Binary_and_AVL_Trees.ipynb

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    "## Binary search trees (BSTs) and AVL trees\n",
    "\n",
    "Jacob L. Fine\n",
    "\n",
    "June 23rd, 2024\n",
    "\n",
    "A binary search tree (BST) is a data structure that can store a list of integers as a rooted binary tree, where each node on the BST has anywhere from zero to two children nodes. The fundamental property of the BST is that for each value stored at each node, the value is greater than every value on the left substree and less than every value on the right subtree. No two nodes can have the same value.\n",
    "\n",
    "BSTs can be useful for searching for a given value in a list of values, by making a series of binary decisions at each node, i.e., whether our query value is greater than, less than, or equal to the value present at a given node. The search space is therefore conveniently halved at each step. Based on the outcome of this decision, we move down in the tree until we reach our value, unless it is not present in the tree. \n",
    "\n",
    "A BST can thus used to perform a binary search, which has a average-case time complexity of O(log n) and a worst-case time complexity of O(n). One of the downsides of a BST is that our tree may become 'unbalanced' where one subtree a depth much greater than any other subtree in the graph. Under such conditions, it may be desirable to 'balance' the tree based on the relative depths of the subtrees present at a given node each step in the algorithm. This is the basis of self-balancing binary search trees, which include AVL trees and red-black trees, for instance.\n",
    "\n",
    "To solve the balancing problem, Adelson-Velsky and Landis proposed a self-balancing binary search tree, named after them: the AVL tree. Before conducting a search on a BST, we must balance the tree using the method of Adelson-Velsky and Landis to construct an AVL tree. The balancing procedure involves ensuring that the height difference between the left and right subtrees of any node is no greater than one. We iteratively rearrange the tree until this criterion is met, guaranteeing a balanced structure where leaf nodes have similar depths. This balance significantly improves operations such as searches, insertions, and deletions, and attains a worst-case time complexity of O(log n); an improvement over the BST's O(n). The method used for searching is the same as in a BST, with the crucial difference being whether the BST was balanced before the search.\n",
    "\n",
    "We will construct BSTs and AVL trees below, and use perform search operations on lists of numbers for varying input sizes, and measure runtimes. "
   ]
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   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Binary Search Tree (BST)\n",
    "\n",
    "import time\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# creating the node object, we give it the properties of having left and right children (only 2 children total, since its binary). We give it a value, which we will be calling 'key'\n",
    "class TreeNodeBST:\n",
    "    def __init__(self, key):\n",
    "        self.left = None\n",
    "        self.right = None\n",
    "        self.value = key\n",
    "\n",
    "# we are going to place every element in a random list of numbers onto a BST\n",
    "# we will iterate through each key and compare its magnitude to each node and place it on the left or right (or further down) depending on the comparisons\n",
    "class BST:\n",
    "    # we first initialize the node  node\n",
    "    def __init__(self):\n",
    "        self.node = None\n",
    "\n",
    "    def insert(self, key):  \n",
    "        # first, if the node is empty, we add the key from the random list of numbers to it.\n",
    "        if self.node is None:\n",
    "            self.node = TreeNodeBST(key)\n",
    "        # otherwise, we call the helper function\n",
    "        else:\n",
    "            self._insert(self.node, key)\n",
    "\n",
    "    def _insert(self, node, key):\n",
    "        # we compare the value of the new to-be-added key to the current value present in the node.\n",
    "        # consistent with the definition of a BST, if this new value is less than the current value, we want it on the left subtree of the current node, so do the following...\n",
    "        if key < node.value:\n",
    "            # we place the new value on the left child of the current node if the left child is empty\n",
    "            if node.left is None:\n",
    "                node.left = TreeNodeBST(key)\n",
    "            # if the left child is not empty, we will call the function again (recursion) until we reach an empty node or leaf node\n",
    "            else:\n",
    "                self._insert(node.left, key)\n",
    "        else:\n",
    "            # if the new to-be-added key is not less than the current value, we want it on the right subtree, so do the following...\n",
    "            # if the right child node is empty, fill it with that value\n",
    "            if node.right is None:\n",
    "                node.right = TreeNodeBST(key)\n",
