mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
419 lines
12 KiB
Python
419 lines
12 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 trie with find, insert, remove, and list_words methods.\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 assume we are working with strings?\n",
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" * Yes\n",
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"* Are the strings in ASCII?\n",
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" * Yes\n",
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"* Should `find` only match exact words with a terminating character?\n",
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" * Yes\n",
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"* Should `list_words` only return words with a terminating character?\n",
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" * Yes\n",
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"* Can we assume this fits 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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"<pre>\n",
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"\n",
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"root node is denoted by ''\n",
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"\n",
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" ''\n",
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" / | \\\n",
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" h a* m\n",
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" / \\ \\ \\\n",
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" a e* t* e*\n",
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" / \\ / \\\n",
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" s* t* n* t*\n",
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" /\n",
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" s*\n",
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"\n",
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"find\n",
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"\n",
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"* Find on an empty trie\n",
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"* Find non-matching\n",
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"* Find matching\n",
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"\n",
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"insert\n",
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"\n",
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"* Insert on empty trie\n",
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"* Insert to make a leaf terminator char\n",
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"* Insert to extend an existing terminator char\n",
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"\n",
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"remove\n",
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"\n",
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"* Remove me\n",
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"* Remove mens\n",
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"* Remove a\n",
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"* Remove has\n",
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"\n",
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"list_words\n",
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"\n",
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"* List empty\n",
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"* List general case\n",
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"</pre>\n",
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"\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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"## Algorithm\n",
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"\n",
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"### find\n",
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"\n",
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"* Set node to the root\n",
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"* For each char in the input word\n",
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" * Check the current node's children to see if it contains the char\n",
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" * If a child has the char, set node to the child\n",
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" * Else, return None\n",
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"* Return the last child node if it has a terminator, else None\n",
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"\n",
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"Complexity:\n",
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"* Time: O(m), where m is the length of the word\n",
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"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
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"\n",
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"### insert\n",
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"\n",
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"* set node to the root\n",
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"* For each char in the input word\n",
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" * Check the current node's children to see if it contains the char\n",
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" * If a child has the char, set node to the child\n",
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" * Else, insert a new node with the char\n",
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" * Update children and parents\n",
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"* Set the last node as a terminating node\n",
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"\n",
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"Complexity:\n",
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"* Time: O(m), where m is the length of the word\n",
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"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
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"\n",
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"### remove\n",
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"\n",
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"* Determine the matching terminating node by calling the find method\n",
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"* If the matching node has children, remove the terminator to prevent orphaning its children\n",
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"* Set the parent node to the matching node's parent\n",
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"* We'll be looping up the parent chain to propagate the delete\n",
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"* While the parent is valid\n",
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" * If the node has children\n",
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" * Return to prevent orphaning its remaining children\n",
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" * If the node is a terminating node and it isn't the original matching node from the find call\n",
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" * Return to prevent deleting this additional valid word\n",
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" * Remove the parent node's child entry matching the node\n",
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" * Set the node to the parent\n",
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" * Set the parent to the parent's parent\n",
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"\n",
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"Complexity:\n",
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"* Time: O(m+h), where where m is the length of the word and h is the tree height\n",
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"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
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"\n",
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"### list_words\n",
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"\n",
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"* Do a pre-order traversal, passing down the current word\n",
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" * When you reach a terminating node, add it to the list of results\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n)\n",
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"* Space: O(h) for the recursion depth (tree height), 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 trie.py\n"
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]
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}
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],
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"source": [
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"%%writefile trie.py\n",
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"from collections import OrderedDict\n",
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"\n",
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"\n",
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"class Node(object):\n",
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"\n",
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" def __init__(self, key, parent=None, terminates=False):\n",
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" self.key = key\n",
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" self.terminates = False\n",
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" self.parent = parent\n",
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" self.children = {}\n",
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"\n",
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"\n",
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"class Trie(object):\n",
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"\n",
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" def __init__(self):\n",
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" self.root = Node('')\n",
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"\n",
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" def find(self, word):\n",
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" if word is None:\n",
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" raise TypeError('word cannot be None')\n",
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" node = self.root\n",
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" for char in word:\n",
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" if char in node.children:\n",
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" node = node.children[char]\n",
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" else:\n",
