Colab_Codes/chapter_search_strategies.ipynb

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    "colab": {
      "name": "chapter_search_strategies.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ev0G5LfkFTzu",
        "colab_type": "text"
      },
      "source": [
        "## Linear Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "23e3DXOGE59o",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Linear Search\n",
        "def linear_search(A, t):\n",
        "  for i, v in enumerate(A):\n",
        "    if A[i] == t:\n",
        "      return i\n",
        "  return -1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hfcQ8BdWSO8U",
        "colab_type": "text"
      },
      "source": [
        "## Uninformed Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ncgNw3NUJ3lC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import inspect\n",
        "\n",
        "\n",
        "def get_methods(cls_):\n",
        "    methods = inspect.getmembers(cls_, inspect.isfunction)\n",
        "    return dict(methods)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OJ9IAM2uIfci",
        "colab_type": "code",
        "outputId": "8bd64ccf-3b66-4025-df1c-8544e38e52a7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        }
      },
      "source": [
        "from graphviz import Digraph\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = ['S', 'A', 'B', 'G']\n",
        "for node in nodes:\n",
        "  dot.node(node)\n",
        "dot.edge('S', 'A', _attributes={'label': '4'})\n",
        "dot.edge('S', 'B', _attributes={'label': '5'})\n",
        "dot.edge('A', 'G', _attributes={'label': '7'})\n",
        "dot.edge('B', 'G', _attributes={'label': '3'})\n",
        "dot.render('test-output/ucs', view=True) \n",
        "\n",
        "dot"
      ],
      "execution_count": 478,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b634884e0>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: %3 Pages: 1 -->\n<svg width=\"134pt\" height=\"218pt\"\n viewBox=\"0.00 0.00 134.00 218.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 214)\">\n<title>%3</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-214 130,-214 130,4 -4,4\"/>\n<!-- S -->\n<g id=\"node1\" class=\"node\">\n<title>S</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"62\" cy=\"-192\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"62\" y=\"-188.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">S</text>\n</g>\n<!-- A -->\n<g id=\"node2\" class=\"node\">\n<title>A</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-105\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">A</text>\n</g>\n<!-- S&#45;&gt;A -->\n<g id=\"edge1\" class=\"edge\">\n<title>S&#45;&gt;A</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.9172,-174.3943C50.0309,-162.2482 43.4409,-145.8674 37.8907,-132.0711\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"41.0517,-130.5506 34.0722,-122.5796 34.5575,-133.1633 41.0517,-130.5506\"/>\n<text text-anchor=\"middle\" x=\"51\" y=\"-144.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">4</text>\n</g>\n<!-- B -->\n<g id=\"node3\" class=\"node\">\n<title>B</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-105\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-101.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">B</text>\n</g>\n<!-- S&#45;&gt;B -->\n<g id=\"edge2\" class=\"edge\">\n<title>S&#45;&gt;B</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M69.4875,-174.3943C74.6531,-162.2482 81.6196,-145.8674 87.487,-132.0711\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"90.8308,-133.1517 91.5236,-122.5796 84.3891,-130.4121 90.8308,-133.1517\"/>\n<text text-anchor=\"middle\" x=\"86\" y=\"-144.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">5</text>\n</g>\n<!-- G -->\n<g id=\"node4\" class=\"node\">\n<title>G</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"62\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"62\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">G</text>\n</g>\n<!-- A&#45;&gt;G -->\n<g id=\"edge3\" class=\"edge\">\n<title>A&#45;&gt;G</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M34.0828,-87.3943C38.9691,-75.2482 45.5591,-58.8674 51.1093,-45.0711\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"54.4425,-46.1633 54.9278,-35.5796 47.9483,-43.5506 54.4425,-46.1633\"/>\n<text text-anchor=\"middle\" x=\"51\" y=\"-57.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">7</text>\n</g>\n<!-- B&#45;&gt;G -->\n<g id=\"edge4\" class=\"edge\">\n<title>B&#45;&gt;G</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M91.5125,-87.3943C86.3469,-75.2482 79.3804,-58.8674 73.513,-45.0711\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"76.6109,-43.4121 69.4764,-35.5796 70.1692,-46.1517 76.6109,-43.4121\"/>\n<text text-anchor=\"middle\" x=\"86\" y=\"-57.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">3</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 478
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nRps_otMIJGX",
        "colab_type": "code",
        "outputId": "04e2165f-a5d3-4da8-de4a-876de4a47089",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "## Graph Search\n",
        "from collections import defaultdict\n",
        "al = defaultdict(list)\n",
        "al['S'] = [('A', 4), ('B', 5)]\n",
        "al['A'] = [('G', 7)]\n",
        "al['B'] = [('G', 3)]\n",
        "al"
      ],
      "execution_count": 479,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "defaultdict(list,\n",
              "            {'A': [('G', 7)], 'B': [('G', 3)], 'S': [('A', 4), ('B', 5)]})"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 479
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YT0tkaJ4SifH",
        "colab_type": "text"
      },
      "source": [
        "### Breath-first Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2yOpMY0_U-ov",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def bfs(g, s):\n",
        "  q = [s]\n",
        "  while q:\n",
        "    n = q.pop(0)\n",
        "    print(n, end = ' ')\n",
        "    for v, _ in g[n]:\n",
        "      q.append(v)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LqiB-SJ8VJMg",
        "colab_type": "code",
        "outputId": "98a4fbbf-ebef-41a2-f911-b49bc1c9b45e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "bfs(al, 'S')"
      ],
      "execution_count": 481,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "S A B G G "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PJ2MLkuJSTf_",
        "colab_type": "text"
      },
      "source": [
        "### Depth-first Search\n",
        "The completeness of DFS depends on the search space. If your search space is finite, then Depth-First Search is complete. However, if there are infinitely many alternatives, it might not find a solution. For example, suppose you were coding a path-search problem on city streets, and every time your partial path came to an intersection, you always searched the left-most street first. Then you might just keep going around the same block indefinitely.\n",
        "\n",
        "Sometimes there are ways to bound the search to get completeness even when the search space is unbounded. For example, for the path-search problem above, if we prune the search whenever a path returns to a previous location on the path, then DFS will always find a solution if one exists.\n",
        "\n",
        "There are variants of DFS that are complete. One is iterative deepening: you set a maximum search depth for DFS, and only search that far down the search tree. If you don’t find a solution, then you increase the bound and try again. (Note, however, that this method might run forever if there is no solution.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IH9FpE8DTce7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Implementation of recursive dfs\n",
        "def dfs(g, vi):\n",
        "  print(vi, end=' ')\n",
        "  for v, _ in g[vi]:   \n",
        "    dfs(g, v)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q9tKweIvUHFC",
        "colab_type": "code",
        "outputId": "de3e961e-8181-4b30-ab94-dc9319a32c39",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "dfs(al, 'S')"
      ],
      "execution_count": 483,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "S A G B G "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fikls4VUUReu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Implementation of iterative dfs\n",
        "def dfs_iter(g, s):\n",
        "  stack = [s]\n",
        "  while stack:\n",
        "    n = stack.pop()\n",
        "    print(n, end = ' ')\n",
        "    for v, _ in g[n]:\n",
        "      stack.append(v)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KegJMT0iUyJ3",
        "colab_type": "code",
        "outputId": "287815f2-1fbf-4b4c-cd84-4ca905d3b616",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "dfs_iter(al, 'S')"
      ],
