{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small><i>This notebook was prepared by Marco Guajardo. Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Implement a binary search tree with insert, delete, different traversals & max/min node values\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)\n",
    "* [Solution Notebook](#Solution-Notebook)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "* Is this a binary tree?\n",
    "  * Yes\n",
    "* Is the root set to None initially?\n",
    "  * Yes\n",
    "* Do we care if the tree is balanced?\n",
    "  * No\n",
    "* What do we return for the traversals?\n",
    "  * Return a list of the data in the desired order\n",
    "* What type of data can the tree hold?\n",
    "  * Assume the tree only takes ints. In a realistic example, we'd use a hash table to convert other types to ints."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "### Insert \n",
    "\n",
    "* Always start with the root\n",
    "* If value is less than the root, go to the left child\n",
    "* if value is more than the root, go to the right child\n",
    "\n",
    "\n",
    "### Delete\n",
    "\n",
    "* Deleting a node from a binary tree is tricky. Make sure you arrange the tree correctly when deleting a node.\n",
    "* Here are some basic [instructions](http://www.algolist.net/Data_structures/Binary_search_tree/Removal)\n",
    "* If the value to delete isn't on the tree return False\n",
    "\n",
    "\n",
    "### Traverals \n",
    "\n",
    "* In order traversal -left, center, right\n",
    "* Pre order traversal - center, left, right\n",
    "* Post order traversal - left, right, center\n",
    "* Return list for all traverals \n",
    "\n",
    "### Max & Min\n",
    "* Find the max node in the binary search tree\n",
    "* Find the min node in the binary search tree\n",
    "\n",
    "### treeIsEmpty\n",
    "* check if the tree is empty\n",
    "\n",
    "\n",
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/binary_tree_implementation/binary_tree_solution.ipynb).  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### Insert\n",
    "\n",
    "* If root is none, insert at root\n",
    "* Else\n",
    "  * While node is not None\n",
    "      * if value is less go left child\n",
    "      * If value is more go right child\n",
    "\n",
    "\n",
    "* Time complexity: O(log(n))\n",
    "* Space complexity: O(n)\n",
    "\n",
    "### Min Node\n",
    "\n",
    "* Keep going to the left child until you reach None and return the value\n",
    "\n",
    "\n",
    "* Time complexity: O(log(n))\n",
    "* Space complexity: O(n)\n",
    "\n",
    "### Max Node\n",
    "\n",
    "* Keep going to the right child until you reach None and return the value\n",
    "\n",
    "\n",
    "* Time complexity: O(log(n))\n",
    "* Space complexity: O(n)\n",
    "\n",
    "### Traversals\n",
    "\n",
    "* In order\n",
    "  * While the node is not None\n",
    "      * Call left child recursively\n",
    "      * Append data\n",
    "      * Call right child recursively \n",
    "   \n",
    "* Post order\n",
    "  * While the node is not None\n",
    "      * Call left child recursively\n",
    "      * Call right child recursively \n",
    "      * Append data\n",
    " \n",
    "* Pre order\n",
    "  * While the node is not None\n",
    "      * Append data\n",
    "      * Call left child recursively\n",
    "      * Call right child recursively \n",
    "\n",
    "\n",
    "* Time complexity: O(n) for all traversals\n",
    "* Space complexity: O(n)\n",
    "\n",
    "### Delete\n",
    "\n",
    "* First, find value to delete\n",
    "* If value is not in tree \n",
    "  * Return False\n",
    "* If value found\n",
    "  * Check if the node is a left child or right child\n",
    "    * If node is left child\n",
    "      * Find the biggest value in all the node's children and replace it with it\n",
    "    * If node is right child\n",
    "      * Find the smalles value in all the node's children and replace it with it\n",
    "\n",
    "\n",
    "* Time complexity: O(log(n))\n",
    "* Space complexity: O(n)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting binary_search_tree.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile binary_search_tree.py\n",
    "\n",
    "class Node (object):\n",
    "\tdef __init__ (self, data):\n",