    "            # otherwise, call the function again until we reach an empty node or leaf node\n",
    "            else:\n",
    "                self._insert(node.right, key)\n",
    "\n",
    "    def search(self, key):\n",
    "        return self._search(self.node, key)\n",
    "\n",
    "    def _search(self, node, key):\n",
    "        # we will keep looking through the tree by making binary decisions at each node\n",
    "        # if the node is empty (i.e., our key wasn't in the tree) or the node has our key, we return the node\n",
    "        if node is None or node.value == key:\n",
    "            return node\n",
    "        # this is our binary decision: if the key we are searching for is less than the current value at the node, because of the BST property, it must be on the left subtree\n",
    "        if key < node.value:\n",
    "            return self._search(node.left, key)\n",
    "        # otherwise, it must be on the right subtree\n",
    "        return self._search(node.right, key)\n",
    "\n",
    "\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# AVL trees\n",
    "\n",
    "class TreeNodeAVL:\n",
    "    # we initialize a node as having properties left child, right child, value, and a height. Each node starts with height of 1, and when we create our tree, we will use recrusion to define heights of each node\n",
    "    def __init__(self, key):\n",
    "        self.left = None\n",
    "        self.right = None\n",
    "        self.value = key\n",
    "        self.height = 1\n",
    "\n",
    "\n",
    "# the AVL tree class\n",
    "class AVLTree:\n",
    "    # similar to BST, we define the method to insert new keys into the tree\n",
    "    def insert(self, node, key):\n",
    "        # first, if the node is empty, we fill it with the key, otherwise...\n",
    "        # before considering children nodes, we always ask first if our node is empty.\n",
    "        if not node:\n",
    "            return TreeNodeAVL(key)\n",
    "        # as with the BST, if the new key to add to the tree is less than the current node value, we want it on the left subtree so our current node is greater than it to satisfy the BST property.\n",
    "        elif key < node.value:\n",
    "            node.left = self.insert(node.left, key)\n",
    "            # otherwise, we put it on the right subtree\n",
    "        else:\n",
    "            node.right = self.insert(node.right, key)\n",
    "        \n",
    "        # we now update the height of our node based on which of its children has a greater height, so its 1 + (the child node with a greater height)\n",
    "\n",
    "        node.height = 1 + max(self.determine_height(node.left), self.determine_height(node.right))\n",
    "\n",
    "        # we define the balance factor of the node using the getBalance function, which is simply the differnece in heights of the children nodes\n",
    "        balance = self.getBalance(node)\n",
    "\n",
    "        # the four possible ways to rearrange the node structure based on the balance factor and the magnitude of the value in the current node (2 x 2 = 4)\n",
    "        if balance > 1 and key < node.left.value:\n",
    "            return self.rotate_right(node)\n",
    "        if balance < -1 and key > node.right.value:\n",
    "            return self.rotate_left(node)\n",
    "        if balance > 1 and key > node.left.value:\n",
    "            node.left = self.rotate_left(node.left)\n",
    "            return self.rotate_right(node)\n",
    "        if balance < -1 and key < node.right.value:\n",
    "            node.right = self.rotate_right(node.right)\n",
    "            return self.rotate_left(node)\n",
    "        # we return the node, if we don't need to rotate it\n",
    "        return node\n",
    "\n",
    "    # there are two types of rotations: left and right\n",
    "    def rotate_right(self, z):\n",
    "        # select the left child of the current node (z)\n",
    "        y = z.left\n",
    "        # select the right child of the left child of the current node (U)\n",
    "        U = y.right\n",
    "        # then set the right child of the left child (y) of the current node to the current node (z)\n",
    "        y.right = z\n",
    "        # set the left child of the current node (z) to U (the original right child of y)\n",
    "        z.left = U\n",
    "        # next, update the heights of the nodes z and y accordingly, based on their children\n",
    "        z.height = 1 + max(self.determine_height(z.left), self.determine_height(z.right))\n",
    "        y.height = 1 + max(self.determine_height(y.left), self.determine_height(y.right))\n",
    "        # we return y, which is the new node of the subtree after the rotation (it was initially the left child of the current node z)\n",
    "        return y\n",
    "\n",
    "\n",
    "    def rotate_left(self, z):\n",
    "        # select the right child of the current node (z)\n",
    "        y = z.right\n",
    "        # we select the left child of the right child of the current node (V)\n",
    "        V = y.left\n",
    "        # set the left child of the right child (y) of the current node to the current node\n",
