'] == Gf.node[p]['height'] + 1 and (Gf[v][p]['capacity'] - Gf[v][p]['flow']) > 0):\n",
    "                w = p\n",
    "                break\n",
    "\n",
    "        # そのような点wがない場合、increment h(v)\n",
    "        if w == None:\n",
    "            Gf.node[v]['height'] += 1\n",
    "\n",
    "        # ある場合\n",
    "        else:\n",
    "            Push(Gf, v, w, forwardEdges)\n",
    "\n",
    "    # もともと無かったedgeを消去\n",
    "    for edge in Gf.edges():\n",
    "        if not edge in forwardEdges:\n",
    "            Gf.remove_edge(edge[0],edge[1])\n",
    "    \n",
    "    return Gf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*PushRelabel* が動くかどうか試してみる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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5UJlkRGGggDt16hSjR49m8uTJVK9enYkTJ2ppYcm+X3+FLHqNp/Hzz1C1as7V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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104723e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# もろもろをインポート\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "\n",
    "# Lecture1の例のグラフGを生成\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from([('s','v',{'capacity': 3}),('s','w',{'capacity': 2}),('v','w',{'capacity': 5}),('v','t',{'capacity': 2}),('w','t',{'capacity': 3})])\n",
    "for e in G.edges():\n",
    "    G[e[0]][e[1]]['flow'] = 0\n",
    "\n",
    "# 描画\n",
    "\n",
    "pos={'s':(0,2),'v':(3,4),'w':(3,0),'t':(6,2)}\n",
    "edge_labels = {(i, j): (w['capacity'], str((w['flow'])) ) for i, j, w in G.edges(data=True)}\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_color='r')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw(G, pos)\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "H = PushRelabel(G, 's', 't')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "code_folding": [],
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RGCjizpw5w9ixY5k2bRo1a9Zk6tSpWlpY8u7nnyGXXuNX+fFHqFEj/+qRQmXN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef963c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 描画(flowがどう変わったか)\n",
    "# heightも表示したいけどやり方がわからず\n",
    "\n",
    "pos={'s':(0,2),'v':(3,4),'w':(3,0),'t':(6,2)}\n",
    "edge_labels = {(i, j): (w['capacity'], str((w['flow'])) ) for i, j, w in H.edges(data=True)}\n",
    "nx.draw_networkx_edge_labels(H, pos, edge_labels=edge_labels, font_color='r')\n",
    "nx.draw_networkx_labels(H, pos)\n",
    "nx.draw(H, pos)\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上手く動いていそう"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "もとのグラフに長さ２のループがあった場合、residual graphはmultiple edgeを持つはず。\n",
