Lecture_9_~_Graph_Traversal.ipynb

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        "<a href=\"https://colab.research.google.com/github/LunaEyad/Deep-Learning-Foundations/blob/main/Lecture_9_~_Graph_Traversal.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# Graph Representation\n",
        "* Graph is a data structure $\\text {G = (V, E)}$: consist of $Vertices$ and $Edges$ \n",
        "* Can be either directed or undirected "
      ],
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      "cell_type": "markdown",
      "source": [
        "\n",
        "![graphs](https://i.ibb.co/1JrXZXb/graphs.png)\n"
      ],
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        "id": "n1jLKtypDeMO"
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      "source": [
        "# adjacency list representation\n",
        "graph_1_vertices = set (list (range (8)))\n",
        "graph_1_edges = {\n",
        "  0: [1, 4],\n",
        "  1: [0, 5],\n",
        "  2: [5, 6],\n",
        "  3: [7],\n",
        "  4: [0],\n",
        "  5: [1, 2, 6],\n",
        "  6: [2, 5, 7],\n",
        "  7: [3, 6]\n",
        "}\n",
        "graph_2_vertices = set (list (range (6)))\n",
        "graph_2_edges = {\n",
        "0: [1, 3],\n",
        "1: [4],\n",
        "2: [4, 5],\n",
        "3: [1],\n",
        "4: [3],\n",
        "5: [5]\n",
        "}\n",
        "from graphviz import Digraph \n",
        "def draw_graph(vertices, edges):\n",
        "  dot = Digraph(format=\"svg\")\n",
        "  for v in vertices:\n",
        "    dot.node (name = str(v), label = f\" {v} \")\n",
        "  for k, v in edges.items ():\n",
        "    for curr_v in v:\n",
        "      dot.edge(str(k), str(curr_v))\n",
        "  return dot\n",
        "\n",
        "draw_graph (graph_2_vertices, graph_2_edges)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Graph Traversal \n",
        "It is an algorithm (program) that is given: \n",
        "* a graph: $G$ and\n",
        "* a distinguished source vertex: $s$.\n",
        "\n",
        "The program ${Systematically}$\n",
        " follows the edges of the graph so as to visit the vertices.\n",
        "\n",
        "Today, we are exploring: \n",
        "\n",
        "* $\\textbf{Breadth First Traversal}$: This systematically visits every vertex $v$ in the graph reachable from $s$, while identifying the shortest path from $s$ to $v$.\n",
        "\n",
        "* $\\textbf{Depth First Traversal}$: This systematically visits every vertex  $v$ in the graph reachable from  $s$ following the strategy: \n",
        " 1. explores edges out of the most recently discovered vertex $v$ \n",
        " 2. Once all of the edges of  $v$ have been explored, the search ${{backtracks}}$ to explore other edges leaving the vertex from which $v$ was discovered. \n",
        "\n",
        "* $\\textbf{Topological Sort}$: Specific only to DAGs (Directed acyclic Graphs), It visists all nodes reachable from s, so as to return a linear sorting of all its vertices such that if C contains an edge from u and v. Then it appears before in this ordering. \n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "MK3DaqG2Dns9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1. Breadth First Traversal"
      ],
      "metadata": {
        "id": "u68IByPLJ20s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from collections import deque \n",
        "\n",
        "graph_vertics=graph_1_vertices\n",
        "graph_edges=graph_1_edges\n",
        "\n",
        "s =1 \n",
        "d= deque()\n",
        "visited = set()\n",
        "d.append(s)\n",
        "visited.add(s)\n",
        "while len(d)>0:\n",
        "    curr_vertex= d.popleft()\n",
        "\n",
        "    print(f\"visiting : {curr_vertex}\")\n",
        "    for nighapors in graph_edges[curr_vertex]:\n",
        "      if nighapors not in visited:\n",
        "        d.append(nighapors)\n",
        "        visited.add(nighapors)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9pFsQ86nI9dd",
        "outputId": "f7e122fb-4540-448d-a132-df6dd625304f"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "visiting : 1\n",
            "visiting : 0\n",
            "visiting : 5\n",
            "visiting : 4\n",
            "visiting : 2\n",
            "visiting : 6\n",
            "visiting : 7\n",
            "visiting : 3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 2.Depth First Search\n"
      ],
      "metadata": {
        "id": "4h-EGUHVgZSP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "graph_vertics=graph_1_vertices\n",
        "graph_edges=graph_1_edges\n",
        "\n",
        "s =1 \n",
        "visited = set()\n",
        "\n",
        "def dfs(v):\n",
        "  if v in visited:\n",
        "    return\n",
        "  else:\n",
        "    visited.add(v)\n",
        "    print(f\"visit before nighpors:{v}\") \n",
        "    for neighpor in graph_edges[v]:\n",
        "      dfs(neighpor)\n",
        "dfs(s)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nI60wIdygg6X",
        "outputId": "74a60000-82b0-4201-d70d-830a90d888ce"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "visit before nighpors:1\n",
            "visit before nighpors:0\n",
            "visit before nighpors:4\n",
            "visit before nighpors:5\n",
            "visit before nighpors:2\n",
            "visit before nighpors:6\n",
            "visit before nighpors:7\n",
            "visit before nighpors:3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph_vertics=graph_1_vertices\n",
        "graph_edges=graph_1_edges\n",
        "\n",
        "s =1 \n",
        "visited = set()\n",
        "\n",
        "def dfs(v):\n",
        "  if v in visited:\n",
        "    return\n",
        "  else:\n",
        "    visited.add(v)\n",
        "    \n",
        "    for neighpor in graph_edges[v]:\n",
        "      dfs(neighpor)\n",
        "    print(f\"visit after nighpors:{v}\")   \n",
        "dfs(s)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IwGtgACnt9N8",
        "outputId": "2e2b3683-2221-4c41-b6c8-5617b9556407"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "visit after nighpors:4\n",
            "visit after nighpors:0\n",
            "visit after nighpors:3\n",
            "visit after nighpors:7\n",
            "visit after nighpors:6\n",
            "visit after nighpors:2\n",
            "visit after nighpors:5\n",
            "visit after nighpors:1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph_vertics=graph_2_vertices\n",
        "graph_edges=graph_2_edges\n",
        "visited = set()  \n",
        "def dfs(v):\n",
        "  if v in visited:\n",
        "    return\n",
        "  else:\n",
        "    visited.add(v)\n",
        "    print(f\"visit before nighpors:{v}\") \n",
        "    for neighpor in graph_edges[v]:\n",
        "      dfs(neighpor)\n",
        "\n",
        "for node in graph_vertics:      \n",
        "  if node not in visited:    \n",
        "    print(\"new DFS search\") \n",
        "    dfs(node)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y2jbdkJLwHYS",
        "outputId": "7d1d4813-5603-458e-e635-68c8c8837037"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "new DFS search\n",
            "visit before nighpors:0\n",
            "visit before nighpors:1\n",
            "visit before nighpors:4\n",
            "visit before nighpors:3\n",
            "new DFS search\n",
            "visit before nighpors:2\n",
            "visit before nighpors:5\n"
          ]
        }
      ]
    }
  ]
}