01_slides/4_recursive_ds.ipynb

{
  "cells": [
    {
      "attachments": {
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yMiUyMHklM0QlMjIxODklMjIlMjBhcyUzRCUyMnRhcmdldFBvaW50JTIyJTIwJTJGJTNF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\nJSeneItAoUKFBIlSChYs6O1A2HtgEOD+1bdUrhD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C0tigH/wBa6jkNVE5qEwF/Coyj99BRqggXWA+HIBxUItMQaQula2AX/JUhYNkBB1oDBOh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\nMkeul5/LhTJMjuC+qZP8A4zyrPgI2n3BAAAAAElFTkSuQmCC\n"
        }
      },
      "cell_type": "markdown",
      "id": "e606b619-c770-4437-9a7e-b5af87141aaf",
      "metadata": {},
      "source": [
        "# Recursive Data Structures\n",
        "\n",
        "## Outline\n",
        "\n",
        "-   Trees\n",
        "\n",
        "-   Anatomy, tree traversal methods\n",
        "\n",
        "-   Binary Search Trees\n",
        "\n",
        "-   Graphs\n",
        "\n",
        "-   Nearest Neighbor Problem\n",
        "\n",
        "# Trees\n",
        "\n",
        "## Introduction to Trees\n",
        "\n",
        "-   Not all data has a natural linear order. Organization charts and\n",
        "    file storage systems have a *hierarchical structure*, in which each\n",
        "    entity is linked to multiple entities below it\n",
        "\n",
        "-   This type of data is represented using a *tree*. A tree is either\n",
        "\n",
        "    -   Empty\n",
        "\n",
        "    -   Has a *root value* connected to any number of other trees,\n",
        "        called *subtrees*\n",
        "\n",
        "-   We draw the root at the top of the tree\n",
        "\n",
        "## Anatomy of a Tree\n",
        "\n",
        "-   The *size* of a tree is the number of values in the tree\n",
        "\n",
        "-   A *leaf* is a value with no subtrees. The leaves of this tree are\n",
        "    labeled E, F, G, J, and I\n",
        "\n",
        "-   The *height* of a tree is the longest path from its root to its\n",
        "    leaves. The height of this tree is 4\n",
        "\n",
        "![](attachment:images/tree.png)\n",
        "\n",
        "## Anatomy of a Tree\n",
        "\n",
        "-   The *children* of a value are all values directly connected\n",
        "    underneath that value. The children of A are B, C, and D\n",
        "\n",
        "-   The *descendants* of a value are it’s children, the children of its\n",
        "    children, etc. This can be defined recursively\n",
        "\n",
        "-   The *parent* of a value is the value immediately above and connected\n",
        "    to it. The parent of H is C\n",
        "\n",
        "-   The *ancestors* of a value are its parent, the parent of its parent,\n",
        "    etc.\n",
        "\n",
        "![](attachment:images/tree.png)\n",
        "\n",
        "## Tree Traversal Methods\n",
        "\n",
        "-   Linear data structures only have one logical way to traverse them.\n",
        "    Trees can be traversed in different ways\n",
        "\n",
        "-   We’ll look at the following methods of tree traversal and their\n",
        "    applications\n",
        "\n",
        "    -   *Depth First Search* (DFS): Inorder, Preorder, and Postorder\n",
        "        traversal\n",
        "\n",
        "    -   *Breadth First Search* (BFS)\n",
        "\n",
        "-   Note there are other methods not covered\n",
        "\n",
        "## DFS: Inorder Traversal\n",
        "\n",
        "1.  Traverse the left subtree\n",
        "\n",
        "2.  Visit the root\n",
        "\n",
        "3.  Traverse the right subtree\n",
        "\n",
        "**Result: 4 2 5 1 6 3**\n",
        "\n",
        "![](attachment:images/tree_num.png)\n",
        "\n",
        "## DFS: Inorder Traversal Code\n",
        "\n",
        "Let’s look at the code to do this"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "4914a874",
      "metadata": {},
      "outputs": [],
      "source": [
