mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
508 lines
15 KiB
Plaintext
508 lines
15 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<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>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Implement a binary search tree with insert, delete, different traversals & max/min node values\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"* Is this a binary tree?\n",
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" * Yes\n",
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"* Is the root set to None initially?\n",
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" * Yes\n",
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"* Do we care if the tree is balanced?\n",
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" * No\n",
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"* What do we return for the traversals?\n",
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" * Return a list of the data in the desired order\n",
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"* What type of data can the tree hold?\n",
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" * Assume the tree only takes ints. In a realistic example, we'd use a hash table to convert other types to ints."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"### Insert \n",
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"\n",
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"* Always start with the root\n",
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"* If value is less than the root, go to the left child\n",
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"* if value is more than the root, go to the right child\n",
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"\n",
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"\n",
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"### Delete\n",
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"\n",
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"* Deleting a node from a binary tree is tricky. Make sure you arrange the tree correctly when deleting a node.\n",
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"* Here are some basic [instructions](http://www.algolist.net/Data_structures/Binary_search_tree/Removal)\n",
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"* If the value to delete isn't on the tree return False\n",
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"\n",
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"\n",
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"### Traverals \n",
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"\n",
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"* In order traversal -left, center, right\n",
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"* Pre order traversal - center, left, right\n",
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"* Post order traversal - left, right, center\n",
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"* Return list for all traverals \n",
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"\n",
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"### Max & Min\n",
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"* Find the max node in the binary search tree\n",
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"* Find the min node in the binary search tree\n",
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"\n",
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"### treeIsEmpty\n",
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"* check if the tree is empty\n",
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"\n",
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"\n",
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"## Algorithm\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"### Insert\n",
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"\n",
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"* If root is none, insert at root\n",
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"* Else\n",
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" * While node is not None\n",
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" * if value is less go left child\n",
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" * If value is more go right child\n",
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"\n",
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"\n",
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"* Time complexity: O(log(n))\n",
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"* Space complexity: O(n)\n",
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"\n",
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"### Min Node\n",
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"\n",
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"* Keep going to the left child until you reach None and return the value\n",
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"\n",
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"\n",
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"* Time complexity: O(log(n))\n",
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"* Space complexity: O(n)\n",
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"\n",
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"### Max Node\n",
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"\n",
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"* Keep going to the right child until you reach None and return the value\n",
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"\n",
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"\n",
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"* Time complexity: O(log(n))\n",
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"* Space complexity: O(n)\n",
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"\n",
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"### Traversals\n",
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"\n",
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"* In order\n",
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" * While the node is not None\n",
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" * Call left child recursively\n",
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" * Append data\n",
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" * Call right child recursively \n",
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" \n",
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"* Post order\n",
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" * While the node is not None\n",
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" * Call left child recursively\n",
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" * Call right child recursively \n",
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" * Append data\n",
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" \n",
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"* Pre order\n",
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" * While the node is not None\n",
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" * Append data\n",
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" * Call left child recursively\n",
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" * Call right child recursively \n",
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"\n",
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"\n",
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"* Time complexity: O(n) for all traversals\n",
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"* Space complexity: O(n)\n",
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"\n",
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"### Delete\n",
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"\n",
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"* First, find value to delete\n",
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"* If value is not in tree \n",
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" * Return False\n",
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"* If value found\n",
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" * Check if the node is a left child or right child\n",
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" * If node is left child\n",
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" * Find the biggest value in all the node's children and replace it with it\n",
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" * If node is right child\n",
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" * Find the smalles value in all the node's children and replace it with it\n",
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"\n",
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"\n",
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"* Time complexity: O(log(n))\n",
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"* Space complexity: O(n)\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting binary_search_tree.py\n"
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]
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}
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],
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"source": [
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"%%writefile binary_search_tree.py\n",
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"\n",
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"class Node (object):\n",
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"\tdef __init__ (self, data):\n",