    "\t\tself.data = data\n",
    "\t\tself.rightChild = None\n",
    "\t\tself.leftChild = None\n",
    "\n",
    "class BinaryTree (object):\n",
    "\tdef __init__ (self):\n",
    "\t\tself.root = None\n",
    "\n",
    "\tdef insert (self, newData):\n",
    "\t\tleaf = Node(newData)\n",
    "\n",
    "\t\tif self.root is None:\n",
    "\t\t\tself.root = leaf\n",
    "\t\telse:\n",
    "\t\t\tcurrent = self.root\n",
    "\t\t\tparent = self.root\n",
    "\t\t\twhile current is not None:\n",
    "\t\t\t\tparent = current\n",
    "\t\t\t\tif newData < current.data:\n",
    "\t\t\t\t\tcurrent = current.leftChild\n",
    "\t\t\t\telse:\n",
    "\t\t\t\t\tcurrent = current.rightChild\n",
    "\n",
    "\t\t\tif newData < parent.data:\n",
    "\t\t\t\tparent.leftChild = leaf\n",
    "\t\t\telse:\n",
    "\t\t\t\tparent.rightChild = leaf\n",
    "\n",
    "\t# returns false if the item to be deleted is not on the tree\n",
    "\tdef delete (self, data):\n",
    "\t\tcurrent = self.root\n",
    "\t\tparent = self.root\n",
    "\t\tisLeft = False\n",
    "\n",
    "\t\tif current is None:\n",
    "\t\t\treturn False\n",
    "\n",
    "\t\twhile current is not None and current.data is not data:\n",
    "\t\t\tparent = current\n",
    "\t\t\tif data < current.data:\n",
    "\t\t\t\tcurrent = current.leftChild\n",
    "\t\t\t\tisLeft = True \n",
    "\t\t\telse:\n",
    "\t\t\t\tcurrent = current.rightChild\n",
    "\t\t\t\tisLeft = False\n",
    "\n",
    "\t\tif current is None:\n",
    "\t\t\treturn False\n",
    "\n",
    "\t\tif current.leftChild is None and current.rightChild is None:\n",
    "\t\t\tif current is self.root:\n",
    "\t\t\t\tself.root = None\n",
    "\t\t\telif isLeft:\n",
    "\t\t\t\tparent.leftChild = None\n",
    "\t\t\telse:\n",
    "\t\t\t\tparent.rightChild = None\n",
    "\n",
    "\t\telif current.rightChild is None:\n",
    "\t\t\tif current is self.root:\n",
    "\t\t\t\tself.root = current.leftChild\n",
    "\t\t\telif isLeft:\n",
    "\t\t\t\tparent.leftChild = current.leftChild\n",
    "\t\t\telse:\n",
    "\t\t\t\tparent.rightChild = current.leftChild\n",
    "\n",
    "\t\telif current.rightChild is None:\n",
    "\t\t\tif current is self.root:\n",
    "\t\t\t\tself.root = current.rightChild\n",
    "\t\t\telif isLeft:\n",
    "\t\t\t\tparent.lChild = current.rightChild\n",
    "\t\t\telse:\n",
    "\t\t\t\tparent.rightChild = current.rightChild\n",
    "\n",
    "\t\telse:\n",
    "\t\t\tsuccesor = current.rightChild\n",
    "\t\t\tsuccesorParent = current\n",
    "\n",
    "\t\t\twhile succesor.leftChild is not None:\n",
    "\t\t\t\tsuccesorParent = succesor\n",
    "\t\t\t\tsuccesor = succesor.leftChild\n",
    "\n",
    "\t\t\tif current is self.root:\n",
    "\t\t\t\tself.root = succesor\n",
    "\t\t\telif isLeft:\n",
    "\t\t\t\tparent.leftChild = succesor\n",
    "\t\t\telse:\n",
    "\t\t\t\tparent.rightChild = succesor\n",
    "\n",
    "\t\t\tsuccesor.leftChild = current.leftChild\n",
    "\n",
    "\t\t\tif succesor is not current.rightChild:\n",
    "\t\t\t\tsuccesorParent.leftChild = succesor.rightChild\n",
    "\t\t\t\tsuccesor.rightChild = current.rightChild\n",
    "\n",
    "\t\treturn True \n",
    "\n",
    "\n",
    "\tdef minNode (self):\n",
    "\t\tcurrent = self.root\n",
    "\t\twhile current.leftChild is not None:\n",
    "\t\t\tcurrent = current.leftChild\n",
    "\n",
    "\t\treturn current.data\n",
    "\n",
    "\tdef maxNode (self):\n",
    "\t\tcurrent = self.root\n",
    "\t\twhile current.rightChild is not None:\n",
    "\t\t\tcurrent = current.rightChild\n",
    "\n",
    "\t\treturn current.data\n",
    "\n",
    "\tdef printPostOrder (self):\n",
    "\t\tglobal postOrder\n",
    "\t\tpostOrder = []\n",
    "\n",
    "\t\tdef PostOrder(node):\n",
    "\t\t\tif node is not None:\n",
    "\t\t\t\tPostOrder(node.leftChild)\n",
    "\t\t\t\tPostOrder(node.rightChild)\n",
    "\t\t\t\tpostOrder.append(node.data)\n",
    "\n",
    "\t\tPostOrder(self.root)\n",
    "\t\treturn postOrder\n",
    "\n",
    "\tdef printInOrder (self):\n",
    "\t\tglobal inOrder \n",
    "\t\tinOrder = []\n",
    "\n",
    "\t\tdef InOrder (node):\n",
    "\t\t\tif node is not None:\n",
    "\t\t\t\tInOrder(node.leftChild)\n",
    "\t\t\t\tinOrder.append(node.data)\n",
    "\t\t\t\tInOrder(node.rightChild)\n",
    "\n",
    "\t\tInOrder(self.root)\n",