        "class Node:\n",
        "  \"\"\"Tree class\n",
        "  \"\"\"\n",
        "  def __init__(self, key):\n",
        "    self.left = None\n",
        "    self.right = None\n",
        "    self.val = key\n",
        "    \n",
        "def print_inorder(root):\n",
        "  if root:\n",
        "    print_inorder(root.left)\n",
        "    print(root.val, end = \" \")\n",
        "    print_inorder(root.right)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "abb121a0-9014-4411-8250-bb0fe5a46eee",
      "metadata": {},
      "source": [
        "## DFS: Inorder Traversal Code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "8e4b78cb",
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "4 2 5 1 6 3 "
          ]
        }
      ],
      "source": [
        "root = Node(1)\n",
        "root.left = Node(2)\n",
        "root.right = Node(3)\n",
        "root.left.left = Node(4)\n",
        "root.left.right = Node(5)\n",
        "root.right.left = Node(6)\n",
        "print_inorder(root)"
      ]
    },
    {
      "attachments": {
        "images/insertion.png": {
          "image/png": 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UGtUSoXTt7PtRq5CqFbYvsoBaBRXMQ75FkRHMxsKtXA5PpbswubE5o65U6S5w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\nZ3dhWQJ+xOykkrkpSxOj01BA9FoAABi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        },
        "images/tree_num.png": {
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yMiUyMHklM0QlMjIxODklMjIlMjBhcyUzRCUyMnRhcmdldFBvaW50JTIyJTIwJTJGJTNF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\nJSeneItAoUKFBIlSChYs6O1A2HtgEOD+1bdUrhD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        },
        "images/tree_unbal.png": {
          "image/png": 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xJTIyJTIweSUzRCUyMjE4OSUyMiUyMGFzJTNEJTIydGFyZ2V0UG9pbnQlMjIlMjAlMkYl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\n"
        }
      },
      "cell_type": "markdown",
      "id": "91306dbf-a4f2-47f3-a88a-1c5da831baae",
      "metadata": {},
      "source": [
        "In binary search trees (next section), inorder traversal gives the nodes\n",
        "in a non-decreasing order.\n",
        "\n",
        "## DFS: Inorder Traversal Complexity\n",
        "\n",
        "Time complexity\n",
        "\n",
        "-   Each node is visited exactly once. The work done at each node is\n",
        "    constant. $O(n)$\n",
        "\n",
        "Space complexity\n",
        "\n",
        "-   Dependent on the maximum depth of the recursion, which is the height\n",
        "    of the tree. $O(h)$\n",
        "\n",
        "## DFS: Preorder Traversal\n",
        "\n",
        "1.  Visit the root\n",
        "\n",
        "2.  Traverse the left subtree\n",
        "\n",
        "3.  Traverse the right subtree\n",
        "\n",
        "**Result: 1 2 4 5 3 6**\n",
        "\n",
        "Preorder traversal is used to create a copy of the tree\n",
        "\n",
        "![](attachment:images/tree_num.png)\n",
        "\n",
        "## DFS: Postorder Traversal\n",
        "\n",
        "1.  Traverse the left subtree\n",
        "\n",
        "2.  Traverse the right subtree\n",
        "\n",
        "3.  Visit the root\n",
        "\n",
        "**Result: 4 5 2 6 3 1**\n",
        "\n",
        "Preorder traversal is used to delete subtrees. (why?)\n",
        "\n",
        "![](attachment:images/tree_num.png)\n",
        "\n",
        "## BFS\n",
        "\n",
        "BFS (or Level Order Traversal) traverses nodes present in the same level\n",
        "before traversing the next level\n",
        "\n",
        "1.  For each node\n",
        "\n",
        "-   The node is visited\n",
        "\n",
        "-   The child nodes are enqueued in a FIFO queue\n",
        "\n",
        "1.  First node is dequeued\n",
        "\n",
        "2.  Child nodes are enqueued\n",
        "\n",
        "3.  Repeat until the queue is empty\n",
        "\n",
        "**Result: 1 2 3 4 5 6**\n",