    "\n",
    "しかし、[networkXの有向グラフ](https://networkx.readthedocs.io/en/stable/reference/classes.digraph.html)はmultiple edgeをサポートしていない。この場合、テキストにあるようなmultiple edgesを持つようなresidual graphは作れない（residual graphを作るときに*flow, capacity*の変数名を変えればいいかもしれないが、とてもめんどくさそう。）\n",
    "\n",
    "長さ２のループがある場合、いまのような*makeResidual*でも、maximum flow関連のアルゴリズムはキチンと動くのか？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最後に、今回作った関数をまとめておく。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "code_folding": [
     4,
     24,
     64,
     92,
     102
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# ch03で作成したものたち\n",
    "# makeResidualは前回作ったものだが、PushRelabelに必要\n",
    "import numpy as np\n",
    "\n",
    "def makeResidualGraph(G):\n",
    "    '''\n",
    "    Input: a graph G\n",
    "    Output: its residual graph Gf\n",
    "    '''\n",
    "    Gf = G.copy()\n",
    "    edgeList = G.edges()\n",
    "    \n",
    "    for edge in edgeList:\n",
    "        # Initialize flow\n",
    "        Gf[edge[0]][edge[1]]['flow'] = 0\n",
    "        \n",
    "        # 逆向きのedgeがないものは追加\n",
    "        if not (edge[1], edge[0]) in edgeList:\n",
    "            Gf.add_edge(edge[1],edge[0])\n",
    "            Gf[edge[1]][edge[0]]['capacity'] = Gf[edge[0]][edge[1]]['flow']\n",
    "            Gf[edge[1]][edge[0]]['flow'] = 0\n",
    "    \n",
    "    return Gf\n",
    "\n",
    "def Initialize(G, s, t):\n",
    "    '''\n",
    "    Inputs:\n",
    "        G: a residual graph\n",
    "            V: verteces\n",
    "                height\n",
    "                excess\n",
    "            E: edges\n",
    "                flow(preflow)\n",
    "                capacity\n",
    "                    NB: flow <= capacity\n",
    "        s: a start point\n",
    "        t: an end point\n",
    "    Output:\n",
    "        None\n",
    "    \n",
    "    Initialize the height and excess of each vertex.\n",
    "    '''\n",
    "    for v in G.nodes():\n",
    "        G.node[v]['excess'] = 0\n",
    "\n",
    "    for v in G.nodes():\n",
    "        # 始点以外の点について\n",
    "        if v != s:\n",
    "            G.node[v]['height'] = 0\n",
    "            # G.node[v]['excess'] = 0\n",
    "            for p in G.neighbors(v):\n",
    "                G[v][p]['flow'] = 0\n",
    "        # 始点について\n",
    "        else:\n",
    "            # 始点の高さをnに\n",
    "            G.node[v]['height'] = G.number_of_nodes() # n\n",
    "            # 始点から出る枝のpreflowをcapacityギリギリに\n",
    "            # このとき、始点に隣接する点のexcessを更新\n",
