{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fdcf04c6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Searching, Removing From, and Balancing Binary Search Trees\n",
    "\n",
    "**CS 66: Introduction to Computer Science II**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10964bce",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A post-class survey on your thoughts on ChatGPT\n",
    "\n",
    "Please fill this out\n",
    "\n",
    "[https://forms.gle/E6FKsKtvDkw1QeQt7](https://forms.gle/E6FKsKtvDkw1QeQt7)\n",
    "\n",
    "Reminder - your name will be removed before we look at your answers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa72fac7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## References for this lecture\n",
    "\n",
    "Problem Solving with Algorithms and Data Structures using Python\n",
    "\n",
    "Sections 7.11 - 7.14: [https://runestone.academy/runestone/books/published/pythonds/Trees/toctree.html](https://runestone.academy/runestone/books/published/pythonds/Trees/toctree.html)\n"
   ]
  },
  {
   "attachments": {
    "simpleBST.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "c241e67c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Review: Binary Search Tree Nodes\n",
    "\n",
    "BST Nodes have at most 2 children, called _left child_ and _right child_\n",
    "\n",
    "Nodes in left subtree have value less than this node\n",
    "\n",
    "Nodes in right subtree have value more than this node\n",
    "\n",
    "This is true for every node!\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:simpleBST.png\" width=\"350\"/>\n",
    "</div>\n",
    "</center>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52822f1d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Binary Search Tree Code from last time\n",
    "\n",
    "Here's the code we came up with in class last time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fc336878",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4(2(None,None),7(None,9(None,None)))\n",
      "  2 4  7  9\n"
     ]
    }
   ],
   "source": [
    "class BSTNode:\n",
    "    def __init__(self,initdata):\n",
    "        self.data = initdata\n",
    "        self.left = None\n",
    "        self.right = None\n",
    "\n",
    "        \n",
    "    def __repr__(self):\n",
    "        return repr(self.data)+\"(\"+repr(self.left)+\",\"+repr(self.right)+\")\"\n",
    "        \n",
    "        \n",
    "    def __str__(self):\n",
    "        str_rep = \"\"\n",
    "        if self.left != None:\n",
    "            str_rep += \" \"+str(self.left)\n",
    "        str_rep += \" \"+str(self.data)\n",
    "        if self.right != None:\n",
    "            str_rep += \" \"+str(self.right)\n",
    "        return str_rep\n",
    "            \n",
    "        \n",
    "    def getData(self):\n",
    "        return self.data\n",
    "\n",
    "    def setData(self,newdata):\n",
    "        self.data = newdata\n",
    "        \n",
    "    def getLeft(self):\n",
    "        return self.left\n",
    "\n",
    "    def setLeft(self,newleft):\n",
    "        self.left = newleft\n",
    "        \n",
    "    def getRight(self):\n",
    "        return self.right\n",
    "\n",
    "    def setRight(self,newright):\n",
    "        self.right = newright\n",
    "        \n",
    "    #put this method into BSTNode class\n",
    "    def add(self,new_val):\n",
    "        #implement the code here\n",
    "        \n",
    "        if new_val < self.data:\n",
    "            if self.left == None:\n",
    "                new_node = BSTNode(new_val)\n",
    "                self.setLeft( new_node  )\n",
    "            else:\n",
    "                self.getLeft().add(new_val)\n",
    "        elif new_val > self.data:\n",
    "            if self.right == None:\n",
    "                new_node = BSTNode(new_val)\n",
    "                self.setRight( new_node )\n",
    "            else:\n",
    "                self.getRight().add(new_val)\n",
    "        else:\n",
    "            raise Exception(\"trying to add duplicate \"+str(new_val))\n",
    "                \n",
    "        \n",
    "        \n",
    "class BSTSet:\n",
    "    def __init__(self):\n",
    "        self.__root = None #start with an empty tree!\n",
    "        \n",
    "    def add(self,new_val):\n",
    "        if self.__root == None:\n",
    "            self.__root = BSTNode(new_val)\n",
    "        else:\n",
    "            self.__root.add(new_val)\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return repr(self.__root)\n",
    "    \n",
    "    def __str__(self):\n",
    "        return str(self.__root)\n",
    "            \n",
    "myset = BSTSet()\n",
    "myset.add(4)\n",
    "myset.add(7)\n",
    "myset.add(2)\n",
    "myset.add(9)\n",