      "execution_count": 485,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "S B G A G "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yZ3viz03H4EJ",
        "colab_type": "text"
      },
      "source": [
        "### Uniform-Cost Search"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fdT2z_NrLKJP",
        "colab_type": "text"
      },
      "source": [
        "```\n",
        "q = [(0, S)]\n",
        "Expand S, add A and B\n",
        "q = [(4, A), (5, B)]\n",
        "Expand A, add G\n",
        "q = [(5, B), (11, G)]\n",
        "Expand B, add G\n",
        "q = [(8, G), (11, G)]\n",
        "Expand G, goal found, terminate.\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZhCNgx-rKzHq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import heapq\n",
        "def ucs(graph, s, t):\n",
        "  q = [(0, s)] # initial path with cost 0\n",
        "  while q:\n",
        "    cost, n = heapq.heappop(q)\n",
        "    # Need to check when goal is removed from the priority queue\n",
        "    if n == t:\n",
        "      return cost\n",
        "    else:\n",
        "      for v, c in graph[n]:\n",
        "        heapq.heappush(q, (c + cost, v))\n",
        "  return None"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QQb89fDwMm6V",
        "colab_type": "code",
        "outputId": "e0d318db-87b2-4200-a1f4-07e2d6c12820",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "ucs(al, s='A', t='G')"
      ],
      "execution_count": 487,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 487
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mahGDvIKNs0k",
        "colab_type": "text"
      },
      "source": [
        "### Iterative-Deepening Search (IDS)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MoPms3bOSbIK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Depth limited Search\n",
        "def dls(graph, cur, t, maxDepth):\n",
        "  # End Condition\n",
        "  if maxDepth == 0:\n",
        "    print('test: ', cur, end = ' ')\n",
        "    if cur == t:\n",
        "      return True\n",
        "  if maxDepth < 0:\n",
        "    return False\n",
        "\n",
        "  # Recur for adjacent vertices\n",
        "  for n, _ in graph[cur]:\n",
        "    if dls(graph, n, t, maxDepth - 1):\n",
        "      return True\n",
        "  return False"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5D25vnOVN2H5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Iterative-deepening search\n",
        "def ids(graph, s, t, maxDepth):\n",
        "  for i in range(maxDepth):\n",
        "    print('depth:', i)\n",
        "    if dls(graph, s, t, i):\n",
        "      return True\n",
        "    print('\\n')\n",
        "  return False\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PPUE1EfrTff0",
        "colab_type": "code",
        "outputId": "083f0c90-ab80-4a10-e331-efad578966d7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 156
        }
      },
      "source": [
        "# Find 'B'\n",
        "ids(al, 'S', 'G', 3)"
      ],
      "execution_count": 490,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "depth: 0\n",
            "test:  S \n",
            "\n",
            "depth: 1\n",
            "test:  A test:  B \n",
            "\n",
            "depth: 2\n",
            "test:  G "
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 490
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "84kFFfrjHxH7",
        "colab_type": "text"
      },
      "source": [
        "### Bidirectional Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g7NGJLqrH1AM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def bfs_level(graph, q, bStep):\n",
        "  '''\n",
        "  q: set for better efficiency in intersection checking\n",
        "  '''\n",
        "  if not bStep:\n",
        "    return q\n",
        "  nq = set()\n",
        "  for n in q:\n",
        "    for v, c in graph[n]:\n",
        "      nq.add(v)\n",
        "  return nq\n",
        "\n",
        "def intersect(qs, qt):\n",
        "  if qs & qt: # intersection \n",
        "    return True\n",
        "  return False"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6a9IpOExIXXm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def bis(graph, s, t):\n",
        "  # First build a graph with opposite edges \n",
        "  bgraph = defaultdict(list)\n",
        "  for key, value in graph.items():\n",
        "    for n, c in value:\n",
        "      bgraph[n].append((key, c))\n",
        "  print(graph, bgraph)\n",
        "  # Start bidirectional search\n",
        "  qs = {s}\n",
        "  qt = {t}\n",
        "  step = 0\n",
        "  while qs and qt:\n",
        "    print(qs, qt)\n",
        "    if intersect(qs, qt):\n",
        "      return True\n",
        "    qs = bfs_level(graph, qs, step%2 == 0)\n",
        "    qt = bfs_level(bgraph, qt, step%2 == 1)\n",
        "    step = 1 - step\n",
        "  return False\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nrZW4C9_K37z",
        "colab_type": "code",
        "outputId": "56c325a2-63a9-4247-ba7e-87e461bf896c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 106
        }
      },
      "source": [
        "bis(al, 'S', 'A')"
      ],
      "execution_count": 493,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "defaultdict(<class 'list'>, {'S': [('A', 4), ('B', 5)], 'A': [('G', 7)], 'B': [('G', 3)], 'G': []}) defaultdict(<class 'list'>, {'A': [('S', 4)], 'B': [('S', 5)], 'G': [('A', 7), ('B', 3)]})\n",
            "{'S'} {'A'}\n",
            "{'B', 'A'} {'A'}\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 493
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ByphOhrKZtMj",
        "colab_type": "text"
      },
      "source": [
        "## Graph Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E7ZgUDIIaSaD",
        "colab_type": "code",
        "outputId": "b4b4bbaa-2199-4415-b31e-28eda9b623bf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        }
      },
      "source": [
        "from graphviz import Digraph, Graph\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "for node in nodes:\n",
        "  dot.node(str(node))\n",
        "dot.edges(['01','12', '24', '43', '45'])\n",
        "dot.render('test-output/free_tree', view=True) \n",
        "dot"
      ],
      "execution_count": 494,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b6345eda0>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 494
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-5v2VZ8bImzM",
        "colab_type": "code",
        "outputId": "eb70eca0-d48b-45c6-9141-b8685859e244",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        }
      },
      "source": [
        "dot = Graph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "# for node in nodes:\n",
        "#   dot.node(str(node))\n",
        "dot.edges(['01','02', '12','13', '24','34', '45'])\n",
        "rank1 = [0]\n",
        "rank2 = [1, 2]\n",
        "rank3 = [3, 4]\n",
        "rank4 = [5]\n",
        "for rank in [rank1, rank2, rank3, rank4]:\n",
        "  with dot.subgraph() as s:\n",
        "    s.attr(rank='same')\n",
        "    for node in rank:\n",
        "      s.node(str(node))\n",
        "dot.render('test-output/undirected_cyclic_graph', view=True) \n",
        "dot"
      ],
      "execution_count": 495,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Graph at 0x7f6b634b9630>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 495
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cI2CmyM-eGna",
        "colab_type": "code",
        "outputId": "f5f64c50-7e20-403c-a32a-36db75db2f52",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        }
      },
      "source": [
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "# for node in nodes:\n",
        "#   dot.node(str(node))\n",
        "dot.edges(['01', '12','31', '20', '24','43', '45'])\n",
        "rank1 = [0]\n",
        "rank2 = [1, 2]\n",
        "rank3 = [3, 4]\n",
        "rank4 = [5]\n",
        "for rank in [rank1, rank2, rank3, rank4]:\n",
        "  with dot.subgraph() as s:\n",
        "    s.attr(rank='same')\n",
        "    for node in rank:\n",
        "      s.node(str(node))\n",
        "dot.render('test-output/directed_cyclic_graph', view=True) \n",
        "dot"
      ],
      "execution_count": 496,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b63488048>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 496
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2K9nipQJff_F",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Prepare Graph Example\n",
        "# Adjacency List with cycle\n",
        "ft = [[] for _ in range(6)]\n",
        "ft[0] = [1]\n",
        "ft[1] = [2]\n",
        "ft[2] = [4]\n",
        "ft[4] = [3, 5]\n",
        "ft[5] = []"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ajKsBPhBgQcN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# directed cyclc graph\n",
        "dcg = [[] for _ in range(6)]\n",