    "            for p in G.neighbors(v):\n",
    "                G[v][p]['flow'] = G[v][p]['capacity']\n",
    "                # backward edgeのcapacityの更新\n",
    "                G[p][v]['capacity'] = G[v][p]['flow']\n",
    "                G.node[p]['excess'] = G[v][p]['flow']\n",
    "\n",
    "def Push(G, v, w, forwardEdges):\n",
    "    '''\n",
    "    G: a graph(a residual graph)\n",
    "    v, w: vertices of G such that h(v) = h(w) + 1\n",
    "    forwardEdges: a list of the edges of the original graph\n",
    "    \n",
    "    augment the flow of (v,w)\n",
    "    '''\n",
    "\n",
    "    # 更新量diffを計算\n",
    "    residualCapacity = G[v][w]['capacity'] - G[v][w]['flow']\n",
    "    diff = np.min([G.node[v]['excess'], residualCapacity])\n",
    "\n",
    "    # (v,w), (w,v)を更新, p.3を参考に\n",
    "    if (v,w) in forwardEdges:\n",
    "        G[v][w]['flow'] += diff\n",
    "        G[w][v]['capacity'] += diff\n",
    "        G.node[v]['excess'] -= diff\n",
    "        G.node[w]['excess'] += diff\n",
    "    else:\n",
    "        G[w][v]['flow'] -= diff\n",
    "        G[v][w]['capacity'] -= diff\n",
    "        G.node[w]['excess'] += diff\n",
    "        G.node[v]['excess'] -= diff\n",
    "        \n",
    "\n",
    "        \n",
    "\n",
    "def loopCondition(G, s, t):\n",
    "    nodelist = G.nodes()\n",
    "    nodelist.remove(s)\n",
    "    nodelist.remove(t)\n",
    "\n",
    "    for v in nodelist:\n",
    "        if(G.node[v]['excess'] > 0):\n",
    "            return True\n",
    "    return False\n",
    "\n",
    "def PushRelabel(G, s, t):\n",
    "    '''\n",
    "    Inputs:\n",
    "        G: a graph\n",
    "        s: a starting point\n",
    "        t: an end point\n",
    "    Output:\n",
    "        the graph G with its maximum flow\n",
    "    '''\n",
    "\n",
    "    # Forward Edges を記録\n",
    "    forwardEdges = G.edges()\n",
    "\n",
    "    # s,tを除いたnodeのlistを作る\n",
    "    nodeList = G.nodes()\n",
    "    nodeList.remove(s)\n",
    "    nodeList.remove(t)\n",
    "\n",
    "    # residual graph の作成\n",
    "    Gf = makeResidualGraph(G)\n",
    "\n",
    "    # Initialization\n",
    "    Initialize(Gf, s, t)\n",
    "\n",
    "    # Main Loop\n",
    "    while(loopCondition(Gf, s, t)):\n",
    "        # 高さが最も高く、かつexcess > 0の点vを探す\n",
    "        height = -100 # 適当に負の値を設定\n",
    "        for p in nodeList:\n",
    "            if(Gf.node[p]['excess'] > 0 and Gf.node[p]['height'] > height):\n",
    "                v = p\n",