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" return None\n",
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" return node if node.terminates else None\n",
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"\n",
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" def insert(self, word):\n",
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" if word is None:\n",
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" raise TypeError('word cannot be None')\n",
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" node = self.root\n",
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" parent = None\n",
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" for char in word:\n",
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" if char in node.children:\n",
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" node = node.children[char]\n",
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" else:\n",
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" node.children[char] = Node(char, parent=node)\n",
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" node = node.children[char]\n",
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" node.terminates = True\n",
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"\n",
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" def remove(self, word):\n",
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" if word is None:\n",
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" raise TypeError('word cannot be None')\n",
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" node = self.find(word)\n",
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" if node is None:\n",
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" raise KeyError('word does not exist')\n",
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" node.terminates = False\n",
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" parent = node.parent\n",
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" while parent is not None:\n",
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" # As we are propagating the delete up the \n",
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" # parents, if this node has children, stop\n",
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" # here to prevent orphaning its children.\n",
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" # Or\n",
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" # if this node is a terminating node that is\n",
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" # not the terminating node of the input word, \n",
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" # stop to prevent removing the associated word.\n",
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" if node.children or node.terminates:\n",
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" return\n",
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" del parent.children[node.key]\n",
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" node = parent\n",
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" parent = parent.parent\n",
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"\n",
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" def list_words(self):\n",
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" result = []\n",
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" curr_word = ''\n",
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" self._list_words(self.root, curr_word, result)\n",
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" return result\n",
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"\n",
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" def _list_words(self, node, curr_word, result):\n",
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" if node is None:\n",
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" return\n",
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" for key, child in node.children.items():\n",
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" if child.terminates:\n",
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" result.append(curr_word + key)\n",
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" self._list_words(child, curr_word + key, result)"
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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 trie.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": 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_trie.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_trie.py\n",
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"from nose.tools import assert_true\n",
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"from nose.tools import raises\n",
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"\n",
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"\n",
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"class TestTrie(object): \n",
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"\n",
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" def test_trie(self):\n",
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" trie = Trie()\n",
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"\n",
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" print('Test: Insert')\n",
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" words = ['a', 'at', 'has', 'hat', 'he',\n",
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" 'me', 'men', 'mens', 'met']\n",
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" for word in words:\n",
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" trie.insert(word)\n",
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" for word in trie.list_words():\n",
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" assert_true(trie.find(word) is not None)\n",
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" \n",
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" print('Test: Remove me')\n",
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" trie.remove('me')\n",
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" words_removed = ['me']\n",
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" words = ['a', 'at', 'has', 'hat', 'he',\n",
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" 'men', 'mens', 'met']\n",
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" for word in words:\n",
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" assert_true(trie.find(word) is not None)\n",
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" for word in words_removed:\n",
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" assert_true(trie.find(word) is None)\n",
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"\n",
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" print('Test: Remove mens')\n",
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" trie.remove('mens')\n",
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" words_removed = ['me', 'mens']\n",
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" words = ['a', 'at', 'has', 'hat', 'he',\n",
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" 'men', 'met']\n",
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" for word in words:\n",
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" assert_true(trie.find(word) is not None)\n",
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" for word in words_removed:\n",
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" assert_true(trie.find(word) is None)\n",
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"\n",
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" print('Test: Remove a')\n",
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" trie.remove('a')\n",
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" words_removed = ['a', 'me', 'mens']\n",
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" words = ['at', 'has', 'hat', 'he',\n",
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" 'men', 'met']\n",
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" for word in words:\n",
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" assert_true(trie.find(word) is not None)\n",
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" for word in words_removed:\n",
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" assert_true(trie.find(word) is None)\n",
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"\n",
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" print('Test: Remove has')\n",
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" trie.remove('has')\n",
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" words_removed = ['a', 'has', 'me', 'mens']\n",
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" words = ['at', 'hat', 'he',\n",
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" 'men', 'met']\n",
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" for word in words:\n",
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" assert_true(trie.find(word) is not None)\n",
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" for word in words_removed:\n",
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" assert_true(trie.find(word) is None)\n",
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"\n",
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" print('Success: test_trie')\n",
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"\n",
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" @raises(Exception)\n",
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" def test_trie_remove_invalid(self):\n",
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" print('Test: Remove from empty trie')\n",
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" trie = Trie()\n",
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" assert_true(trie.remove('foo') is None) \n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestTrie()\n",
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" test.test_trie()\n",
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" test.test_trie_remove_invalid()\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": 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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Test: Insert\n",
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"Test: Remove me\n",
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"Test: Remove mens\n",
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"Test: Remove a\n",
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"Test: Remove has\n",
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"Success: test_trie\n",
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"Test: Remove from empty trie\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_trie.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": "3.4.3"
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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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