    "print(repr(myset))\n",
    "print(str(myset))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "969d0a37",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Group Activity Problem 1\n",
    "\n",
    "Implement a `search` method in the `BSTNode` class - again use recursion.\n",
    "\n",
    "Write the associated method in `BSTSet` (suggestion: call it `__contains__` in `BSTSet` so that you can use it with the `in` operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db92e670",
   "metadata": {},
   "outputs": [],
   "source": [
    "myset = BSTSet()\n",
    "myset.add(4)\n",
    "myset.add(7)\n",
    "myset.add(2)\n",
    "myset.add(9)\n",
    "\n",
    "print( 7 in myset ) #should be True\n",
    "print( 1 in myset ) #should be False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85fbdd67",
   "metadata": {},
   "source": [
    "## Group Activity Problem 2\n",
    "\n",
    "What would the tree look like in a worst-case search? So then what is the computational complexity of your search? What about `add`?\n",
    "\n",
    "After you a good guess, check out [https://runestone.academy/ns/books/published/pythonds/Trees/SearchTreeAnalysis.html](https://runestone.academy/ns/books/published/pythonds/Trees/SearchTreeAnalysis.html) to see if you agree with the book."
   ]
  },
  {
   "attachments": {
    "bstdel1.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d06f6d1f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Removing Items\n",
    "\n",
    "Removing nodes is the most difficult part.\n",
    "\n",
    "Three cases to consider:\n",
    "1. The node has no children\n",
    "    * set the reference to it from the parent to None\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:bstdel1.png\" width=\"700\"/>\n",
    "</div>\n",
    "</center>\n"
   ]
  },
  {
   "attachments": {
    "bstdel2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "b199610c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. The node has 1 child\n",
    "    * set the reference from the parent to the 1 child\n",
    "    \n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:bstdel2.png\" width=\"700\"/>\n",
    "</div>\n",
    "</center>"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "06dc9d42",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "3. The node has 2 children\n",
    "    * replacee this node's value with that of its successor\n",
    "    * delete the node that the successor value came from\n",
    "  \n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:bstdel3.png\" width=\"700\"/>\n",
    "</div>\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "007a846d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## Other Considerations\n",
    "\n",
    "* the code will look different depending on whether the node being removed is itself a left child, a right child, or the root\n",
    "* we haven't been keeping track of the number of items - how could wee do that\n",
    "* we _might_ be able to make a BST to implement an _ordered list_ ADT (defind here: [https://runestone.academy/ns/books/published/pythonds/BasicDS/TheOrderedListAbstractDataType.html](https://runestone.academy/ns/books/published/pythonds/BasicDS/TheOrderedListAbstractDataType.html) ). \n",
    "    * The main difficulty is implementing an __index__ method - can you find the number of items in the tree that are _less than_ a given item?"
   ]
  },
  {
   "attachments": {
    "skewedTree.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "8b03f703",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Unbalanced Binary Search Trees\n",
    "\n",
    "In the worst case, a BST could be completely skewed in one direction\n",
    "\n",
    "All operations: $O(n)$\n",
    "\n",
    "\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:skewedTree.png\" width=\"300\"/>\n",
    "</div>\n",
    "</center>\n"
   ]
  },
  {
   "attachments": {
    "unbalanced.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "aaa7d4ff",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Measuring Balance at Each Node\n",
    "\n",
    "$balanceFactor = height(leftSubTree) - height(rightSubTree)$\n",
    "\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:unbalanced.png\" width=\"300\"/>\n",
    "</div>\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89de53c4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## AVL Trees\n",
    "\n",
    "__Inventors:__ G.M. Adelson-Velskii and E.M. Landis\n",
    "\n",
    "__Idea:__ balance factor is only allowed to be 0, 1, or -1\n",
    "\n",
    "__Approach:__ Whenever you add or remove items, if the balance factor is > 1 or < -1, perform _rotations_ to get it back in balance (check all nodes back up to the root)\n",
    "\n",
    "__Result:__ The tree will bee guaranteed to have a height of at most $1.44*\\log_2 N$\n",