    "                height = Gf.node[p]['height']\n",
    "\n",
    "        # h(v) = h(w) + 1 を満たす点wを探す\n",
    "        # vのneighborsの中から探す(そうじゃないとkey eroorに)\n",
    "        w = None\n",
    "        for p in Gf.neighbors(v):\n",
    "            if(Gf.node[v]['height'] == Gf.node[p]['height'] + 1 and (Gf[v][p]['capacity'] - Gf[v][p]['flow']) > 0):\n",
    "                w = p\n",
    "                break\n",
    "\n",
    "        # そのような点wがない場合、increment h(v)\n",
    "        if w == None:\n",
    "            Gf.node[v]['height'] += 1\n",
    "\n",
    "        # ある場合\n",
    "        else:\n",
    "            Push(Gf, v, w, forwardEdges)\n",
    "\n",
    "    # もともと無かったedgeを消去\n",
    "    for edge in Gf.edges():\n",
    "        if not edge in forwardEdges:\n",
    "            Gf.remove_edge(edge[0],edge[1])\n",
    "    \n",
    "    return Gf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "例のグラフを作るのと、描画するのも便利なので、再掲しておく。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "code_folding": [
     0
    ],
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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5UJlkRGGggDt16hSjR49m8uTJVK9enYkTJ2ppYcm+X3+FLHqNp/Hzz1C1as7V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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1100aafd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 例のグラフを作成\n",
    "\n",
    "# もろもろをインポート\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "\n",
    "# Lecture1の例のグラフGを生成\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from([('s','v',{'capacity': 3}),('s','w',{'capacity': 2}),('v','w',{'capacity': 5}),('v','t',{'capacity': 2}),('w','t',{'capacity': 3})])\n",
    "for e in G.edges():\n",
    "    G[e[0]][e[1]]['flow'] = 0\n",
    "\n",
    "# 描画\n",
    "\n",
    "pos={'s':(0,2),'v':(3,4),'w':(3,0),'t':(6,2)}\n",
    "edge_labels = {(i, j): (w['capacity'], str((w['flow'])) ) for i, j, w in G.edges(data=True)}\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_color='r')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw(G, pos)\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5UJlkRGGggDt16hSjR49m8uTJVK9enYkTJ2ppYcm+X3+FLHqNp/Hzz1C1as7V\nI/nKihUrGDhwILGxsVke27FjRyIiIrjzzjtzoTK5msJAAeVyuZgzZw6vvfYaZ86cYdSoUQwePFhL\nC4tIrrpw4QKTJk1i9OjRJCYmZnps0aJFGTFiBEOHDs3yVoN4lsJAAbRt2zZefvllNmzYQJcuXRg/\nfryWFpabs3w5JCdDaKi3K5F86vDhw7z22mvMdfc7yYS/vz8ffvghoaGh6s+US9SBsAA5fvw4/fr1\no2HDhpw5c4bVq1czb948BQG5ea+/fm1fgPBw8PFJ+yWSgdtuu405c+bw3XffUadOnUyPPXDgAB06\ndCA0NJR9+/blUoX2ppaBXJaYmEh8fDxJSUkUKVKEgIAASpQocVPnvHjxItOmTeONN94gJSWFMWPG\n8NJLL2lpYfGc0