    "        y.left = z\n",
    "        # set the right node of the current node to V, the original left child of y\n",
    "        z.right = V\n",
    "        # next, update the heights of the nodes z and y accordingly, based on their children\n",
    "        z.height = 1 + max(self.determine_height(z.left), self.determine_height(z.right))\n",
    "        y.height = 1 + max(self.determine_height(y.left), self.determine_height(y.right))\n",
    "        return y\n",
    "    # gets the height of a given node\n",
    "    def determine_height(self, node):\n",
    "        if not node:\n",
    "            return 0\n",
    "        return node.height\n",
    "\n",
    "    # the way to get the balance; simply the difference in heights of the children nodes\n",
    "    def getBalance(self, node):\n",
    "        if not node:\n",
    "            return 0\n",
    "        return self.determine_height(node.left) - self.determine_height(node.right)\n",
    "\n",
    "    # the standard binary search method, same as for our non-AVL BST\n",
    "    def search(self, node, key):\n",
    "        if not node or node.value == key:\n",
    "            return node\n",
    "        if key < node.value:\n",
    "            return self.search(node.left, key)\n",
    "        return self.search(node.right, key)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
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",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for measuring runtimes\n",
    "def measure_runtime(tree_type, elements_to_add):\n",
    "    # the function will be called for BST and AVL, so we compute run times accordingly\n",
    "    if tree_type == 'AVL':\n",
    "        tree = AVLTree()\n",
    "        node  = None\n",
    "        # we use the time library to record the start time and insert time\n",
    "        start_time = time.time()\n",
    "        for element in elements_to_add:\n",
    "            node  = tree.insert(node, element)\n",
    "        insert_time = time.time() - start_time # the time to make all the insertions for each node in the element_list. Same procedures as below\n",
    "\n",
    "        start_time = time.time()\n",
    "        for element in elements_to_add:\n",
    "            tree.search(node , element)\n",
    "        search_time = time.time() - start_time\n",
    "\n",
    "    elif tree_type == 'BST':\n",
    "        tree = BST()\n",
    "        start_time = time.time()\n",
    "        for element in elements_to_add:\n",
    "            tree.insert(element)\n",
    "        insert_time = time.time() - start_time\n",
    "\n",
    "        start_time = time.time()\n",
    "        for element in elements_to_add:\n",
    "            tree.search(element)\n",
    "        search_time = time.time() - start_time\n",
    "\n",
    "    return insert_time, search_time\n",
    "\n",
    "sizes = [100, 500, 1000, 5000, 10000]\n",
    "\n",
    "# stores the values of insertion times for different sizes, for the BSL and AVL trees\n",
    "result_times = {'AVL': {'insert': [], 'search': []}, 'BST': {'insert': [], 'search': []}}\n",
    "\n",
    "for size in sizes:\n",
    "    # generates the list of elements to add based on the size\n",
    "    elements_to_add = random.sample(range(1, size * 10), size)\n",
    "    # calls the functions to measure runtime\n",
    "    insert_time_AVL, search_time_AVL = measure_runtime('AVL', elements_to_add)\n",
    "    insert_time_BST, search_time_BST = measure_runtime('BST', elements_to_add)\n",
    "\n",
    "    # updates the values accordingly for each tree and method being tested\n",
    "\n",
    "    result_times['AVL']['insert'].append(insert_time_AVL)\n",
    "    result_times['AVL']['search'].append(search_time_AVL)\n",
    "    result_times['BST']['insert'].append(insert_time_BST)\n",
    "    result_times['BST']['search'].append(search_time_BST)\n",
    "\n",
    "# Plotting the result_times\n",
    "plt.figure(figsize=(12, 6))\n",
    "\n",
    "# plots insertion times\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(sizes, result_times['AVL']['insert'], marker='o', label='AVL Insert')\n",
    "plt.plot(sizes, result_times['BST']['insert'], marker='o', label='BST Insert')\n",
    "plt.xlabel('Number of elements (n)')\n",
    "plt.ylabel('Time (s)')\n",
    "plt.title('Run time comparison: insertions')\n",
    "plt.legend()\n",
    "\n",
    "# plots search times\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(sizes, result_times['AVL']['search'], marker='o', label='AVL Search')\n",
    "plt.plot(sizes, result_times['BST']['search'], marker='o', label='BST Search')\n",
    "plt.xlabel('Number of elements (n)')\n",
    "plt.ylabel('Time (s)')\n",
    "plt.title('Run time comparison: searches')\n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is shown, while it may take longer to construct the AVL tree, due to the balancing component of the algorithm to insert values, we can see that it consistently outperforms the BST for searching for elements."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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