        "dcg[0] = [1]\n",
        "dcg[1] = [2]\n",
        "dcg[2] = [0, 4]\n",
        "dcg[3] = [1]\n",
        "dcg[4] = [3, 5]\n",
        "dcg[5] = []"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0385JGxBPGWl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Prepare Graph Example\n",
        "# Adjacency List with cycle\n",
        "ucg = [[] for _ in range(6)]\n",
        "ucg[0] = [1, 2]\n",
        "ucg[1] = [0, 2, 3]\n",
        "ucg[2] = [0, 1,  4]\n",
        "ucg[3] = [1, 4]\n",
        "ucg[4] = [2, 3, 5]\n",
        "ucg[5] = [4]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E_EBbni8WYoB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#STATE Class\n",
        "class STATE:\n",
        "    white = 0\n",
        "    gray = 1\n",
        "    black = 2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fjb4NQ4QGRIu",
        "colab_type": "text"
      },
      "source": [
        "### Depth-first Search in Graph"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7O4uRkjzouHz",
        "colab_type": "text"
      },
      "source": [
        "#### Track Paths and Avoid Cycle in the tree-based search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BnwTjoskRGm0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Free Tree Search\n",
        "def dfs(g, vi):\n",
        "  print(vi, end=' ')\n",
        "  for nv in g[vi]:   \n",
        "    dfs(g, nv)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oo4bQGakSble",
        "colab_type": "code",
        "outputId": "7491e818-5a1c-4c48-a95c-9901eb5a2edc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "dfs(ft, 0)"
      ],
      "execution_count": 502,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0 1 2 4 3 5 "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CpnZbW1nUV5v",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Failed with directed cyclic graph\n",
        "# dfs(dcg, 0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "95BRIU3VlyAb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Graph Search, track paths and avoids cycle\n",
        "def dfs(g, vi, path):\n",
        "  paths.append(path)\n",
        "  orders.append(vi)\n",
        "  for nv in g[vi]:  \n",
        "    if nv not in path: \n",
        "      dfs(g, nv, path+[nv])\n",
        "  return "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LjXfmd17mKAi",
        "colab_type": "code",
        "outputId": "8526d563-8e86-4508-84c2-c9b4cf393cec",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# Test free tree\n",
        "paths, orders = [], []\n",
        "dfs(ft, 0, [0])\n",
        "paths, orders"
      ],
      "execution_count": 505,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0], [0, 1], [0, 1, 2], [0, 1, 2, 4], [0, 1, 2, 4, 3], [0, 1, 2, 4, 5]],\n",
              " [0, 1, 2, 4, 3, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 505
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ki0HtnO8mgD4",
        "colab_type": "code",
        "outputId": "546bd0ca-41ca-413d-923c-7ec57f1f8a05",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# Test dcg\n",
        "paths, orders = [], []\n",
        "dfs(dcg, 0, [0])\n",
        "paths, orders"
      ],
      "execution_count": 506,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0], [0, 1], [0, 1, 2], [0, 1, 2, 4], [0, 1, 2, 4, 3], [0, 1, 2, 4, 5]],\n",
              " [0, 1, 2, 4, 3, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 506
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nARQsx-3nlGd",
        "colab_type": "code",
        "outputId": "fe99a308-04d7-44ab-80f7-e0b90cb91f33",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 364
        }
      },
      "source": [
        "# Test ucg\n",
        "paths, orders = [], []\n",
        "dfs(ucg, 0, [0])\n",
        "paths, orders"
      ],
      "execution_count": 507,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0],\n",
              "  [0, 1],\n",
              "  [0, 1, 2],\n",
              "  [0, 1, 2, 4],\n",
              "  [0, 1, 2, 4, 3],\n",
              "  [0, 1, 2, 4, 5],\n",
              "  [0, 1, 3],\n",
              "  [0, 1, 3, 4],\n",
              "  [0, 1, 3, 4, 2],\n",
              "  [0, 1, 3, 4, 5],\n",
              "  [0, 2],\n",
              "  [0, 2, 1],\n",
              "  [0, 2, 1, 3],\n",
              "  [0, 2, 1, 3, 4],\n",
              "  [0, 2, 1, 3, 4, 5],\n",
              "  [0, 2, 4],\n",
              "  [0, 2, 4, 3],\n",
              "  [0, 2, 4, 3, 1],\n",
              "  [0, 2, 4, 5]],\n",
              " [0, 1, 2, 4, 3, 5, 3, 4, 2, 5, 2, 1, 3, 4, 5, 4, 3, 1, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 507
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZVhNQx4DgDe6",
        "colab_type": "text"
      },
      "source": [
        "Draw the search tree"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mSYmoZ_0gG4B",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Only keep the longest path\n",
        "def dfs_helper(g, vi, path):\n",
        "  orders.append(vi)\n",
        "  bpath = True\n",
        "  for nv in g[vi]:  \n",
        "    if nv not in path: \n",
        "      dfs_helper(g, nv, path+[nv])\n",
        "      bpath = False\n",
        "  if bpath:\n",
        "    paths.append(path)\n",
        "  return "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C0wF99z6huEu",
        "colab_type": "code",
        "outputId": "96f8adfa-b67d-4751-9fc1-44648993cb49",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 156
        }
      },
      "source": [
        "paths, orders = [], []\n",
        "dfs_helper(ucg, 0, [0])\n",
        "paths, orders"
      ],
      "execution_count": 509,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0, 1, 2, 4, 3],\n",
              "  [0, 1, 2, 4, 5],\n",
              "  [0, 1, 3, 4, 2],\n",
              "  [0, 1, 3, 4, 5],\n",
              "  [0, 2, 1, 3, 4, 5],\n",
              "  [0, 2, 4, 3, 1],\n",
              "  [0, 2, 4, 5]],\n",
              " [0, 1, 2, 4, 3, 5, 3, 4, 2, 5, 2, 1, 3, 4, 5, 4, 3, 1, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 509
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4TVSieudlvH3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Track edges\n",
        "def dfs_helper(g, vi, path):\n",
        "  orders.append(vi)\n",
        "  node = (vi, 0)\n",
        "  if vi in tracker:\n",
        "    node = (vi, tracker[vi] + 1)\n",
        "    tracker[vi] += 1\n",
        "  else:\n",
        "    tracker[vi] = 0\n",
        "  for nv in g[vi]:  \n",
        "    if nv not in path: \n",
        "      # add an edge\n",
        "      node1 = (nv, 0)\n",
        "      if nv in tracker:\n",
        "        node1 = (nv, tracker[nv]+1)\n",
        "      edges[node].append(node1)\n",
        "      dfs_helper(g, nv, path+[nv]) \n",
        "  return "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WwGSwE4PnRbB",
        "colab_type": "code",
        "outputId": "1dffc8ad-fa7e-4694-ea51-ad50d18cd0e6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        }
      },
      "source": [
        "paths, orders = [], []\n",
        "tracker = defaultdict(int) # node: maximum count\n",
        "edges = defaultdict(list) # node: node\n",
        "dfs_helper(ucg, 0, [0])\n",
        "paths, orders, edges, tracker, len(orders)"
      ],
      "execution_count": 511,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([],\n",
              " [0, 1, 2, 4, 3, 5, 3, 4, 2, 5, 2, 1, 3, 4, 5, 4, 3, 1, 5],\n",
              " defaultdict(list,\n",
              "             {(0, 0): [(1, 0), (2, 2)],\n",
              "              (1, 0): [(2, 0), (3, 1)],\n",
              "              (1, 1): [(3, 2)],\n",
              "              (2, 0): [(4, 0)],\n",
              "              (2, 2): [(1, 1), (4, 3)],\n",
              "              (3, 1): [(4, 1)],\n",
              "              (3, 2): [(4, 2)],\n",
              "              (3, 3): [(1, 2)],\n",
              "              (4, 0): [(3, 0), (5, 0)],\n",
              "              (4, 1): [(2, 1), (5, 1)],\n",
              "              (4, 2): [(5, 2)],\n",
              "              (4, 3): [(3, 3), (5, 3)]}),\n",
              " defaultdict(int, {0: 0, 1: 2, 2: 2, 3: 3, 4: 3, 5: 3}),\n",
              " 19)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 511
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s8Ti-Bo-ic0J",
        "colab_type": "code",
        "outputId": "bbdb4d18-1cc1-426e-ef12-168ecdefd045",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 561
        }
      },
      "source": [
        "# Plot the search tree\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "for node, count in tracker.items():\n",
        "  for i in range(count+1):\n",
        "    name=str(node)+str(i)\n",
        "    label=str(node)\n",
        "    #print(name, label)\n",
        "    dot.node(name=str(node)+str(i), label=str(node))\n",