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"\t\tself.data = data\n",
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"\t\tself.rightChild = None\n",
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"\t\tself.leftChild = None\n",
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"\n",
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"class BinaryTree (object):\n",
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"\tdef __init__ (self):\n",
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"\t\tself.root = None\n",
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"\n",
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"\tdef insert (self, newData):\n",
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"\t\tleaf = Node(newData)\n",
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"\n",
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"\t\tif self.root is None:\n",
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"\t\t\tself.root = leaf\n",
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"\t\telse:\n",
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"\t\t\tcurrent = self.root\n",
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"\t\t\tparent = self.root\n",
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"\t\t\twhile current is not None:\n",
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"\t\t\t\tparent = current\n",
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"\t\t\t\tif newData < current.data:\n",
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"\t\t\t\t\tcurrent = current.leftChild\n",
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"\t\t\t\telse:\n",
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"\t\t\t\t\tcurrent = current.rightChild\n",
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"\n",
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"\t\t\tif newData < parent.data:\n",
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"\t\t\t\tparent.leftChild = leaf\n",
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"\t\t\telse:\n",
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"\t\t\t\tparent.rightChild = leaf\n",
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"\n",
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"\t# returns false if the item to be deleted is not on the tree\n",
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"\tdef delete (self, data):\n",
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"\t\tcurrent = self.root\n",
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"\t\tparent = self.root\n",
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"\t\tisLeft = False\n",
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"\n",
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"\t\tif current is None:\n",
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"\t\t\treturn False\n",
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"\n",
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"\t\twhile current is not None and current.data is not data:\n",
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"\t\t\tparent = current\n",
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"\t\t\tif data < current.data:\n",
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"\t\t\t\tcurrent = current.leftChild\n",
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"\t\t\t\tisLeft = True \n",
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"\t\t\telse:\n",
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"\t\t\t\tcurrent = current.rightChild\n",
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"\t\t\t\tisLeft = False\n",
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"\n",
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"\t\tif current is None:\n",
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"\t\t\treturn False\n",
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"\n",
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"\t\tif current.leftChild is None and current.rightChild is None:\n",
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"\t\t\tif current is self.root:\n",
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"\t\t\t\tself.root = None\n",
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"\t\t\telif isLeft:\n",
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"\t\t\t\tparent.leftChild = None\n",
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"\t\t\telse:\n",
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"\t\t\t\tparent.rightChild = None\n",
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"\n",
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"\t\telif current.rightChild is None:\n",
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"\t\t\tif current is self.root:\n",
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"\t\t\t\tself.root = current.leftChild\n",
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"\t\t\telif isLeft:\n",
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"\t\t\t\tparent.leftChild = current.leftChild\n",
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"\t\t\telse:\n",
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"\t\t\t\tparent.rightChild = current.leftChild\n",
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"\n",
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"\t\telif current.rightChild is None:\n",
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"\t\t\tif current is self.root:\n",
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"\t\t\t\tself.root = current.rightChild\n",
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"\t\t\telif isLeft:\n",
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"\t\t\t\tparent.lChild = current.rightChild\n",
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"\t\t\telse:\n",
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"\t\t\t\tparent.rightChild = current.rightChild\n",
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"\n",
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"\t\telse:\n",
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"\t\t\tsuccesor = current.rightChild\n",
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"\t\t\tsuccesorParent = current\n",
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"\n",
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"\t\t\twhile succesor.leftChild is not None:\n",
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"\t\t\t\tsuccesorParent = succesor\n",
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"\t\t\t\tsuccesor = succesor.leftChild\n",
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"\n",
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"\t\t\tif current is self.root:\n",
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"\t\t\t\tself.root = succesor\n",
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"\t\t\telif isLeft:\n",
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"\t\t\t\tparent.leftChild = succesor\n",
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"\t\t\telse:\n",
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"\t\t\t\tparent.rightChild = succesor\n",
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"\n",
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"\t\t\tsuccesor.leftChild = current.leftChild\n",
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"\n",
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"\t\t\tif succesor is not current.rightChild:\n",
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"\t\t\t\tsuccesorParent.leftChild = succesor.rightChild\n",
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"\t\t\t\tsuccesor.rightChild = current.rightChild\n",
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"\n",
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"\t\treturn True \n",
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"\n",
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"\n",
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"\tdef minNode (self):\n",
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"\t\tcurrent = self.root\n",
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"\t\twhile current.leftChild is not None:\n",
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"\t\t\tcurrent = current.leftChild\n",
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"\n",
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"\t\treturn current.data\n",
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"\n",
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"\tdef maxNode (self):\n",
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"\t\tcurrent = self.root\n",
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"\t\twhile current.rightChild is not None:\n",
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"\t\t\tcurrent = current.rightChild\n",
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"\n",
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"\t\treturn current.data\n",
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"\n",
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"\tdef printPostOrder (self):\n",
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"\t\tglobal postOrder\n",
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"\t\tpostOrder = []\n",
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"\n",
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"\t\tdef PostOrder(node):\n",
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"\t\t\tif node is not None:\n",
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"\t\t\t\tPostOrder(node.leftChild)\n",