        "\n",
        "![](attachment:images/tree_num.png)\n",
        "\n",
        "# Binary Search Trees\n",
        "\n",
        "## BST Definitions\n",
        "\n",
        "-   You can think of a BST as a sorted tree\n",
        "\n",
        "-   A *binary tree* is a tree in which every item has at most two\n",
        "    subtrees\n",
        "\n",
        "    -   The tree used in illustrating DFS and BFS methods is a binary\n",
        "        tree\n",
        "\n",
        "-   A binary tree is a *binary search tree property* if its value is\n",
        "    greater than or equal to all items in the left subtree\n",
        "\n",
        "-   A binary tree is a *binary search tree* if every item in the tree\n",
        "    satisfies the binary search tree property\n",
        "\n",
        "## BST Efficiency\n",
        "\n",
        "-   Consider the BST on the right. Verify that it is a BST.\n",
        "\n",
        "-   The worst-case run time is $O(h)$, $h$ being the height of the tree\n",
        "\n",
        "    -   So the tree on the right is $O(n)$\n",
        "\n",
        "-   A tree of height $h$ can have at most $2^h - 1$ nodes. So we need at\n",
        "    least log$n$ height to store all of them.\n",
        "\n",
        "    -   So if the tree was balanced, then it would be $O(\\text{log}n)$\n",
        "\n",
        "![](attachment:images/tree_unbal.png)\n",
        "\n",
        "## BST Efficiency\n",
        "\n",
        "-   Convince yourself that for a balanced BST the search, insert, and\n",
        "    delete Big-O is all $O(\\text{log}n)$\n",
        "\n",
        "-   Ensuring that a tree is balanced is important\n",
        "\n",
        "    -   Red-Black trees (not covered) are trees that balance themselves\n",
        "\n",
        "    -   You may also be interested in B-trees, which are used in\n",
        "        databases\n",
        "\n",
        "## Live Coding\n",
        "\n",
        "Given a BST, insert a new node in this BST.\n",
        "\n",
        "![](attachment:images/insertion.png)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0fffca91",
      "metadata": {},
      "outputs": [],
      "source": [
        "# Your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "61fb5b0a",
      "metadata": {},
      "source": [
        "\n",
        "# Graphs\n",
        "\n",
        "## Introduction\n",
        "\n",
        "-   We looked at lists and trees, which represent linear and\n",
        "    hierarchical relationships respectively\n",
        "\n",
        "    -   But many relationships are neither\n",
        "\n",
        "    -   Friend networks, internet connections, flight connections\n",
        "\n",
        "-   Graphs consist of two parts, *nodes* and *edges*\n",
        "\n",
        "    -   A node connected to another is a *neighbor*\n",
        "\n",
        "![](attachment:images/graph_anat.png)\n",
        "\n",
        "## Types of Graphs\n",
        "\n",
        "There are directed and undirected graphs to represent different\n",
        "situations\n",
        "\n",
        "-   Friendships: undirected\n",
        "\n",
        "-   Twitter followers: directed\n",
        "\n",
        "-   Who owes who money: directed\n",
        "\n",
        "-   Note that trees are special cases of directed graphs\n",
        "\n",
        "Graphs can also be weighted, to differentiate strengths between nodes\n",
        "\n",
        "There are two questions we ask about graphs: Is there a path from node A\n",
        "to B? What is the shortest path from node A to B? BFS answers both!\n",
        "\n",
        "![](attachment:images/graph_weight.png)\n",
        "\n",
        "## BFS of Graphs\n",
        "\n",
        "-   *Breadth First Search* (BFS) searches graph for a node that meets a\n",
        "    set of criteria. It starts at the root of the graph and visits all\n",
        "    nodes at the current depth level before moving on to the nodes at\n",