    "\t\treturn inOrder\n",
    "\n",
    "\tdef printPreOrder (self):\n",
    "\t\tglobal preOrder\n",
    "\t\tpreOrder = []\n",
    "\n",
    "\t\tdef PreOrder (node):\n",
    "\t\t\tif node is not None:\n",
    "\t\t\t\tpreOrder.append(node.data)\n",
    "\t\t\t\tPreOrder(node.leftChild)\n",
    "\t\t\t\tPreOrder(node.rightChild)\n",
    "\n",
    "\t\tPreOrder(self.root)\n",
    "\t\treturn preOrder\n",
    "\n",
    "\tdef treeIsEmpty (self):\n",
    "\t\treturn self.root is None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run binary_search_tree.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_binary_search_tree.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_binary_search_tree.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "class TestBinaryTree(object):\n",
    "\n",
    "\tdef test_insert_traversals (self):\n",
    "\t\tmyTree = BinaryTree()\n",
    "\t\tmyTree2 = BinaryTree()\n",
    "\t\tfor num in [50, 30, 70, 10, 40, 60, 80, 7, 25, 38]:\n",
    "\t\t\tmyTree.insert(num)\n",
    "\t\t[myTree2.insert(num) for num in range (1, 100, 10)]\n",
    "\n",
    "\t\tprint(\"Test: insert checking with in order traversal\")\n",
    "\t\texpectVal = [7, 10, 25, 30, 38, 40, 50, 60, 70, 80]\n",
    "\t\tassert_equal(myTree.printInOrder(), expectVal)\n",
    "\t\texpectVal = [1, 11, 21, 31, 41, 51, 61, 71, 81, 91]\n",
    "\t\tassert_equal(myTree2.printInOrder(), expectVal)\n",
    "\n",
    "\t\tprint(\"Test: insert checking with post order traversal\")\n",
    "\t\texpectVal = [7, 25, 10, 38, 40, 30, 60, 80, 70, 50]\n",
    "\t\tassert_equal(myTree.printPostOrder(), expectVal)\n",
    "\t\texpectVal = [91, 81, 71, 61, 51, 41, 31, 21, 11, 1]\n",
    "\t\tassert_equal(myTree2.printPostOrder(), expectVal)\n",
    "\n",
    "\n",
    "\t\tprint(\"Test: insert checking with pre order traversal\")\n",
    "\t\texpectVal = [50, 30, 10, 7, 25, 40, 38, 70, 60, 80]\n",
    "\t\tassert_equal(myTree.printPreOrder(), expectVal)\n",
    "\t\texpectVal = [1, 11, 21, 31, 41, 51, 61, 71, 81, 91]\n",
    "\t\tassert_equal(myTree2.printPreOrder(), expectVal)\n",
    "\n",
    "\n",
    "\t\tprint(\"Success: test_insert_traversals\")\n",
    "\n",
    "\tdef test_max_min_nodes (self):\n",
    "\t\tmyTree = BinaryTree()\n",
    "\t\tmyTree.insert(5)\n",
    "\t\tmyTree.insert(1)\n",
    "\t\tmyTree.insert(21)\n",
    "\n",
    "\t\tprint(\"Test: max node\")\n",
    "\t\tassert_equal(myTree.maxNode(), 21)\n",
    "\t\tmyTree.insert(32)\n",
    "\t\tassert_equal(myTree.maxNode(), 32)\n",
    "\n",
    "\t\tprint(\"Test: min node\")\n",
    "\t\tassert_equal(myTree.minNode(), 1)\n",
    "\n",
    "\t\tprint(\"Test: min node inserting negative number\")\n",
    "\t\tmyTree.insert(-10)\n",
    "\t\tassert_equal(myTree.minNode(), -10)\n",
    "\n",
    "\t\tprint(\"Success: test_max_min_nodes\")\n",
    "\n",
    "\tdef test_delete (self):\n",
    "\t\tmyTree = BinaryTree()\n",
    "\t\tmyTree.insert(5)\n",
    "\n",
    "\t\tprint(\"Test: delete\")\n",
    "\t\tmyTree.delete(5)\n",
    "\t\tassert_equal(myTree.treeIsEmpty(), True)\n",
    "\t\t\n",
    "\t\tprint(\"Test: more complex deletions\")\n",
    "\t\t[myTree.insert(x) for x in range(1, 5)]\n",
    "\t\tmyTree.delete(2)\n",
    "\t\tassert_equal(myTree.root.rightChild.data, 3)\n",
    "        \n",
    "\t\tprint(\"Test: delete invalid value\")\n",
    "\t\tassert_equal(myTree.delete(100), False)\n",
    "\n",
    "\n",
    "\t\tprint(\"Success: test_delete\")\n",
    "\n",
    "def main():\n",
    "    testing = TestBinaryTree()\n",
    "    testing.test_insert_traversals()\n",
    "    testing.test_max_min_nodes()\n",
    "    testing.test_delete()\n",
    "    \n",
    "if __name__=='__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: insert checking with in order traversal\n",
      "Test: insert checking with post order traversal\n",
      "Test: insert checking with pre order traversal\n",
      "Success: test_insert_traversals\n",
      "Test: max node\n",
      "Test: min node\n",
      "Test: min node inserting negative number\n",
      "Success: test_max_min_nodes\n",
      "Test: delete\n",
      "Test: more complex deletions\n",
      "Test: delete invalid value\n",
      "Success: test_delete\n"
     ]
    }
   ],
   "source": [
    "%run -i test_binary_search_tree.py"
   ]
  }
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