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"\t\t\t\tPostOrder(node.rightChild)\n",
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"\t\t\t\tpostOrder.append(node.data)\n",
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"\n",
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"\t\tPostOrder(self.root)\n",
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"\t\treturn postOrder\n",
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"\n",
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"\tdef printInOrder (self):\n",
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"\t\tglobal inOrder \n",
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"\t\tinOrder = []\n",
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"\n",
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"\t\tdef InOrder (node):\n",
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"\t\t\tif node is not None:\n",
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"\t\t\t\tInOrder(node.leftChild)\n",
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"\t\t\t\tinOrder.append(node.data)\n",
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"\t\t\t\tInOrder(node.rightChild)\n",
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"\n",
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"\t\tInOrder(self.root)\n",
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"\t\treturn inOrder\n",
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"\n",
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"\tdef printPreOrder (self):\n",
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"\t\tglobal preOrder\n",
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"\t\tpreOrder = []\n",
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"\n",
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"\t\tdef PreOrder (node):\n",
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"\t\t\tif node is not None:\n",
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"\t\t\t\tpreOrder.append(node.data)\n",
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"\t\t\t\tPreOrder(node.leftChild)\n",
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"\t\t\t\tPreOrder(node.rightChild)\n",
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"\n",
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"\t\tPreOrder(self.root)\n",
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"\t\treturn preOrder\n",
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"\n",
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"\tdef treeIsEmpty (self):\n",
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"\t\treturn self.root is None"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"%run binary_search_tree.py"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_binary_search_tree.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_binary_search_tree.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"class TestBinaryTree(BinaryTree):\n",
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"\n",
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"\tdef test_insert_traversals (self):\n",
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"\t\tmyTree = BinaryTree()\n",
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"\t\tmyTree2 = BinaryTree()\n",
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"\t\tfor num in [50, 30, 70, 10, 40, 60, 80, 7, 25, 38]:\n",
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"\t\t\tmyTree.insert(num)\n",
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"\t\t[myTree2.insert(num) for num in range (1, 100, 10)]\n",
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"\n",
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"\t\tprint(\"Test: insert checking with in order traversal\")\n",
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"\t\tassert_equal(myTree.printInOrder(), [7, 10, 25, 30, 38, 40, 50, 60, 70, 80])\n",
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"\t\tassert_equal(myTree2.printInOrder(), [1, 11, 21, 31, 41, 51, 61, 71, 81, 91])\n",
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"\t\tprint(\"Test: insert checking with post order traversal\")\n",
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"\t\tassert_equal(myTree.printPostOrder(), [7, 25, 10, 38, 40, 30, 60, 80, 70, 50])\n",
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"\t\tassert_equal(myTree2.printPostOrder(), [91, 81, 71, 61, 51, 41, 31, 21, 11, 1])\n",
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"\n",
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"\n",
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"\t\tprint(\"Test: insert checking with pre order traversal\")\n",
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"\t\tassert_equal(myTree.printPreOrder(), [50, 30, 10, 7, 25, 40, 38, 70, 60, 80])\n",
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"\t\tassert_equal(myTree2.printPreOrder(), [1, 11, 21, 31, 41, 51, 61, 71, 81, 91])\n",
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"\n",
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"\n",
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"\t\tprint(\"Success: test_insert_traversals\")\n",
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"\n",
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"\tdef test_max_min_nodes (self):\n",
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"\t\tmyTree = BinaryTree()\n",
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"\t\tmyTree.insert(5)\n",
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"\t\tmyTree.insert(1)\n",
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"\t\tmyTree.insert(21)\n",
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"\n",
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"\t\tprint(\"Test: max node\")\n",
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"\t\tassert_equal(myTree.maxNode(), 21)\n",
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"\t\tmyTree.insert(32)\n",
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"\t\tassert_equal(myTree.maxNode(), 32)\n",
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"\n",
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"\t\tprint(\"Test: min node\")\n",
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"\t\tassert_equal(myTree.minNode(), 1)\n",
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"\n",
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"\t\tprint(\"Test: min node inserting negative number\")\n",
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"\t\tmyTree.insert(-10)\n",
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"\t\tassert_equal(myTree.minNode(), -10)\n",
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"\n",
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"\t\tprint(\"Success: test_max_min_nodes\")\n",
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"\n",
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"\tdef test_delete (self):\n",
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"\t\tmyTree = BinaryTree()\n",
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"\t\tmyTree.insert(5)\n",
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"\n",
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"\t\tprint(\"Test: delete\")\n",
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"\t\tmyTree.delete(5)\n",
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"\t\tassert_equal(myTree.treeIsEmpty(), True)\n",
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"\t\t\n",
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"\t\tprint(\"Test: more complex deletions\")\n",
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"\t\t[myTree.insert(x) for x in range(1, 5)]\n",
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"\t\tmyTree.delete(2)\n",
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"\t\tassert_equal(myTree.root.rightChild.data, 3)\n",
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"\t\tprint(\"Test: delete invalid value\")\n",
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"\t\tassert_equal(myTree.delete(100), False)\n",
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"\n",
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"\n",
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"\t\tprint(\"Success: test_delete\")\n",
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"\n",
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"def main():\n",
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" testing = TestBinaryTree()\n",
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" testing.test_insert_traversals()\n",
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" testing.test_max_min_nodes()\n",
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" testing.test_delete()\n",
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" \n",
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"if __name__=='__main__':\n",
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" main()"
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]
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},
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|
{
|
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"cell_type": "code",
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|
"execution_count": 37,
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|
"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"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"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",
|
|
"version": "3.4.3"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 0
|
|
}
|