        "    the next depth level\n",
        "\n",
        "    -   If there are multiple nodes meeting the criteria, then BFS will\n",
        "        also find the nearest node!\n",
        "\n",
        "-   The issue is that graphs contain *cycles*, so we may visit the same\n",
        "    node more than once\n",
        "\n",
        "    -   Let’s split edges into visited and not visited\n",
        "\n",
        "-   We use a list to keep track of visited nodes\n",
        "\n",
        "-   All the adjacent unvisited nodes of the current level are pushed\n",
        "    into the queue and the nodes of the current level are marked visited\n",
        "    and popped from the queue\n",
        "\n",
        "-   Is BFS a recursive or iterative graph search method?\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   Let’s traverse a graph with BFS starting at node “1”\n",
        "\n",
        "-   Visited list and queue start as empty\n",
        "\n",
        "Visited: \\[ , , , , \\]\n",
        "\n",
        "Queue: \\[ , , , , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   We’re at node 1, so we push it onto the visited list and push it\n",
        "    onto the queue\n",
        "\n",
        "Visited: \\[1, , , , \\]\n",
        "\n",
        "Queue: \\[1, , , , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   Now we visited 1, so it is dequeued.\n",
        "\n",
        "-   At the first level away from node 1, there is 3 and 6.\n",
        "\n",
        "-   We visit 3 and 6, but we have not visited any of it’s neighbors\n",
        "    (other than 1), so 3 and 6 are enqueued.\n",
        "\n",
        "Visited: \\[1, 3, 6, , \\]\n",
        "\n",
        "Queue: \\[3, 6, , , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   Visit the neighbors of node 3, so we dequeue it\n",
        "\n",
        "-   But we need to enqueue 10, because we haven’t visited its neighbors\n",
        "\n",
        "Visited: \\[1, 3, 6, 10, \\]\n",
        "\n",
        "Queue: \\[6, 10, , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   Visit the neighbors of node 6, which is just 7, so we dequeue it\n",
        "\n",
        "-   But we need to enqueue 7\n",
        "\n",
        "Visited: \\[1, 3, 6, 10, 7\\]\n",
        "\n",
        "Queue: \\[10, 7, , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   Visit the neighbors of node 10, and dequeue 10\n",
        "\n",
        "-   But we already visited those nodes, so the visited list does not\n",
        "    change\n",
        "\n",
        "Visited: \\[1, 3, 6, 10, 7\\]\n",
        "\n",
        "Queue: \\[7, , , , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## BFS Example\n",
        "\n",
        "-   Visit neighbors of 7, which are also all visited\n",
        "\n",
        "-   The queue is empty, so the algorithm ends\n",
        "\n",
        "Visited: \\[1, 3, 6, 10, 7\\]\n",
        "\n",
        "Queue: \\[ , , , , \\]\n",
        "\n",
        "![](attachment:images/graph_bfs.png)\n",
        "\n",
        "## Time and Space Complexity of BFS\n",
        "\n",
        "-   Each edge and each node must be visited once, so the time complexity\n",
        "    is $O(n + e)$\n",
        "\n",
        "-   Since we need to store each node of the graph by the end of the\n",
        "    algorithm, the space complexity is $O(n)$\n",
        "\n",
        "## Implementing Graphs and BFS\n",
        "\n",
        "We can represent graphs using the *adjacency list* representation\n",
        "\n",
        "-   Other options include adjacency matrix or using a Python library"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "23428e44",
      "metadata": {},
      "outputs": [],
      "source": [
        "from collections import deque\n",
        "\n",
        "class Graph:\n",
        "  def __init__(self):\n",
        "    self.graph = {}\n",
        "\n",
        "  def add_edge(self, vertex, neighbors):\n",