        "for node1, nlist in edges.items():\n",
        "  for node2 in nlist:\n",
        "    a = str(node1[0])+str(node1[1])\n",
        "    b = str(node2[0])+str(node2[1])\n",
        "    #print(a, b)\n",
        "    dot.edge(a, b)\n",
        "#dot.edges(['01', '12','31', '20', '24','43', '45'])\n",
        "dot.render('test-output/search_tree_dfs', view=True) \n",
        "dot"
      ],
      "execution_count": 512,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b63488da0>"
            ],
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id=\"edge18\" class=\"edge\">\n<title>33&#45;&gt;12</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M387,-143.8314C387,-136.131 387,-126.9743 387,-118.4166\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"390.5001,-118.4132 387,-108.4133 383.5001,-118.4133 390.5001,-118.4132\"/>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 512
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZD5tQSWFoVOK",
        "colab_type": "text"
      },
      "source": [
        "We can see as the edges in the directed graph increase, the search tree explode exponentially with the number of edges. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yCuIaMa4c-Cl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Graph Search, track paths and avoids cycle\n",
        "def recursive(g, vi, path):\n",
        "  '''\n",
        "  g: graph as an adjacency list\n",
        "  vi: the vertex index\n",
        "  '''\n",
        "  #print(vi, end=' ')\n",
        "  paths, nodes = [[]], []\n",
        "  for nv in g[vi]:  \n",
        "    if nv not in path: \n",
        "      spaths, snodes = recursive(g, nv, path+[nv])\n",
        "      paths.extend(spaths)\n",
        "      nodes.extend(snodes)\n",
        "  paths = [[vi] + p for p in paths]\n",
        "  return paths, [vi] + nodes\n",
        "  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FUkmQgjndWkn",
        "colab_type": "code",
        "outputId": "d10feafd-209b-43fd-c43d-fd9f5ef00fd6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 364
        }
      },
      "source": [
        "# print path with free tree\n",
        "recursive(ucg, 0, [0])\n"
      ],
      "execution_count": 514,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0],\n",
              "  [0, 1],\n",
              "  [0, 1, 2],\n",
              "  [0, 1, 2, 4],\n",
              "  [0, 1, 2, 4, 3],\n",
              "  [0, 1, 2, 4, 5],\n",
              "  [0, 1, 3],\n",
              "  [0, 1, 3, 4],\n",
              "  [0, 1, 3, 4, 2],\n",
              "  [0, 1, 3, 4, 5],\n",
              "  [0, 2],\n",
              "  [0, 2, 1],\n",
              "  [0, 2, 1, 3],\n",
              "  [0, 2, 1, 3, 4],\n",
              "  [0, 2, 1, 3, 4, 5],\n",
              "  [0, 2, 4],\n",
              "  [0, 2, 4, 3],\n",
              "  [0, 2, 4, 3, 1],\n",
              "  [0, 2, 4, 5]],\n",
              " [0, 1, 2, 4, 3, 5, 3, 4, 2, 5, 2, 1, 3, 4, 5, 4, 3, 1, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 514
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qG_4NLC-o4bn",
        "colab_type": "text"
      },
      "source": [
        "#### Graph-based Search that avoids repeating vertex"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NTH_S5wQi_Lf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Avoid Repeating Vertex\n",
        "def dfgs(g, vi, visited, path):\n",
        "  visited.add(vi)\n",
        "  orders.append(vi)\n",
        "  bEnd = True # node without unvisited adjacent nodes    \n",
        "  for nv in g[vi]:  \n",
        "    if nv not in visited: \n",
        "      if bEnd:\n",
        "        bEnd = False\n",
        "      dfgs(g, nv, visited, path + [nv])\n",
        "  if bEnd:\n",
        "    paths.append(path)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "037PpuQvjMTj",
        "colab_type": "code",
        "outputId": "0f8982ed-76ef-4e3d-faf6-2b317cd6aa15",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "paths, orders = [], []\n",
        "dfgs(ucg, 0, set(), [0])\n",
        "paths, orders"
      ],
      "execution_count": 516,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0, 1, 2, 4, 3], [0, 1, 2, 4, 5]], [0, 1, 2, 4, 3, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 516
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vn-U1OFJof4B",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def backtrace(parent, s, t):\n",
        "  p = t\n",
        "  path = []\n",
        "  while p != s:\n",
        "    path.append(p)\n",
        "    p = parent[p]\n",
        "  path.append(s)\n",
        "  return path[::-1]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1aN6kwYPoH5d",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Backtrace path\n",
        "# s is used to backtrace the path\n",
        "def dfgs(g, vi, s, t, visited, parent):  \n",
        "  visited.add(vi) \n",
        "  if vi == t:\n",
        "    return backtrace(parent, s, t)\n",
        "\n",
        "  for nv in g[vi]:  \n",
        "    if nv not in visited: \n",
        "      parent[nv] = vi\n",
        "      fpath = dfgs(g, nv, s, t, visited, parent)\n",
        "      if fpath:\n",
        "        return fpath\n",
        "  \n",
        "  return None"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_dGSXhR2phQh",
        "colab_type": "code",
        "outputId": "2800b185-daae-46d1-c7d8-7d115fcece60",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "parent = {}\n",
        "path = dfgs(ucg, 0, 0, None, set(),  parent)\n",
        "path, parent"
      ],
      "execution_count": 519,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(None, {1: 0, 2: 1, 3: 4, 4: 2, 5: 4})"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 519
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TXjsA5BRLx87",
        "colab_type": "code",
        "outputId": "b30b4b1f-73fc-4e38-8939-6c8c2b6d61ac",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        }
      },
      "source": [
        "# Visualize the search tree\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "for node in nodes:\n",
        "    dot.node(name=str(node))\n",
        "for s, p in parent.items():\n",
        "    dot.edge(str(p), str(s))\n",
        "#dot.edges(['01', '12','31', '20', '24','43', '45'])\n",
        "dot.render('test-output/depth_first_graph_search_tree', view=True) \n",
        "dot"
      ],
      "execution_count": 520,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b6346b0b8>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 520
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b_55IC6F8iP_",
        "colab_type": "text"
      },
      "source": [
        "### Breath-first Search in Graph"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8YhKn3V3biau",
        "colab_type": "text"
      },
      "source": [
        "#### Track pahts and avoid cycle in the tree-based search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9-iHJjQYWfPy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Track paths and avoid cycles\n",
        "def bfs(g, s):\n",
        "  q = [[s]]\n",
        "  paths, orders = [], []\n",
        "  while q:\n",
        "    path = q.pop(0)\n",
        "    n = path[-1]\n",
        "    orders.append(n)\n",
        "    bEnd = True\n",
        "    for v in g[n]:\n",
        "      if v not in path:\n",
        "        if bEnd:\n",
        "          bEnd = False\n",
        "        q.append(path + [v])\n",
        "    if bEnd:\n",
        "      paths.append(path)\n",
        "  return paths, orders"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LSYyXM_EXHxD",
        "colab_type": "code",
        "outputId": "590521ea-deb7-4f93-dadf-e18881cf634c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# Test free tree\n",
        "bfs(ft, 0)"
      ],
      "execution_count": 522,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0, 1, 2, 4, 3], [0, 1, 2, 4, 5]], [0, 1, 2, 4, 3, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 522
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "00091jV7Yr3z",
        "colab_type": "code",
        "outputId": "6376b5c1-d2c3-4368-84e3-feadcafc95f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# Test dcg\n",
        "bfs(dcg, 0)"
      ],
      "execution_count": 523,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([[0, 1, 2, 4, 3], [0, 1, 2, 4, 5]], [0, 1, 2, 4, 3, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 523
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1xo7CLOBYzyE",
        "colab_type": "code",
        "outputId": "dd54c574-02ee-444d-9c52-c3afa45ae105",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        }
      },
      "source": [
        "# Test ucg\n",
        "paths, orders = bfs(ucg, 0)\n",
        "print(paths, orders)\n",
        "'''\n",
        "From dfs\n",
        "[[0, 1, 2, 4, 3],\n",
        "  [0, 1, 2, 4, 5],\n",