qVh/XoICUndtmGD6VT40Udw6hQ89xxcsXCNSEZSUlKYOnUqI0eO5OTJk5keW7hw\nYV599VXeeOMNihcvft3PlRPX3ALJkhy3Z88ea8CAAVbNGjUsh8NhAZe/HA6HVbNGDWvAgAHWnj17\nrvvc33//vVW/fn0LsHr06GEdOXIkB34Dsb2SJS0rPj7tth07LKt8efP9779blsOR+3VJvvb7779b\nvXr1uua6mN5XlSpVrH/961+Wy+XK8rw5ec0tqBQGctCBAwesRx56yAKsik6n1Q+sGWBtBGvnpX9n\ngNXv0n7AeuShh6wDBw5kee7ffvvN6t69uwVYDRo0sDZs2JALv5HYVv36lvXxx2m3jRtnWffea74/\nelRhQG7Ypk2brHvvvTfLQABYDz74oLVr1650z5OT19yCTmEgh0ybNs0q7udn3el0WnPBSgLLyuQr\nCay5YFV1Oq3ifn7WtGnT0j3vhQsXrPfff98qWbKkVa5cOeuTTz6xUlJScvm3E9uZNs2yihe3rLAw\ny1qyxLLeesuy/Pwsa8YMs//oUcvy8fFqiZK/Xbx40ZoxY4ZVoUKFLAOBr6+vNWjQIOvkyZOXH59T\n11y7UBjIAWFhYRZgvQjW6SxekFd/nb70OMAKCwtLc96VK1datWrVsnx8fKz+/ftbx48f99JvKLY0\nerRllStn3vSrVrWsyZNT9yUlWdb8+d6rTQqMP//80xo4cKDl6+ubZSioWLGi9c9//tMaM2ZMjlxz\n7URhwMOmTZtmAdaY63xBXv31zqUX5/Tp062DBw9aTz31lAVYzZo1s7Zv3+7tX1Ps7MIFb1cgNrBz\n507rgQekXiAkAAAgAElEQVQeyNatA09fc+1Iowk8KCEhgdq1avH0+fNMu8lzWUAvYI7TicPp5JZb\nbmH8+PF07dpV425FxBYsy2L+/Pm8+uqrHD58ON1jfIAewPQMzrEBWAEMBjJbmN0CegPz/PzYFR1N\n9erVb7zwfEhhwIPatW1LzOrV7EpJoaQHzncaCAb87ryT7Tt3UqpUZi9lkRzw8cfQrh3Y7MIoeUti\nYiLh4eHXLGzkA9wKxECG19wI4DUgAchqouzTQG2nk1otW7JsxYqbLzwf0SwhHhIdHc03337LPzwU\nBMCk2PHAgYMH+fXXXz10VpHrEBMDNWtqQiHxqhIlSjB27Fh2797NI488cnm7CxhHxkEAzCf+7CoF\njE1J4ZtvvyUmJubGis2n9BfuIVFRUVR0OumUxXGJwCCgOuAHVALaAjsyOL4jUNHpZMqUKR6rVSTb\nJk+G6GiYOdPblYgQGBjI0qVLWbRoEaVKlaIsZHrNHY1pFQCohnnD8wV+zuQxdr3maoo6D/l26VI6\npqRQOIvj+gBfAgMwtwCOA+swzVz10jm+CNAxJYWVy5Z5slyR7KtRw3yJ5AEOh4MOHTpwa/nytDp9\nOtNrbkcgDvgXMBEod2l7hUweY9drrvoMeMCZM2coXbo0n1oWPbI4tgzQDZh0HeefAbzocHD69GlN\noykitnc919zr6TPgZsdrrm4TeMD+/fuxLIta2Tj2FuAH4LfrOH8IpldtfHz8DdUnIlKQXM8190bY\n8ZqrMOABSUlJABTLxrHjgN3AHUBjzD2thCweU/Sq5xERsbPruebeCDtecxUGPKBIkSIA/JWNY58C\nDgCRwO3ABEwKXZ7JY85d9TwiInZ2PdfcG2HHa67CgAcEBATgcDiIzubxlYC+mI6ECZhOLeGZHL8H\n02kmICDg5goVESkArueaeyNTtNnxmqvRBB5QokQJgvz92bx/f6adWVyYoYVXTh1UHrgNyKwxagtQ\ns0YN23RkkXxk9Oi0P7/1lnfqEFspUaIEAXfeyeaffsqyA2HxS/+eJPsdCO14zVXLgIc81L49C51O\nLmRyzBnMrYEewIeY6TP/jnnhPZPBY5KAhU4nbdq182S5Ip5x8GDaL5EclpKSQmRkJAcPH2Y+ZHrN\nBWiAmXhoBDAHmE/qbYD02PWaq6GFHhIdHU1ISAhzyfiNPRkYhZkn+wCmpSAAc8ugdwaP+Rzoeun8\nwcHBni1aRCQfWbt2LS+//DI7d+68vC2za67bP4AozCguF5kPM7TrNVdhwINyam0CKlXihy1bqFKl\nigfOKnKTkpPhjz/M9+XLQ6FC3q1HCrzDhw8zbNgwPv/88zTbs7M2wfXQ2gTiER9PncofTidDPHAu\nCxgCnChUiAsXLxIUFMS7775rq6Euksd88QU0aQLFisHtt5uvYsXMtvnzvV2dFEAXLlxg/PjxBAUF\nXRMEwHzK/w2zIuHNsoBXgeNOJx9PneqBM+YvCgMeVL16dT6cPJnpQNhNnMe69PhPgcgpU4iPj6dv\n376MHDmS2rVrs8xm02RKHvDxx/D889C4MSxcCBs2mK+FC822556Djz7ydpVSgKxYsYI6derw2muv\nkZiYmOFxLsy10hPX3OnAxMhI2y1fDIAlHhcWFmYB1otgnQbLuo6vU5ceB1jh4eFpzrt7926rVatW\nFmB16NDB2r9/v