mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
302 lines
7.2 KiB
Python
302 lines
7.2 KiB
Python
{
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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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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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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 an insert method.\n",
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"\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)"
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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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"\n",
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"* Can we insert None values?\n",
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" * No\n",
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"* Can we assume we are working with valid integers?\n",
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" * Yes\n",
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"* Can we assume all left descendents <= n < all right descendents?\n",
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" * Yes\n",
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"* Do we have to keep track of the parent nodes?\n",
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" * This is optional\n",
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"* Can we assume this fits in memory?\n",
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" * Yes"
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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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"Insert will be tested through the following traversal:\n",
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"\n",
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"### In-Order Traversal\n",
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"\n",
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"* 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8\n",
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"* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5\n",
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"\n",
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"If the `root` input is `None`, return a tree with the only element being the new root node.\n",
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"\n",
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"You do not have to code the in-order traversal, it is part of the unit test."
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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 the root is None, return Node(data)\n",
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"* If the data is <= the current node's data\n",
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" * If the current node's left child is None, set it to Node(data)\n",
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" * Else, recursively call insert on the left child\n",
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"* Else\n",
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" * If the current node's right child is None, set it to Node(data)\n",
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" * Else, recursively call insert on the right child\n",
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"\n",
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"Complexity:\n",
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"\n",
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"* Time: O(h), where h is the height of the tree\n",
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" * In a balanced tree, the height is O(nlogn)\n",
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" * In the worst case we have a linked list structure with O(n)\n",
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"* Space: O(m), where m is the recursion depth, or O(1) if using an iterative approach"
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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": 1,
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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 bst.py\n"
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]
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}
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],
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"source": [
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"%%writefile bst.py\n",
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"class Node(object):\n",
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"\n",
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" def __init__(self, data):\n",
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" self.data = data\n",
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" self.left = None\n",
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" self.right = None\n",
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" self.parent = None\n",
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"\n",
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" def __repr__(self):\n",
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" return str(self.data)\n",
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"\n",
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"\n",
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"class Bst(object):\n",
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"\n",
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" def __init__(self, root=None):\n",
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" self.root = root\n",
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"\n",
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" def insert(self, data):\n",
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" if data is None:\n",
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" raise Exception('Data cannot be None')\n",
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" if self.root is None:\n",
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" self.root = Node(data)\n",
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" return self.root\n",
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" return self._insert(self.root, data)\n",
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"\n",
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" def _insert(self, node, data):\n",
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" # Constraint: Assume we are working with valid ints\n",
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" if node is None:\n",
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" return Node(data)\n",
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" if data <= node.data:\n",
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" if node.left is None:\n",
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" node.left = self._insert(node.left, data)\n",
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" node.left.parent = node\n",
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" return node.left\n",
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" else:\n",
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" return self._insert(node.left, data)\n",
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" else:\n",
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" if node.right is None:\n",
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" node.right = self._insert(node.right, data)\n",
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" node.right.parent = node\n",
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" return node.right\n",
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" else:\n",
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" return self._insert(node.right, data)"
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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": 2,
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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 bst.py"
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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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"## Unit Test"
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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": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%run dfs.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": 4,
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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 ../utils/results.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": 5,
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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_bst.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_bst.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestTree(object):\n",
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"\n",
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" def __init__(self):\n",
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" self.results = Results()\n",
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"\n",
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" def test_tree_one(self):\n",
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" bst = Bst()\n",
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" bst.insert(5)\n",
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" bst.insert(2)\n",
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" bst.insert(8)\n",
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" bst.insert(1)\n",
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" bst.insert(3)\n",
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" in_order_traversal(bst.root, self.results.add_result)\n",
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" assert_equal(str(self.results), '[1, 2, 3, 5, 8]')\n",
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" self.results.clear_results()\n",
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"\n",
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" def test_tree_two(self):\n",
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" bst = Bst()\n",
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" bst.insert(1)\n",
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" bst.insert(2)\n",
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" bst.insert(3)\n",
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" bst.insert(4)\n",
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" bst.insert(5)\n",
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" in_order_traversal(bst.root, self.results.add_result)\n",
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" assert_equal(str(self.results), '[1, 2, 3, 4, 5]')\n",
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"\n",
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" print('Success: test_tree')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestTree()\n",
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" test.test_tree_one()\n",
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" test.test_tree_two()\n",
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"\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": 6,
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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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"Success: test_tree\n"
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]
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}
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],
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"source": [
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"%run -i test_bst.py"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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