        "    self.graph[vertex] = neighbors"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9f393b7b-3af9-4a07-861c-9e14bc7bea47",
      "metadata": {},
      "source": [
        "## Implementing Graphs and BFS"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "32ada213",
      "metadata": {},
      "outputs": [],
      "source": [
        "def bfs(graph, start):\n",
        "  visited = set()\n",
        "  queue = deque([start])\n",
        "\n",
        "  while queue:\n",
        "    current_vertex = queue.popleft()\n",
        "\n",
        "    if current_vertex not in visited:\n",
        "      # Process the current vertex\n",
        "      print(current_vertex, end=' ')\n",
        "      visited.add(current_vertex)\n",
        "\n",
        "      # Enqueue unvisited neighbors\n",
        "      for neighbor in graph.graph.get(current_vertex, []):\n",
        "        if neighbor not in visited:\n",
        "          queue.append(neighbor)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3965d53d-8ca1-4372-8e0b-35a2a1486159",
      "metadata": {},
      "source": [
        "## Implementing Graphs and BFS"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "3b8d278a",
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1 3 6 10 7 "
          ]
        }
      ],
      "source": [
        "# Represent graph from above\n",
        "ex_graph = Graph()\n",
        "ex_graph.add_edge(1, [3, 6])\n",
        "ex_graph.add_edge(3, [10, 6])\n",
        "ex_graph.add_edge(6, [3, 7])\n",
        "ex_graph.add_edge(10, [3, 7])\n",
        "ex_graph.add_edge(7, [10, 6])\n",
        "\n",
        "# Perform BFS starting from vertex 1\n",
        "bfs(ex_graph, 1)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "909bfd55-42c3-4c3c-8279-6489791e4f51",
      "metadata": {},
      "source": [
        "## Recursive Graph Search: Preorder Traversal\n",
        "\n",
        "-   Using the same `Graph` class, let’s implement preorder traversal"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "d883118d",
      "metadata": {},
      "outputs": [],
      "source": [
        "def recursive_preorder_traversal(graph, start, visited=None):\n",
        "  if visited is None:\n",
        "    visited = set()\n",
        "\n",
        "  # Process the current vertex\n",
        "  print(start, end=' ')\n",
        "  visited.add(start)\n",
        "\n",
        "    # Recursive traversal of neighbors\n",
        "  for neighbor in graph.graph.get(start, []):\n",
        "    if neighbor not in visited:\n",
        "      recursive_preorder_traversal(graph, neighbor, visited)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "60bf08d2-4747-41c3-b128-ff00d1bc771d",
      "metadata": {},
      "source": [
        "## Recursive Graph Search: Preorder Traversal"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "c4b48ff8",
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1 3 6 10 7 "
          ]
        }
      ],
      "source": [
        "bfs(ex_graph, 1)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c3b6c651-0046-4740-babf-41a312cf51bc",
      "metadata": {},
      "source": [
        "# Nearest Neighour Problem\n",
        "\n",
        "## Nearest Neighbour Problem\n",
        "\n",
        "-   As you may have encountered already, machine learning and\n",
        "    statistical methods often depend on finding the nearest neighbor to\n",
        "    a data point\n",
        "\n",
        "    -   K-nearest neighbors regression, propensity score matching\n",
        "\n",
        "-   In a $k$ dimensional space, if we conduct a linear search for\n",
        "    points, the running time will be $O(kn)$ for $n$ data points.\n",
        "\n",
        "-   Can we do better?\n",
        "\n",
        "## k-d Trees\n",
        "\n",
        "-   k-d trees is short for k dimensional tree (notation is a bit\n",
        "    unfortunate, different K than KNN)\n",
        "\n",
        "    -   It is useful for multidimensional searches\n",