5d+Q7GdO++0rFmzMt4/a5ZlVauWa+VIwZWQkGA98cQTFpeug5l9BQcHWytXrsyx\na66dKAzkkGnTplnF/fysqk6nNRespCxekOfBmgtWVafTKu7nZ02fPj3d87pcLmvBggXWHXfcYRUp\nUsQaNWqUdfbs2Vz+7cR2/PwsKyYm4/0xMeYYkRv0119/WW+//bbl5+eXZQgoWbKkFRERYV24cOHy\n43PqmmsXCgM56MCBA9YjDz1kAVZFp9PqB9anYG0E68dL/34KVr9L+wHrkYcesg4cOJDluRMTE603\n3njDKly4sFW1alVr4cKFlsvlyoXfSmypSRPL6t3bstJ7jblcZl/jxrlfl+R7LpfL+uqrr6xq1apl\nqzWge/fu1uHDh9M9V05ecws6jSbIBdHR0URFRbFy2TL2Xlpgw83hcFCzRg3atGtHv379rnsoS3x8\nPIMHD+brr7+mTZs2TJo0yVbDYSSXbNkCDz9sOgy2bg2VKpntR4/CypXw11+wfDk0auTdOiVfiY2N\n5ZVXXmH58swmZDfq1atHZGQkzZo1y/LYnLzmFlQKA7ksMTGR+Ph4kpKSKFKkCAEBAR6Z5errr79m\n0KBBHDx4kEGDBjFq1ChKlSqV9QNFsuvYMZg5E9avhyNHzLbKlaFpU+jZ0wwzFMmGxMREwsLCeP/9\n90lOTs702DJlyhAeHk7v3r3x9fW9oefKiWtuQaMwUICcP3+e999/n7CwMEqXLs348ePp2rUrDseN\nzM4tIuJZlmXxr3/9i6FDh3L48OFMj3U4HPTu3ZuwsDDKK2jmOIWBAujnn39m6NChLFiwgPvvv5/J\nkydTr149b5clIja2c+dOBgwYwHfffZflsU2aNCEyMpIGDRrkQmUCmmegQKpatSpffPEFq1at4sSJ\nEzRo0ID+/ftz4sQJb5cmBU2rVtCyZeqXyFVOnjzJwIEDqV+/fpZBoGLFisycOZPvv/9eQSCXqWWg\ngEtOTiYyMpK33nqLwoULM3bsWHr27HlD995ErvHZZ2l/7t7dO3VInuNyuZg5cybDhw/n2LFjmR7r\n6+vLwIEDeeuttyhdunQuVShXUhiwiSNHjjB8+HBmzZpFgwYNiIyMpEmTJt4uS0QKoM2bN/Pyyy+z\nadOmLI9t2bIlkydPJiQkJBcqk4zoNoFNVK5c+XLzm8vlomnTpvTs2ZOjR496uzTJy7Lo6X3Tx0uB\ncuzYMXr16kXjxo2zDAJVqlRh/vz5rFq1SkEgD1AYsJn77ruPzZs3ExUVxaJFiwgMDGTixImkpKR4\nuzTJi8aPhy5dzDoEmTl50qxfEBiYO3VJnpKSkkJkZCSBgYFMnz6dzBqcCxcuzIgRI9i7dy+dO3fW\naKc8QrcJbOz48eOMHDmSqVOnEhISwuTJk3nwwQe9XZbkJUlJ8OGHMG4clCoFzZvD3XdD2bJw7hwc\nPgybNsH338P995vj7rnH21VLLlq7di0vv/wyO3fuzPLY9u3bM3HiRAICAnKhMrkeCgPCtm3bePnl\nl9mwYQN///vfmTBhAlWqVPF2WZKXJCWZFQqXL4ft280ERMWKwZ13moDQpQtoJjdbOXz4MMOGDUt3\naeGr+fv7M3HiREJDQ3OhMrkRCgMCmJ6/c+bM4bXXXuPMmTOMGjWKwYMHU6RIEW+XJiJ5iMvlIiIi\ngnfeeSfTpYUBihYtyogRIxg6dCh+fn65VKHcCPUZEAB8fHzo3r07sbGx9O3bl5EjR1K7dm2WLVvm\n7dJEJA9xOBysWrUqyyDQqVMn9u7dy8iRIxUE8gGFAUmjdOnSRERE8OOPP3LHHXfQvn17Hn/8cQ4c\nOODt0kQkD3A4HIwcORIfn/TfPoKDg1m5ciULFiygatWquVyd3CiFAUlXSEjI5T/o7du3U6tWLd58\n803++usvb5cmIl6SnJzMBx98QPv27SlcuHCafSVLlrz8QaJ169ZeqlBulMKAZMjhcNCpUydiYmIY\nOnQo7733HsHBwXz55ZeZDh2SguvChQv88ssvXLhwwdulSC5btWoV9erVY+jQoZdvKd52220Al38e\nMmQIhQoV8nKlciMUBiRLxYsXJywsjD179lCnTh06duxI27ZtiYmJ8XZpkst2795N1apV2b17t7dL\nkVzy888/07lzZ9q0aUOZMmXYunUrkZGRVK1alU8//ZR169Yxa9Ysbr31Vm+XKjdBYUCyLSAggMWL\nF7N48WISEhKoU6cOw4YN4/Tp094uTUQ87Pz584SHhxMcHMzatWuZPXs2a9euTbMC6iOPPEKzZs28\nWKV4isKAXLfQ0FB2797N6NGj+eijjwgKCmLOnDm6dSBSQCxZsoS7776bt99+m5deeonY2FieffZZ\nzRZYgCkMyA3x8/O7PKVo8+bN6datGy1atGDHjh3eLk1EblB8fDyhoaGEhoZSvXp1du7cyfjx4ylV\nqpS3S5McpjAgN6Vq1ap88cUXrFq1ihMnTtCgQQP69+/PiRMnvF2aiGTT2bNnGTlyJCEhIezatYuF\nCxeyYsUKgjWrpG