{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The BSTree data structure\n",
    "\n",
    "## Agenda\n",
    "\n",
    "- API\n",
    "- Implementation\n",
    "    - Search\n",
    "    - Addition\n",
    "    - Removal\n",
    "    - Iteration / Traversal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BSTree:\n",
    "    class Node:\n",
    "        def __init__(self, val, left=None, right=None):\n",
    "            self.val = val\n",
    "            self.left = left\n",
    "            self.right = right\n",
    "            \n",
    "    def __init__(self):\n",
    "        self.size = 0\n",
    "        self.root = None\n",
    "    \n",
    "    def add(self, val):\n",
    "        \"\"\"Adds `val` to this tree while maintaining BSTree properties.\"\"\"\n",
    "        assert(val not in self)\n",
    "        pass\n",
    "    \n",
    "    def __contains__(self, val):\n",
    "        \"\"\"Returns `True` if val is in this tree and `False` otherwise.\"\"\"\n",
    "        pass\n",
    "    \n",
    "    def __delitem__(self, val):\n",
    "        \"\"\"Removes `val` from this tree while maintaining BSTree properties.\"\"\"\n",
    "        assert(val in self)\n",
    "        pass\n",
    "    \n",
    "    def __iter__(self):\n",
    "        \"\"\"Returns an iterator over all the values in the tree, in ascending order.\"\"\"\n",
    "        pass\n",
    "\n",
    "    def __len__(self):\n",
    "        return self.size\n",
    "\n",
    "    def pprint(self, width=64):\n",
    "        \"\"\"Attempts to pretty-print this tree's contents.\"\"\"\n",
    "        height = self.height()\n",
    "        nodes  = [(self.root, 0)]\n",
    "        prev_level = 0\n",
    "        repr_str = ''\n",
    "        while nodes:\n",
    "            n,level = nodes.pop(0)\n",
    "            if prev_level != level:\n",
    "                prev_level = level\n",
    "                repr_str += '\\n'\n",
    "            if not n:\n",
    "                if level < height-1:\n",
    "                    nodes.extend([(None, level+1), (None, level+1)])\n",
    "                repr_str += '{val:^{width}}'.format(val='-', width=width//2**level)\n",
    "            elif n:\n",
    "                if n.left or level < height-1:\n",
    "                    nodes.append((n.left, level+1))\n",
    "                if n.right or level < height-1:\n",
    "                    nodes.append((n.right, level+1))\n",
    "                repr_str += '{val:^{width}}'.format(val=n.val, width=width//2**level)\n",
    "        print(repr_str)\n",
    "    \n",
    "    def height(self):\n",
    "        \"\"\"Returns the height of the longest branch of the tree.\"\"\"\n",
    "        def height_rec(t):\n",
    "            if not t:\n",
    "                return 0\n",
    "            else:\n",
    "                return max(1+height_rec(t.left), 1+height_rec(t.right))\n",
    "        return height_rec(self.root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "t.root = BSTree.Node(5,\n",
    "                    left=BSTree.Node(2),\n",
    "                    right=BSTree.Node(10))\n",
    "t.size = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t.height()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BSTree(BSTree):\n",
    "    def __contains__(self, val):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "t.root = BSTree.Node(5,\n",
    "                    left=BSTree.Node(2),\n",
    "                    right=BSTree.Node(10))\n",
    "t.size = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "5 in t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BSTree(BSTree):\n",
    "    def add(self, val):\n",
    "        assert(val not in self)\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "t = BSTree()\n",
    "vals = list(range(5))\n",
    "random.shuffle(vals)\n",
    "for x in vals:\n",
    "    t.add(x)\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "t = BSTree()\n",
    "vals = list(range(1, 10, 2))\n",
    "random.shuffle(vals)\n",
    "for x in vals:\n",
    "    t.add(x)\n",
    "\n",
    "assert(all(x in t for x in range(1, 10, 2)))\n",
    "assert(all(x not in t for x in range(0, 12, 2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Removal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BSTree(BSTree):\n",
    "    def __delitem__(self, val):\n",
    "        assert(val in self)\n",
    "        # deal with relatively simple cases first!\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "for x in [10, 5, 15, 2, 17]:\n",
    "    t.add(x)\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "del t[2]\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "for x in [10, 5, 15, 2, 17]:\n",
    "    t.add(x)\n",
    "del t[5]\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "for x in [10, 5, 15, 2, 17]:\n",
    "    t.add(x)\n",
    "del t[15]\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BSTree(BSTree):\n",
    "    def __delitem__(self, val):\n",
    "        # fully working delete\n",
    "        assert(val in self)\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "for x in [10, 5, 2, 7, 9, 8, 1, 15, 12, 18]:\n",
    "    t.add(x)\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "del t[15]\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "for x in [10, 5, 2, 7, 9, 8, 1, 15, 12, 18]:\n",
    "    t.add(x)\n",
    "del t[5]\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = BSTree()\n",
    "for x in [10, 5, 2, 7, 9, 8, 1, 15, 12, 18]:\n",
    "    t.add(x)\n",
    "del t[10]\n",
    "t.pprint()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iteration / Traversal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BSTree(BSTree):\n",
    "    def __iter__(self):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "t = BSTree()\n",
    "vals = list(range(20))\n",
    "random.shuffle(vals)\n",
    "for x in vals:\n",
    "    t.add(x)\n",
    "for x in t:\n",
    "    print(x)"
   ]
  }
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