        "\n",
        "-   Let’s discuss the properties of k-d trees and why they work\n",
        "\n",
        "-   Binary tree where each node represents an axis-aligned\n",
        "    hyperrectangle in the k-dimensional space\n",
        "\n",
        "    -   hyperrectangle: rectangle in higher dimensions\n",
        "\n",
        "-   Nodes in the left subtree have coordinates less than the splitting\n",
        "    dimension of the current node, while nodes in the right subtree have\n",
        "    coordinates greater than the splitting dimension.\n",
        "\n",
        "-   At each level of the tree, a specific dimension is chosen to split\n",
        "    the data. The choice of dimension alternates as we traverse down the\n",
        "    tree.\n",
        "\n",
        "-   Each leaf represents a single point in the k-dimensional space\n",
        "\n",
        "## k-d Trees Animation\n",
        "\n",
        "<https://commons.wikimedia.org/wiki/File:KDTree-animation.gif>\n",
        "\n",
        "## Applications and Issues\n",
        "\n",
        "-   Notice k-d trees can also find values within a certain range very\n",
        "    quickly, not just a specific point\n",
        "\n",
        "-   GIS (geographic information systems) queries\n",
        "\n",
        "-   KNN algorithm\n",
        "\n",
        "-   Computer graphics, such as ray tracing to facilitate efficient space\n",
        "    partitioning\n",
        "\n",
        "-   Issues occur in high-dimensional spaces and trees can become\n",
        "    imbalanced\n",
        "\n",
        "# Recommended Problems and References\n",
        "\n",
        "## Recommended Readings\n",
        "\n",
        "-   Bhargava: Chapter 6\n",
        "\n",
        "-   Bhargava: Chapter 11, pages 203 to 206 about Trees\n",
        "\n",
        "## Recommended Problems\n",
        "\n",
        "-   Cormen: Chapter 10 exercises\n",
        "\n",
        "    -   10.3-1, 10.3-2, 10.3-3\n",
        "\n",
        "-   Bhargava: Chapter 6 exercises\n",
        "\n",
        "    -   6.1 to 6.5\n",
        "\n",
        "## Recommended Problems\n",
        "\n",
        "-   Implement preorder, postorder, and level order traversal. Determine\n",
        "    the time and space complexity in each case\n",
        "\n",
        "-   Implement a function that find an element in a BST and deletes it.\n",
        "    The descendants of the deleted node are given to the deleted node’s\n",
        "    parent.\n",
        "\n",
        "-   Using the `graph` class from the slides, implement BST search such\n",
        "    that it stops and tell you the distance the node is from the\n",
        "    starting point.\n",
        "\n",
        "    -   For instance, if we searched for 7 in the graph given in the\n",
        "        slides, it would return `\"Found! Distance 2\"`.\n",
        "\n",
        "    -   If we searched for 100 in the graph, it would return\n",
        "        `\"Not found!\"`\n",
        "\n",
        "-   Implement postorder graph traversal using the `graph` class from the\n",
        "    slides.\n",
        "\n",
        "-   Implement a function using recursion to find the sum heterogeneous\n",
        "    nested lists such as \\[\\[1, \\[2\\]\\], \\[\\[\\[3\\]\\]\\], 4, \\[\\[5, 6\\],\n",
        "    \\[\\[\\[7\\]\\]\\]\\]\\].\n",
        "\n",
        "## References\n",
        "\n",
        "-   Bhargava, A. Y. (2016). *Grokking algorithms: An illustrated guide\n",
        "    for programmers and other curious people.* Manning. Chapter 6, 10,\n",
        "    11.\n",
        "\n",
        "-   Cormen, T. H. (Ed.). (2009). *Introduction to algorithms* (3rd ed).\n",
        "    MIT Press. Chapter 12 and 20.\n",
        "\n",
        "-   Horton, D., & Liu, D. (2023, November 19). *CSC148 Lecture Notes*.\n",
        "    https://www.teach.cs.toronto.edu/~csc148h/winter/notes/"
      ]
    }
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