0oDIhHtGrVih07djBhwgRmz55NYGAg06ZN4+LFi94uTUQyYFkWCxYsIDg4mAkT\nJjB8+HBiYmJ48skndUvAZhQGxGMKFSrE4MGDiYuLIzQ0lN69e9O4cWM2btzo7dJE5Cp79uyhTZs2\ndO7cmfr16xMdHc3o0aMpVqyYt0sTL1AYEI+rXLkyM2fO5Pvvv8flctG0aVN69OjB0aNHvV2aiO2d\nOnWKIUOGULduXX755ReWLl3KokWL8Pf393Zp4kUKA5Jj7rvvPjZv3kxUVBT/93//R2BgIBMnTiQ5\nOdnbpYnYjsvlYtasWQQFBTF16lTCwsLYtWsX7dq183ZpkgcoDEiO8vX1pU+fPsTFxfHMM88wePBg\nOnbs6O2yRGznlVde4fnnn6dly5bExsYyfPhwrUoqlykMSK4oV64cU6ZMYcuWLfTo0SPr1oHPPoOT\nJ3OnOJH87OhReOIJ2Lw5w0OSk5Pp3Lkzq1evZt68eVSpUiUXC5T8wOntAsRe7rnnHurXr59xT+Uj\nR2DSJJg1C+rVg1tuSd1nWaAeziJpVaoEgYEwZAg89RQMHHjNIYUKFaJ58+ZeKE7yC4UByXUZBoHz\n56F3b/Om/9VXUKeO+f7iRXA6U4OAywUZLJ8qYhvbtkHlynDbbfDeezBvHrz6qgnQ3bt7uzrJZ3RF\nlbzh9GkIDzcXuClToFEjs33nTpgwwXzaWbvWbFMQELuwLBN+r7ZlC3TrBps2pW57+ml49ln45BP4\n5pvcq1EKBF1VJW9YuBDWrIGhQ6FKFdMaAHDsGPz6K5w6Ze6L3ncf7Npl9mktBCnoHA4Tfv/8M+3r\nvWFDcxttyxb444/U7b16mb+fceNyv1bJ1xQGxPuSkuDf/4aqVeGZZ8w296f/Nm0gIsL0Idi7F2rU\ngMmTzT71H5CCbtMmaNXKvPl37Ghun7k9/jgsWZIajgHuugs6dYLdu1Nb0kSyQWFAvO9//zOffB54\nACpWNNvcb/SWBYULQ0oKlC9v+hH8979w4ID36hXxtPRaueLjYcAA0znwgw/M30GvXvDRR2Z/587Q\nsyfUr5/2HPfcY76++CJ3apcCQR0Ixft+/dVcyNzrol85asDhMD87L71UL140HaTUKiAFicMByclw\n+DDceafZ5g69K1ZA6dLQoYMJA3PnQoMG0KSJCQtXngPMbYIaNcyttcREKFEi938fyXfUMiDe4/4k\nc/SoGUkQEmJ+vrJVwP3zwYMwfDj885/Qrh1Ur35jzyWSF/35JwwaBGPGpG7bt88E5EKFUrf16gXF\nisGnn5qfLSvta9vdkla+vPm7Kl5cr33JFoUB8R73m/7WraZvAJjbAW7nzsGOHdCjB9x7L2zcCKNH\nwxtvmP3p9bJOj+YnkLyuTBkThhMTTadAgJIlYc8e8wnfrWFD04l2+3YTkK9+Xbvf+B980PQbcDj0\n2pdsURgQ77Is0w/gwgXz5u50mt7R//gHPPYY/O1vcPYszJ4Ny5dDly7g52cem50hhufOmU9bc+Zc\n+wlJn5gkL3C/Dh94wPw7b575t0cP2L/fDLd18/Ex/QEsywQCSPtm7/6bOHrUBII//8zR0qXgUJ8B\n8S6HA8qVgxMnzIXs5EkYNQqmToVHHzWtAZUrpx6f3QmH3K0BO3aYuQqKFLn2E5ImMZK8wP06DAmB\n5s3NJEIuF9xxBzz8MEycaLaXKmWOa9XKTCpUpsy153K/7suVg5o10z9GJB0KA+J9bdtCy5bm+1tu\ngfHjoUIFcxF8+GHo2xdefNHcO83um7b7Art6tbmH+tRT5uekJPjhB9iwwXS06tpVQUA8J71gmZ3b\nVO5j+vdPu33MGGjaFBYsgBdeMNv27DF/C850Lt/u52nTBurWvbHfQWxJV0HxvoAACA4231uW6f38\nzjvmXunzz5uZCcuWhe++S/s498REGTl2zPTOvvVW8Pc3twxefx0eeQTWrYMRI+DuuyE29trH6haC\nXA/368UdBLZvN0H0/Pns3bO/8hj3uVwu00egXz8zC+fTT8Pnn8PLL5vXcJMmmZ/PPUxXJBsclqWr\nnuQxV65H4LZ8uZmiuGxZ8/O5c1C0aPbOd+yYaWl4/XUz0+Hrr5v7sX/8YcZqP/AAvPWWOhpmomnT\npmzcuDHNtiZNmrBhwwYvVZRHzZtnOrn+9ZfpAHjLLSbMPvigeU37+mb/XO5WhsREWLoU5s83E2+1\nawdvv60hg+JRahmQvMfhSA0C7tEFDz+cGgR++80MmVq2LPPzuEcbVKhgAsGkSdCnj7k1AGb4Vc2a\nqedxOFL7LBw7lnqerFogxJ62b0+dCtiyzCiXd94xr7EdO8zrrUKF1KmBrycIQGorQ4kSJrTOnm1u\nEUyYYLbpc5x4kMKA5G1X3xfduRNeecUMNaxTJ/PH+vikvpF/8onpVNW1q+lD4JaYCLffbjowgpnQ\nZc2a1BkO9+2DWrXSDu8SAXML6z//Md87HKbvS0QEDB5sgmvr1uZNOzDQM2/cxYqZfy9eVCuWeJzC\ngOQvRYpA48ZmLYPbb8/6ePensRkzzLDESpVS9+3bZ1oCypVLbXVYtszM+e6eAKlUKTPf+759nv09\nJH87dsz0dalWLXVb8+bQvn3qz/Pnw48/mjDpbmm6eoKgG+HrqyAgHqcwIPlLUJBZs71Klew/Ji7O\n/Nu0adqL6Lp1pgXgkUfMz8uXw5EjZq539/1Yd8fFK2eBE6lQwQx7dbc8XTmK4PBh00rQv7+5DRUZ\naYLC1q1pX396Q5c8RGFACr6SJc2F+tCh1G2//GJaAapUgSefNNseftgM4WrUKPW4//3PzBXvHuMt\n4v5EX6eOWTfgarfdZjqk7t9vXk//+58ZzTJihNnv7gcza1baVQhFvEhhQAq+W281rQJbt8Lp0+aT\n25AhkJBgOntB6gW6evW0b/z795vWgTNncr9uyZscDjNk8K674KefzMiBq+cWaNbMLC4EZuKfRo1M\nC5V7lk2AN99MXVkwu1Nri+QQhQGxhwEDTLOuv7+5r7t2remV3aGD2Z/eBC6nTpn53V2urDsrir34\n+ZkWo2PHzARWkPEb+uHDsGqV6XDo42Om3gYzf4D7NoMmvhIv0wyEYg+NGpkx2qtXm4tx3bpmmuPM\nOnHt3QvffmvWjBe5Wrt2Zt6K5cvNyAH3G7rLBfHxZk2NH36Ajz4ytw6efdbsd49mqVYt84mDRHKR\nwoDYg3vCF/e0x25Xd+JydwQ7ccKMWHC54KWXcq9OyT9q1TLT/q5aBV9/DaGhZvuJEyYgREWZ192A\nAddOMwxmdItIHqEwIPbgHmKY3fHZ06ebT3UDB2qmN8lYz55m4qEhQ0xLga+vmczqscfMzJZX3l66\n3hkIRXKRblSJvWQUBNy3CywLNm0yU8g+9ZS5zyuSkWrVzAyDfn5mzYAffkjd7g4C7s6pCgKShykM\niEBqSJg61fTyfvFF07x7VauAlvKwt2v+/7sX1po/30yR/c47ZlbLK6XXOVUkj1EYEHG7cMEMIXzn\nHQgLM9uuuvhblsX333/PRa1XYCuWZbF+/XocV7csuX8ODjajU4YMgeTk3C9Q5CYpDIi4FS4Mr71m\n1j1wr4h41cX/woULPPzwwzRu3PiaVfykYNqzZw+tW7emefPmHDt2LP3WIfe21q3NvAIi+YzCgMiV\nsuhc6Ofnx4oVK3C5XDRt2pQePXpw9OjRXCpOctOpU6cYMmQIdevW5dChQ3z99ddUqFDh2tYB0NTC\nku8pDIhcp/vuu4/NmzcTFRXF//3f/xEYGMjEiRNJVvNwgeByuZg1axZBQUFMnTqVsLAwdu3aRbt2\n7bxdmkiOURgQuQG+vr706dOHuLg4nnnmGQYPHkz9+vVZvXq1t0uTm7Bt2zbuv/9+nn/+eVq2bEls\nbCzDhw+nSJEi3i5NJEcpDIjchHLlyjFlyhS2bNlCqVKlaNWqFV26dOHQlYsiSZ53/Phx+vbtS8OG\nDTlz5gyrV69m3rx5VLme1TFF8jGFAREPuOeee1i3bh2zZs1izZo1BAUFMXbsWJKSkrxdmmTi4sWL\nREVFERgYyLx58/jwww/Zvn07Dz74oLdLE8lVCgMiHuLj40P37t2JjY2lb9++jBo1irvvvpulS5d6\nuzRJx/r162nUqBH9+vXj8ccfJy4ujoEDB+LUvABiQwoDIh5WunRpIiIi+PHHH6latSqPPvooHTp0\nYP/+/d4uTYAjR47w3HPP0axZM3x8fNiwYQMzZsygUqVK3i5NxGsUBkRySEhICCtXrmTBggXs2LGD\nkJAQ3nzzTf766y9vl2ZLycnJvP/++wQ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1104f2908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 描画(flowがどう変わったか)\n",
    "# heightも表示したいけどやり方がわからず\n",
    "\n",
    "pos={'s':(0,2),'v':(3,4),'w':(3,0),'t':(6,2)}\n",
    "edge_labels = {(i, j): (w['capacity'], str((w['flow'])) ) for i, j, w in G.edges(data=True)}\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_color='r')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw(G, pos)\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "toc": {
   "nav_menu": {
    "height": "30px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": true,
   "toc_number_sections": true,
   "toc_section_display": "block",
   "toc_threshold": 6,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}