        "  [0, 1, 3, 4, 2],\n",
        "  [0, 1, 3, 4, 5],\n",
        "  [0, 2, 1, 3, 4, 5],\n",
        "  [0, 2, 4, 3, 1],\n",
        "  [0, 2, 4, 5]],\n",
        "'''\n",
        "print(len(orders))"
      ],
      "execution_count": 524,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0, 2, 4, 5], [0, 1, 2, 4, 3], [0, 1, 2, 4, 5], [0, 1, 3, 4, 2], [0, 1, 3, 4, 5], [0, 2, 4, 3, 1], [0, 2, 1, 3, 4, 5]] [0, 1, 2, 2, 3, 1, 4, 4, 4, 3, 3, 5, 3, 5, 2, 5, 4, 1, 5]\n",
            "19\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OaceX9XiboJr",
        "colab_type": "text"
      },
      "source": [
        "#### Graph-based search that avoids repeating vertex"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r6g03TClZAJu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Track paths and avoid cycles in a memory efficient way\n",
        "# Only track shortest paths\n",
        "def bfgs(g, s, t):\n",
        "  q = [s]\n",
        "  bfgs.parent = {}\n",
        "  visited = {s}\n",
        "  while q:\n",
        "    n = q.pop(0)\n",
        "    if n == t:\n",
        "      return backtrace(s, t, bfgs.parent)\n",
        "    for v in g[n]:\n",
        "      if v not in visited:\n",
        "        q.append(v)\n",
        "        visited.add(v)\n",
        "        bfgs.parent[v] = n\n",
        "  return None"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p1JuvjNMqZ0O",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Print Shortest Path Iterative\n",
        "def backtrace(s, t, parent):\n",
        "  p = t\n",
        "  path = []\n",
        "  while p != s:\n",
        "    path.append(p)\n",
        "    p = parent[p]\n",
        "  path.append(s)\n",
        "  return path[::-1]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OGUHuKrb6EDu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Print Shortest Path Recursive\n",
        "def get_path(s, t, pl, path):\n",
        "  if s == t:   \n",
        "    pass\n",
        "  elif pl[t] is None:\n",
        "    print('no path from ', s, ' to ', t)\n",
        "  else:\n",
        "    get_path(s, pl[t], pl, path)   \n",
        "  path.append(t)\n",
        "  return"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7129c26IbK0N",
        "colab_type": "code",
        "outputId": "ccb546e7-be27-4573-dfbe-63cf48b5cbbd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# Test ucg\n",
        "bfgs(ucg, 0, 5)"
      ],
      "execution_count": 528,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0, 2, 4, 5]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 528
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mwt51VlKFI5-",
        "colab_type": "code",
        "outputId": "482b57a4-29b1-4136-85fe-835ee577c4c2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        }
      },
      "source": [
        "# Visualize the search tree\n",
        "bfgs(ucg, 0, None)\n",
        "parent = bfgs.parent\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "for node in nodes:\n",
        "    dot.node(name=str(node))\n",
        "for s, p in parent.items():\n",
        "    dot.edge(str(p), str(s))\n",
        "#dot.edges(['01', '12','31', '20', '24','43', '45'])\n",
        "dot.render('test-output/breath_first_graph_search_tree', view=True) \n",
        "dot"
      ],
      "execution_count": 529,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b63488940>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: %3 Pages: 1 -->\n<svg width=\"134pt\" height=\"260pt\"\n viewBox=\"0.00 0.00 134.00 260.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 256)\">\n<title>%3</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-256 130,-256 130,4 -4,4\"/>\n<!-- 0 -->\n<g id=\"node1\" class=\"node\">\n<title>0</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"63\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"63\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">0</text>\n</g>\n<!-- 1 -->\n<g id=\"node2\" class=\"node\">\n<title>1</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">1</text>\n</g>\n<!-- 0&#45;&gt;1 -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;1</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M54.2854,-216.5708C50.0403,-208.0807 44.8464,-197.6929 40.1337,-188.2674\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"43.237,-186.6477 35.6343,-179.2687 36.976,-189.7782 43.237,-186.6477\"/>\n</g>\n<!-- 2 -->\n<g id=\"node3\" class=\"node\">\n<title>2</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">2</text>\n</g>\n<!-- 0&#45;&gt;2 -->\n<g id=\"edge2\" class=\"edge\">\n<title>0&#45;&gt;2</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M71.7146,-216.5708C75.9597,-208.0807 81.1536,-197.6929 85.8663,-188.2674\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"89.024,-189.7782 90.3657,-179.2687 82.763,-186.6477 89.024,-189.7782\"/>\n</g>\n<!-- 3 -->\n<g id=\"node4\" class=\"node\">\n<title>3</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">3</text>\n</g>\n<!-- 1&#45;&gt;3 -->\n<g id=\"edge3\" class=\"edge\">\n<title>1&#45;&gt;3</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M27,-143.8314C27,-136.131 27,-126.9743 27,-118.4166\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"30.5001,-118.4132 27,-108.4133 23.5001,-118.4133 30.5001,-118.4132\"/>\n</g>\n<!-- 4 -->\n<g id=\"node5\" class=\"node\">\n<title>4</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">4</text>\n</g>\n<!-- 2&#45;&gt;4 -->\n<g id=\"edge4\" class=\"edge\">\n<title>2&#45;&gt;4</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M99,-143.8314C99,-136.131 99,-126.9743 99,-118.4166\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"102.5001,-118.4132 99,-108.4133 95.5001,-118.4133 102.5001,-118.4132\"/>\n</g>\n<!-- 5 -->\n<g id=\"node6\" class=\"node\">\n<title>5</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">5</text>\n</g>\n<!-- 4&#45;&gt;5 -->\n<g id=\"edge5\" class=\"edge\">\n<title>4&#45;&gt;5</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M99,-71.8314C99,-64.131 99,-54.9743 99,-46.4166\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"102.5001,-46.4132 99,-36.4133 95.5001,-46.4133 102.5001,-46.4132\"/>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 529
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w0UuaLXj5bgZ",
        "colab_type": "text"
      },
      "source": [
        "#### Multiple Starts"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yg1tgj8Y5czv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Multiple Starts\n",
        "def BFSLevel(starts):\n",
        "    q = starts # a list of nodes\n",
        "    #root.visited = 1\n",
        "    while q:\n",
        "        new_q = []\n",
        "        for node in q:\n",
        "            for neig in node.adjacent:\n",
        "               if not neig.visited:\n",
        "                   neig.visited = 1\n",
        "                   new_q.append(neig)\n",
        "        q = new_q"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I-LT_HgDrrtI",
        "colab_type": "text"
      },
      "source": [
        "####Level by level bfs"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sQyW-n5qrt6k",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def bfs_level(g, s):\n",
        "  '''level by level bfs'''\n",
        "  v = len(g)\n",
        "  state = [False] * v\n",
        "  \n",
        "  orders = []\n",
        "  lst = [s]\n",
        "  state[s] = True\n",
        "  d = 0 # track distance\n",
        "  while lst:\n",
        "    print('distance ', d, ': ', lst)\n",
        "    tmp_lst = []\n",
        "    for u in lst:\n",
        "      orders.append(u)\n",
        "      for v in g[u]:\n",
        "        if not state[v]:\n",
        "          state[v] = True\n",
        "          tmp_lst.append(v)    \n",
        "    lst = tmp_lst\n",
        "    d += 1\n",
        "  return orders\n",
        "          "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KwUfwlRN2qbe",
        "colab_type": "code",
        "outputId": "e2048ab1-018e-4141-ea4f-766d0cefd436",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "source": [
        "print(bfs_level(ucg, 0))"
      ],
      "execution_count": 532,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "distance  0 :  [0]\n",
            "distance  1 :  [1, 2]\n",
            "distance  2 :  [3, 4]\n",
            "distance  3 :  [5]\n",
            "[0, 1, 2, 3, 4, 5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KDFDgG-BOBml",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "## Depth-first Graph Search"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V0lQCtvcWWxi",
        "colab_type": "text"
      },
      "source": [
        "### Recursive Implementation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ddy-8DejWciM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Recursive implementation with three states\n",
        "def dfs(g, s, colors, orders, complete_orders):\n",