    "\n",
    "`add`, `search`, and `remove` will run in $O(\\log N)$ time"
   ]
  },
  {
   "attachments": {
    "simpleunbalanced.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9d8821fd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A simple left rotation\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:simpleunbalanced.png\" width=\"500\"/>\n",
    "</div>\n",
    "</center>"
   ]
  },
  {
   "attachments": {
    "rightrotate1.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "95e84025",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A more complicated right rotation\n",
    "\n",
    "In this example we \n",
    "1. promote C in place of E\n",
    "2. move C's right child (D) and make it into E's left child\n",
    "3. make E the new right child of C\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:rightrotate1.png\" width=\"550\"/>\n",
    "</div>\n",
    "</center>"
   ]
  },
  {
   "attachments": {
    "hardunbalanced.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "5204bce6",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Almost there...\n",
    "\n",
    "balanceFactor 2 -> right rotation\n",
    "\n",
    "balanceFactor -2 -> left rotation\n",
    "\n",
    "Problem:\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:hardunbalanced.png\" width=\"150\"/>\n",
    "</div>\n",
    "</center>\n"
   ]
  },
  {
   "attachments": {
    "badrotate.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "348cc12f",
   "metadata": {},
   "source": [
    "After left rotation:\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:badrotate.png\" width=\"150\"/>\n",
    "</div>\n",
    "</center>"
   ]
  },
  {
   "attachments": {
    "rotatelr.png": {
     "image/png": 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"
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    "Solution\n",
    "\n",
    "\n",
    "$balanceFactor = -2$ and right child's $balanceFactor=1$, do right rotation on right child then left rotation at this node\n",
    "\n",
    "$balanceFactor = 2$ and left child's $balanceFactor=-1$, do left rotation on left child then right rotation at this node\n",
    "\n",
    "<center>\n",
    "<div>\n",
    "<img src=\"attachment:rotatelr.png\" width=\"500\"/>\n",
    "</div>\n",
    "</center>\n"
   ]
  },
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    "## Summary of Different Set Implementations\n",
    "\n",
    "Which data structure should you use to implement a __Set__?\n",
    "\n",
    "_Note: Maps are similar_ [https://runestone.academy/ns/books/published/pythonds/Trees/SummaryofMapADTImplementations.html](https://runestone.academy/ns/books/published/pythonds/Trees/SummaryofMapADTImplementations.html)\n",
    "\n",
    "<table>\n",
    "\n",
    "<colgroup>\n",
    "<col style=\"width: 15%\" />\n",
    "<col style=\"width: 26%\" />\n",
    "<col style=\"width: 14%\" />\n",
    "<col style=\"width: 22%\" />\n",
    "<col style=\"width: 23%\" />\n",
    "</colgroup>\n",
    "<thead>\n",
    "<tr class=\"row-odd\"><th class=\"head\"><p>Operation</p></th>\n",
    "<th class=\"head\"><p>Sorted List</p></th>\n",
    "<th class=\"head\"><p>Hash Table*</p></th>\n",
    "<th class=\"head\"><p>Binary Search Tree</p></th>\n",
    "<th class=\"head\"><p>AVL Tree</p></th>\n",
    "</tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr class=\"row-even\"><td><p>add</p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(n)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(1)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(n)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(\\log_2{n})\\)</span></p></td>\n",
    "</tr>\n",
    "<tr class=\"row-even\"><td><p>in (search)</p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(\\log_2{n})\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(1)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(n)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(\\log_2{n})\\)</span></p></td>\n",
    "</tr>\n",
    "<tr class=\"row-odd\"><td><p>remove</p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(n)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(1)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(n)\\)</span></p></td>\n",
    "<td><p><span class=\"math notranslate nohighlight\">\\(O(\\log_2{n})\\)</span></p></td>\n",
    "</tr>\n",
    "</tbody>\n",
    "</table>\n",
    "\n",
    "* Hash Table is actually $O(1)$ in the _average case_, but this is usually achievable with a good hash function and low load factor\n",
    "\n",
    "Is it ever better to use an AVL Tree instead of a Hash Table as the underlying data structure? Are there memory differences? What happens if you are adding and removing items a lot? What happens when the hash table fills up?"
   ]
  }
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