        "  colors[s] = STATE.gray\n",
        "  orders.append(s)\n",
        "  for v in g[s]:\n",
        "    if colors[v] == STATE.white:\n",
        "      dfs(g, v, colors, orders, complete_orders)\n",
        "  # complete\n",
        "  colors[s] = STATE.black\n",
        "  complete_orders.append(s)\n",
        "  return"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Co2HV7k4XDJm",
        "colab_type": "code",
        "outputId": "4f4b44f1-ce20-4fc3-802b-254aa2d19898",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "# initialization\n",
        "'''start from 0'''\n",
        "v = len(ucg)\n",
        "orders, complete_orders = [], []\n",
        "colors = [STATE.white] * v\n",
        "dfs(ucg,0, colors, orders, complete_orders)\n",
        "print(orders, complete_orders)"
      ],
      "execution_count": 534,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 2, 4, 3, 5] [3, 5, 4, 2, 1, 0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hjByXvweDX3c",
        "colab_type": "text"
      },
      "source": [
        "Visualizing the state change of nodes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jDQvblzsOK9m",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# directed cyclc graph\n",
        "dcg = [[] for _ in range(6)]\n",
        "dcg[0] = [1, 2]\n",
        "dcg[1] = [2, 4]\n",
        "dcg[2] = [0, 4]\n",
        "dcg[3] = [1]\n",
        "dcg[4] = [3, 5]\n",
        "dcg[5] = [3] # cross edge"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7ZK2pX87OvMH",
        "colab_type": "code",
        "outputId": "cb41c3bd-7aa5-4304-c571-0bb39aea86ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        }
      },
      "source": [
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "#print(get_methods(Digraph))\n",
        "#print(Digraph.__dict__)\n",
        "nodes = [0, 1, 2, 3, 4, 5]\n",
        "rank1 = [0]\n",
        "rank2 = [1, 2]\n",
        "rank3=[3, 4]\n",
        "rank4 = [5]\n",
        "ranks=[rank1, rank2, rank3, rank4]\n",
        "for i, rank in enumerate(ranks):\n",
        "      with dot.subgraph(name=name+str(i)) as s:\n",
        "        s.attr(rank='same')\n",
        "        for node in rank:\n",
        "          s.node(str(node))\n",
        "dot.edges(['01', '02', '12', '14', '31', '20', '24','43', '45', '53'])\n",
        "dot.render('test-output/directed_cyclic_graph_2', view=True) \n",
        "dot"
      ],
      "execution_count": 536,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b63430b00>"
            ],
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class=\"node\">\n<title>1</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"27\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">1</text>\n</g>\n<!-- 0&#45;&gt;1 -->\n<g id=\"edge1\" class=\"edge\">\n<title>0&#45;&gt;1</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M83.7307,-218.7307C73.803,-208.803 60.6847,-195.6847 49.5637,-184.5637\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"51.7933,-181.8436 42.2473,-177.2473 46.8436,-186.7933 51.7933,-181.8436\"/>\n</g>\n<!-- 2 -->\n<g id=\"node3\" class=\"node\">\n<title>2</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"99\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">2</text>\n</g>\n<!-- 0&#45;&gt;2 -->\n<g id=\"edge2\" class=\"edge\">\n<title>0&#45;&gt;2</title>\n<path fill=\"none\" stroke=\"#000000\" 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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 536
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8TdvPlxTAVhp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def set_node_style(dot, color, node, name):\n",
        "  dot.attr('node', style='filled', fillcolor=color, fontcolor='red')#color=color)\n",
        "  dot.node(name=name, label=str(node))\n",
        "\n",
        "\n",
        "def plot(g, colors,  dot, edges, nodes):\n",
        "  #dot = Digraph(comment='The Round Table', format='png')\n",
        "  name = str(next(counter))\n",
        "  \n",
        "  with dot.subgraph(name=name) as s:\n",
        "    for node in nodes:\n",
        "      if colors[node] == STATE.gray:\n",
        "        set_node_style(dot, 'gray', node, name=str(node)+name)\n",
        "      elif colors[node] == STATE.black:\n",
        "        set_node_style(dot, 'black', node, name=str(node)+name)\n",
        "      else:\n",
        "        set_node_style(dot, 'white', node, name=str(node)+name)\n",
        "    for s, e in edges:\n",
        "      dot.edge(str(s)+name, str(e)+name)\n",
        "\n",
        "  \n",
        "    #s.edges(['01', '12','31', '20', '24','43', '45'])\n",
        "    #dot.render('test-output/depth_first_graph_search'+str(next(counter)), view=True) \n",
        "    #s.view()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Av-u8YzcCW8_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_state(g, colors,  dot, edges_list):\n",
        "  #dot = Digraph(comment='The Round Table', format='png')\n",
        "  name = str(next(counter))\n",
        "  with dot.subgraph(name=name) as init:\n",
        "    nodes = len(g)\n",
        "    rank1 = [0]\n",
        "    rank2 = [2, 1]\n",
        "    rank3 = [4, 3]\n",
        "    rank4 = [5]\n",
        "    ranks = [rank1, rank2, rank3, rank4]\n",
        "   \n",
        "    for i, rank in enumerate(ranks):\n",
        "      with init.subgraph(name=name+str(i)) as s:\n",
        "        s.attr(rank='same')\n",
        "        for node in rank:\n",
        "          \n",
        "          if colors[node] == STATE.gray:\n",
        "            set_node_style(s, 'gray', node, name=str(node)+name)\n",
        "          elif colors[node] == STATE.black:\n",
        "            set_node_style(s, 'black', node, name=str(node)+name)\n",
        "          else:\n",
        "            set_node_style(s, 'white', node, name=str(node)+name)\n",
        "      # \n",
        "    for s in range(nodes):\n",
        "      for e in g[s]:\n",
        "        init.edge(str(s)+name, str(e)+name)\n",
        "    # tracker = defaultdict(set) # edges\n",
        "    # for s in range(nodes):\n",
        "    #   for e in g[s]:\n",
        "    #     ##print(s, e, tracker)\n",
        "    #     if e in tracker and s in tracker[e]:\n",
        "    #       continue\n",
        "    #     else:\n",
        "    #       tracker[s].add(e)\n",
        "    #     init.edge(str(s)+name, str(e)+name)\n",
        "        init.render('test-output/depth_first_graph_search_process'+name, view=True, format='png') "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dwJMwokbXyPX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def plot_all(g, colors,  dot, edges_list):\n",
        "  #dot = Digraph(comment='The Round Table', format='png')\n",
        "  name = str(next(counter))\n",
        "  with dot.subgraph(name=name) as init:\n",
        "    nodes = set()\n",
        "    rank1 = [0]\n",
        "    rank2 = [1]\n",
        "    rank2_1=[2]\n",
        "    rank3 = [4]\n",
        "    rank4 = [3, 5]\n",
        "    ranks = [rank1, rank2, rank2_1, rank3, rank4]\n",
        "    for edges in edges_list:\n",
        "      for s, e in edges:\n",
        "        nodes.add(s)\n",
        "        nodes.add(e)\n",
        "   \n",
        "    for i, rank in enumerate(ranks):\n",
        "      with init.subgraph(name=name+str(i)) as s:\n",
        "        s.attr(rank='same')\n",
        "        for node in rank:\n",
        "          if node not in nodes:\n",
        "            continue\n",
        "          \n",
        "          if colors[node] == STATE.gray:\n",
        "            set_node_style(s, 'gray', node, name=str(node)+name)\n",
        "          elif colors[node] == STATE.black:\n",
        "            set_node_style(s, 'black', node, name=str(node)+name)\n",
        "          else:\n",
        "            set_node_style(s, 'white', node, name=str(node)+name)\n",
        "      # \n",
        "    # tracker = defaultdict(set) # edges\n",
        "    # for s in range(nodes):\n",
        "    #   for e in g[s]:\n",
        "    #     ##print(s, e, tracker)\n",
        "    #     if e in tracker and s in tracker[e]:\n",
        "    #       continue\n",
        "    #     else:\n",
        "    #       tracker[s].add(e)\n",
        "    #     init.edge(str(s)+name, str(e)+name)\n",
        "      \n",
        "    \n",
        "    colors = ['black', 'red']\n",
        "    for i, edges in enumerate(edges_list):\n",
        "      if not edges:\n",
        "        continue\n",
        "      for start, end in edges:\n",
        "        if start is not None:\n",
        "          init.edge(str(start)+name, str(end)+name,_attributes={'dir':'forward', 'color': colors[i]})\n",
        "    init.render('test-output/depth_first_graph_search_process'+name, view=True, format='png') \n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kLCE2dNJJjum",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!rm test-output/depth_first_graph_search*"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SpzWbATRNjtL",
        "colab_type": "code",
        "outputId": "05521fd1-9abb-46ae-98c4-50d1b2e9e076",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "!rm *.gv*"
      ],
      "execution_count": 541,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "rm: cannot remove '*.gv*': No such file or directory\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TCNTJ6sBADIU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Visualizing\n",
        "edges = []\n",
        "back_edges = []\n",
        "def dfs(g, s, colors, dot, nodes, pre_node):\n",
        "  nodes.add(s)\n",
        "  colors[s] = STATE.gray\n",
        "  #plot(g, colors,  dot, edges, nodes)\n",
        "  global edges\n",
        "  global back_edges\n",
        "  plot_fun(g, colors,  dot, [edges, back_edges])\n",
        "  for v in g[s]:\n",
        "    if colors[v] == STATE.white:\n",
        "      edges += [(s, v)]\n",
        "      dfs(g, v, colors, dot, nodes, s)\n",
        "      back_edges += [(v, s)]\n",
        "      #plot_fun(g, colors,  dot, [edges, back_edges])\n",
        "  # complete\n",
        "  \n",
        "  colors[s] = STATE.black\n",
        "  #plot(g, colors, dot, edges, nodes)\n",
        "  plot_fun(g, colors,  dot, [edges, back_edges])\n",
        "  return"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3y8edac7CkYd",
        "colab_type": "code",
        "outputId": "d562fdbd-be9b-48ee-ebe4-a4ecfaaaa0a3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        }
      },
      "source": [
        "# Plot_state\n",
        "import itertools\n",
        "counter = itertools.count()\n",
        "print(dcg)\n",
        "v = len(dcg)\n",
        "colors = [STATE.white] * v\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "plot_fun = plot_state\n",
        "dfs(dcg,0, colors, dot, set(), None)\n",
        "dot.render('test-output/depth_first_graph_search_process', view=True) \n",
        "dot"
      ],
      "execution_count": 543,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1, 2], [2, 4], [0, 4], [1], [3, 5], [3]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 543
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WBFPoKth-Eui",
        "colab_type": "code",
        "outputId": "77ef6b6b-6ac2-4ee8-a663-0ae3da4ac5e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 769
        }
      },
      "source": [
        "# Classify edges\n",
        "# edges is tree edge\n",
        "# need to formulate better\n",
        "'''\n",
        "dcg[0] = [1, 2]\n",
        "dcg[1] = [2, 4]\n",
        "dcg[2] = [0, 4]\n",
        "dcg[3] = [1]\n",
        "dcg[4] = [3, 5]\n",
        "dcg[5] = [3] # cross edge\n",
        "'''\n",
        "print(edges, back_edges)\n",
        "tree = ft\n",
        "tree_edges = edges\n",
        "nodes = len(dcg)\n",
        "new_edges, n_back_edges, forward_edges, cross_edges = [], [], [], []\n",
        "# reversed tree:\n",
        "reverse_tree = [[] for _ in range(nodes)]\n",
        "for s in range(nodes):\n",
        "  for e in tree[s]: \n",
        "    reverse_tree[e].append(s)\n",
        "for s in range(nodes):\n",
        "  for e in dcg[s]:\n",
        "    print(s, e, tree)\n",
        "    if (s, e) in tree_edges:\n",
        "      new_edges.append((s, e))\n",
        "    elif bfgs(tree, e, s ):\n",
        "      n_back_edges.append((s, e))\n",
        "    elif bfgs(tree, s, e ):\n",
        "      forward_edges.append((s ,e))\n",
        "    else:\n",
        "      cross_edges.append((s, e))\n",
        "\n",
        "edges_list = [new_edges, n_back_edges, forward_edges, cross_edges ]\n",
        "dot = Digraph(comment='The Round Table', format='png')\n",
        "print(edges_list)\n",
        "rank1 = [0]\n",
        "rank2 = [1]\n",
        "rank2_1=[2]\n",
        "rank3 = [4]\n",
        "rank4 = [3, 5]\n",
        "ranks = [rank1, rank2, rank2_1, rank3, rank4]\n",
        "dot.attr(ranksep='0.75', rank='same')\n",
        "\n",
        "  \n",
        "\n",
        "colors = ['black', 'red', 'yellow', 'blue']\n",
        "for i, edgesx in enumerate(edges_list):\n",
        "  if not edgesx:\n",
        "    continue\n",
        "  for start, end in edgesx:\n",
        "    if start is not None:\n",
        "      dot.edge(str(start), str(end),_attributes={ 'color': colors[i]})\n",
        "for i, rank in enumerate(ranks):\n",
        "  with dot.subgraph(name=str(i)) as s:\n",
        "    s.attr(ranksep='0.75', rank='same')\n",
        "    for node in rank:\n",
        "      s.node(name=str(node))\n",
        "dot.render('test-output/depth_first_graph_search_edges', view=True, format='png') \n",
        "#print(dot.source)\n",
        "dot\n"
      ],
      "execution_count": 544,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[(0, 1), (1, 2), (2, 4), (4, 3), (4, 5)] [(3, 4), (5, 4), (4, 2), (2, 1), (1, 0)]\n",
            "0 1 [[1], [2], [4], [], [3, 5], []]\n",
            "0 2 [[1], [2], [4], [], [3, 5], []]\n",
            "1 2 [[1], [2], [4], [], [3, 5], []]\n",
            "1 4 [[1], [2], [4], [], [3, 5], []]\n",
            "2 0 [[1], [2], [4], [], [3, 5], []]\n",
            "2 4 [[1], [2], [4], [], [3, 5], []]\n",
            "3 1 [[1], [2], [4], [], [3, 5], []]\n",
            "4 3 [[1], [2], [4], [], [3, 5], []]\n",
            "4 5 [[1], [2], [4], [], [3, 5], []]\n",
            "5 3 [[1], [2], [4], [], [3, 5], []]\n",
            "[[(0, 1), (1, 2), (2, 4), (4, 3), (4, 5)], [(2, 0), (3, 1)], [(0, 2), (1, 4)], [(5, 3)]]\n"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 544
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fSCrzb82GPUy",
        "colab_type": "text"
      },
      "source": [
        "More about the application of classificatio of edges. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XIfzSpwDYZON",
        "colab_type": "text"
      },
      "source": [
        "Discover and finish time"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XmsNF54Gd0rN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Discovering and finishing time\n",
        "def dfs(g, s, colors):\n",
        "  dfs.t += 1 # static variable\n",
        "  colors[s] = STATE.gray\n",
        "  dfs.discover[s] = dfs.t\n",
        "  for v in g[s]:\n",
        "    if colors[v] == STATE.white:\n",
        "      dfs(g, v, colors)\n",
        "  # complete\n",
        "  dfs.t += 1\n",
        "  dfs.finish[s] = dfs.t\n",
        "  return"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4U0E0RQfeKkh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "43996495-b35e-4dc9-f5c8-34830552c240"
      },
      "source": [
        "v = len(dcg)\n",
        "colors = [STATE.white] * v\n",
        "dfs.t = -1\n",
        "dfs.discover, dfs.finish = [-1] * v, [-1] * v\n",
        "dfs(dcg,0, colors)\n",
        "dfs.discover, dfs.finish"
      ],
      "execution_count": 546,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([0, 1, 2, 4, 3, 6], [11, 10, 9, 5, 8, 7])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 546
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q3qw9TVueO4r",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def parenthesis(dt, ft, n):\n",
        "  merge_orders = [-1] * 2 * n\n",
        "  for v, t in enumerate(dt):\n",
        "    merge_orders[t] = v\n",
        "  for v, t in enumerate(ft):\n",
        "    merge_orders[t] = v\n",
        "\n",
        "  print(merge_orders)\n",
        "  nodes = set()\n",
        "  for i in merge_orders:\n",
        "    if i not in nodes:\n",
        "      print('(', i, end = ', ')\n",
        "      nodes.add(i)\n",
        "    else:\n",
        "      print(i, '),', end = ' ')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bsZ4WOk3e4OT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "6460ea8f-3334-444f-d6ce-cbc0b389c90a"
      },
      "source": [
        "parenthesis(dfs.discover, dfs.finish, v)"
      ],
      "execution_count": 548,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 2, 4, 3, 3, 5, 5, 4, 2, 1, 0]\n",
            "( 0, ( 1, ( 2, ( 4, ( 3, 3 ), ( 5, 5 ), 4 ), 2 ), 1 ), 0 ), "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qRdHVeAG9z29",
        "colab_type": "text"
      },
      "source": [
        "### Iterative Implementation ***"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xT0mVw8gZTIi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Iterative implementation with three states\n",
        "def dftIter(g, s):\n",
        "  '''not preserving the same discovery ordering'''\n",
        "  n = len(g)\n",
        "  orders = []\n",
        "  colors = [STATE.white] * n\n",
        "  stack = [s]\n",
        "\n",
        "  orders.append(s) # track gray order\n",
        "  colors[s] = STATE.gray\n",
        "        \n",
        "  while stack:\n",
        "    u = stack.pop()\n",
        "    \n",
        "    for v in g[u]:\n",
        "      if colors[v] == STATE.white:\n",
        "        colors[v] = STATE.gray\n",
        "        stack.append(v)\n",
        "        orders.append(v) # track gray order\n",
        "    \n",
        "  return orders"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q3hq9ARKqqnw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3d0b9d01-b012-4794-af03-042a1e5512ce"
      },
      "source": [
        "# initialization\n",
        "'''start from 0'''\n",
        "print(dftIter(ucg,0))"
      ],
      "execution_count": 550,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 2, 4, 3, 5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RIVOD221rHii",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9f6a74e9-769b-405c-b518-b88d2c9eeae2"
      },
      "source": [
        "print(dftIter(ucg, 1))"
      ],
      "execution_count": 551,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1, 0, 2, 3, 4, 5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I4eVWYzGj01U",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def dftIter(g, s):\n",
        "  '''preserving only discovery ordering'''\n",
        "  n = len(g)\n",
        "  orders = []\n",
        "  colors = [STATE.white] * n\n",
        "  stack = [s]\n",
        "\n",
        "  #orders.append(s) # track gray order\n",
        "  #colors[s] = STATE.gray\n",
        "        \n",
        "  while stack:\n",
        "    u = stack.pop()\n",
        "    if colors[u] == STATE.white:\n",
        "      orders.append(u) # track gray order\n",
        "    colors[u] = STATE.gray\n",
        "    for v in g[u][::-1]:\n",
        "      if colors[v] == STATE.white:\n",
        "        \n",
        "        stack.append(v)\n",
        "        #orders.append(v) # track gray order\n",
        "    \n",
        "  return orders"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5JWNwi9rlAER",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "61c6eca2-9dcd-4b23-ebe0-fe7fae0ba312"
      },
      "source": [
        "print(dftIter(ucg, 0))"
      ],
      "execution_count": 553,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 2, 4, 3, 5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mBqP-iy9ma3d",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "dbad8a60-6b64-432b-e053-ab3aade53a5a"
      },
      "source": [
        "print(dftIter(ucg, 1))"
      ],
      "execution_count": 554,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1, 0, 2, 4, 3, 5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rrFl2gwokZON",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def dfsIter(g, s):\n",
        "  '''iterative dfs'''\n",
        "  v = len(g)\n",
        "  orders, complete_orders = [], []\n",
        "  colors = [STATE.white] * v\n",
        "  stack = [s]\n",
        "\n",
        "  orders.append(s) # track gray order\n",
        "  colors[s] = STATE.gray\n",
        "        \n",
        "  while stack:\n",
        "    u = stack[-1]\n",
        "    bAdj = False\n",
        "    for v in g[u]:\n",
        "      if colors[v] == STATE.white:\n",
        "        colors[v] = STATE.gray\n",
        "        stack.append(v)\n",
        "        orders.append(v) # track gray order\n",
        "        bAdj = True\n",
        "        break\n",
        "     \n",
        "    if not bAdj: # if no adjacent is found, pop out\n",
        "      # complete\n",
        "      colors[u] = STATE.black # this is not necessary in the code, just to help track the state\n",
        "      complete_orders.append(u)\n",
        "      stack.pop()\n",
        "    \n",
        "  return orders, complete_orders       "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vGaO1vCbly-a",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5f6a1035-9b9f-40dd-be46-34686fdb9534"
      },
      "source": [
        "print(dfsIter(ucg, 0))"
      ],
      "execution_count": 556,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "([0, 1, 2, 4, 3, 5], [3, 5, 4, 2, 1, 0])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oAxBg1ZR-ct5",
        "colab_type": "text"
      },
      "source": [
        "## Breath-first Graph Search"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aR60hTwOQOo0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def bfgs_state(g, s):\n",
        "  v = len(g)\n",
        "  colors = [STATE.white] * v\n",
        "  \n",
        "  q, orders = [s], [s]\n",
        "  complete_orders = []\n",
        "  colors[s] = STATE.gray # make the state of the visiting node\n",
        "  while q:\n",
        "    u = q.pop(0)   \n",
        "    for v in g[u]:\n",
        "      if colors[v] == STATE.white:\n",
        "        colors[v] = STATE.gray\n",
        "        q.append(v)\n",
        "        orders.append(v)\n",
        "\n",
        "    # complete \n",
        "    colors[u] = STATE.black\n",
        "    complete_orders.append(u)\n",
        "  return orders, complete_orders"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ld25XyC8Uxun",
        "colab_type": "code",
        "outputId": "539d70aa-6c17-48b1-b328-6a9aa97b4649",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "bfgs_state(dcg, 0)"
      ],
      "execution_count": 558,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([0, 1, 2, 4, 3, 5], [0, 1, 2, 4, 3, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 558
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GxtnwF3_XN1F",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Plot state\n",
        "def plot_state_bfs(g, colors,  dot, png_name):\n",
        "  #dot = Digraph(comment='The Round Table', format='png')\n",
        "  #name = str(next(counter))\n",
        "  with dot.subgraph(name=png_name) as init:\n",
        "    nodes = len(g)\n",
        "    rank1 = [0]\n",
        "    rank2 = [2, 1]\n",
        "    rank3 = [4, 3]\n",
        "    rank4 = [5]\n",
        "    ranks = [rank1, rank2, rank3, rank4]\n",
        "   \n",
        "    for i, rank in enumerate(ranks):\n",
        "      subgraph_name = png_name + str(i)\n",
        "      with init.subgraph() as s:\n",
        "        s.attr(rank='same')\n",
        "        for node in rank:\n",
        "          \n",
        "          if colors[node] == STATE.gray:\n",
        "            set_node_style(s, 'gray', node, name=str(node)+png_name)\n",
        "          elif colors[node] == STATE.black:\n",
        "            set_node_style(s, 'black', node, name=str(node)+png_name)\n",
        "          else:\n",
        "            set_node_style(s, 'white', node, name=str(node)+png_name)\n",
        "      # \n",
        "    for s in range(nodes):\n",
        "      for e in g[s]:\n",
        "        init.edge(str(s)+png_name, str(e)+png_name)\n",
        "    init.render('test-output/'+png_name, view=True, format='png') "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sFud8KIWVZka",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def bfgs_state_plot(g, s):\n",
        "  v = len(g)\n",
        "  colors = [STATE.white] * v\n",
        "\n",
        "  dot = Digraph(comment='The Round Table', format='png')\n",
        "\n",
        "  \n",
        "  q = [s]\n",
        "  colors[s] = STATE.gray # make the state of the visiting node\n",
        "  counter = itertools.count()\n",
        "  plot_state_bfs(g, colors,  dot, png_name='breath_first_graph_search_process'+str(next(counter)))\n",
        "  while q:\n",
        "    u = q.pop(0)   \n",
        "    for v in g[u]:\n",
        "      if colors[v] == STATE.white:\n",
        "        colors[v] = STATE.gray\n",
        "        q.append(v)\n",
        "        plot_state_bfs(g, colors,  dot, png_name='breath_first_graph_search_process'+str(next(counter)))\n",
        "\n",
        "    # complete \n",
        "    colors[u] = STATE.black\n",
        "    plot_state_bfs(g, colors,  dot, png_name='breath_first_graph_search_process'+str(next(counter)))\n",
        "  #dot.render('test-output/breath_first_graph_search_process', view=True) \n",
        "  return dot\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b6C9AhL5WCPH",
        "colab_type": "code",
        "outputId": "82ca88fe-7e9e-40b8-ac00-1af9dc05b62a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 389
        }
      },
      "source": [
        "dot = bfgs_state_plot(dcg, 0)\n",
        "dot"
      ],
      "execution_count": 561,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f6b6347cf98>"
            ],
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 561
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I0j42hiHHZBq",
        "colab_type": "text"
      },
      "source": [
        "## Tree Search\n",
        "\n",
        "The sample code is writen in [tree_datastructure_and_traversal](https://colab.research.google.com/drive/1pg49npUd4Rhbg5fggs8ZYakA563YATeA)."
      ]
    }
  ]
}