interactive-coding-challenges/graphs_trees/trie/trie_solution.ipynb
2017-03-30 05:38:16 -04:00

419 lines
12 KiB
Python

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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)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solution Notebook"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem: Implement a trie with find, insert, remove, and list_words methods.\n",
"\n",
"* [Constraints](#Constraints)\n",
"* [Test Cases](#Test-Cases)\n",
"* [Algorithm](#Algorithm)\n",
"* [Code](#Code)\n",
"* [Unit Test](#Unit-Test)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Constraints\n",
"\n",
"* Can we assume we are working with strings?\n",
" * Yes\n",
"* Are the strings in ASCII?\n",
" * Yes\n",
"* Should `find` only match exact words with a terminating character?\n",
" * Yes\n",
"* Should `list_words` only return words with a terminating character?\n",
" * Yes\n",
"* Can we assume this fits memory?\n",
" * Yes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"<pre>\n",
"\n",
"root node is denoted by ''\n",
"\n",
" ''\n",
" / | \\\n",
" h a* m\n",
" / \\ \\ \\\n",
" a e* t* e*\n",
" / \\ / \\\n",
" s* t* n* t*\n",
" /\n",
" s*\n",
"\n",
"find\n",
"\n",
"* Find on an empty trie\n",
"* Find non-matching\n",
"* Find matching\n",
"\n",
"insert\n",
"\n",
"* Insert on empty trie\n",
"* Insert to make a leaf terminator char\n",
"* Insert to extend an existing terminator char\n",
"\n",
"remove\n",
"\n",
"* Remove me\n",
"* Remove mens\n",
"* Remove a\n",
"* Remove has\n",
"\n",
"list_words\n",
"\n",
"* List empty\n",
"* List general case\n",
"</pre>\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"### find\n",
"\n",
"* Set node to the root\n",
"* For each char in the input word\n",
" * Check the current node's children to see if it contains the char\n",
" * If a child has the char, set node to the child\n",
" * Else, return None\n",
"* Return the last child node if it has a terminator, else None\n",
"\n",
"Complexity:\n",
"* Time: O(m), where m is the length of the word\n",
"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
"\n",
"### insert\n",
"\n",
"* set node to the root\n",
"* For each char in the input word\n",
" * Check the current node's children to see if it contains the char\n",
" * If a child has the char, set node to the child\n",
" * Else, insert a new node with the char\n",
" * Update children and parents\n",
"* Set the last node as a terminating node\n",
"\n",
"Complexity:\n",
"* Time: O(m), where m is the length of the word\n",
"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
"\n",
"### remove\n",
"\n",
"* Determine the matching terminating node by calling the find method\n",
"* If the matching node has children, remove the terminator to prevent orphaning its children\n",
"* Set the parent node to the matching node's parent\n",
"* We'll be looping up the parent chain to propagate the delete\n",
"* While the parent is valid\n",
" * If the node has children\n",
" * Return to prevent orphaning its remaining children\n",
" * If the node is a terminating node and it isn't the original matching node from the find call\n",
" * Return to prevent deleting this additional valid word\n",
" * Remove the parent node's child entry matching the node\n",
" * Set the node to the parent\n",
" * Set the parent to the parent's parent\n",
"\n",
"Complexity:\n",
"* Time: O(m+h), where where m is the length of the word and h is the tree height\n",
"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
"\n",
"### list_words\n",
"\n",
"* Do a pre-order traversal, passing down the current word\n",
" * When you reach a terminating node, add it to the list of results\n",
"\n",
"Complexity:\n",
"* Time: O(n)\n",
"* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting trie.py\n"
]
}
],
"source": [
"%%writefile trie.py\n",
"from collections import OrderedDict\n",
"\n",
"\n",
"class Node(object):\n",
"\n",
" def __init__(self, key, parent=None, terminates=False):\n",
" self.key = key\n",
" self.terminates = False\n",
" self.parent = parent\n",
" self.children = {}\n",
"\n",
"\n",
"class Trie(object):\n",
"\n",
" def __init__(self):\n",
" self.root = Node('')\n",
"\n",
" def find(self, word):\n",
" if word is None:\n",
" raise TypeError('word cannot be None')\n",
" node = self.root\n",
" for char in word:\n",
" if char in node.children:\n",
" node = node.children[char]\n",
" else:\n",
" return None\n",
" return node if node.terminates else None\n",
"\n",
" def insert(self, word):\n",
" if word is None:\n",
" raise TypeError('word cannot be None')\n",
" node = self.root\n",
" parent = None\n",
" for char in word:\n",
" if char in node.children:\n",
" node = node.children[char]\n",
" else:\n",
" node.children[char] = Node(char, parent=node)\n",
" node = node.children[char]\n",
" node.terminates = True\n",
"\n",
" def remove(self, word):\n",
" if word is None:\n",
" raise TypeError('word cannot be None')\n",
" node = self.find(word)\n",
" if node is None:\n",
" raise KeyError('word does not exist')\n",
" node.terminates = False\n",
" parent = node.parent\n",
" while parent is not None:\n",
" # As we are propagating the delete up the \n",
" # parents, if this node has children, stop\n",
" # here to prevent orphaning its children.\n",
" # Or\n",
" # if this node is a terminating node that is\n",
" # not the terminating node of the input word, \n",
" # stop to prevent removing the associated word.\n",
" if node.children or node.terminates:\n",
" return\n",
" del parent.children[node.key]\n",
" node = parent\n",
" parent = parent.parent\n",
"\n",
" def list_words(self):\n",
" result = []\n",
" curr_word = ''\n",
" self._list_words(self.root, curr_word, result)\n",
" return result\n",
"\n",
" def _list_words(self, node, curr_word, result):\n",
" if node is None:\n",
" return\n",
" for key, child in node.children.items():\n",
" if child.terminates:\n",
" result.append(curr_word + key)\n",
" self._list_words(child, curr_word + key, result)"
]
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{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
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"outputs": [],
"source": [
"%run trie.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unit Test"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting test_trie.py\n"
]
}
],
"source": [
"%%writefile test_trie.py\n",
"from nose.tools import assert_true\n",
"from nose.tools import raises\n",
"\n",
"\n",
"class TestTrie(object): \n",
"\n",
" def test_trie(self):\n",
" trie = Trie()\n",
"\n",
" print('Test: Insert')\n",
" words = ['a', 'at', 'has', 'hat', 'he',\n",
" 'me', 'men', 'mens', 'met']\n",
" for word in words:\n",
" trie.insert(word)\n",
" for word in trie.list_words():\n",
" assert_true(trie.find(word) is not None)\n",
" \n",
" print('Test: Remove me')\n",
" trie.remove('me')\n",
" words_removed = ['me']\n",
" words = ['a', 'at', 'has', 'hat', 'he',\n",
" 'men', 'mens', 'met']\n",
" for word in words:\n",
" assert_true(trie.find(word) is not None)\n",
" for word in words_removed:\n",
" assert_true(trie.find(word) is None)\n",
"\n",
" print('Test: Remove mens')\n",
" trie.remove('mens')\n",
" words_removed = ['me', 'mens']\n",
" words = ['a', 'at', 'has', 'hat', 'he',\n",
" 'men', 'met']\n",
" for word in words:\n",
" assert_true(trie.find(word) is not None)\n",
" for word in words_removed:\n",
" assert_true(trie.find(word) is None)\n",
"\n",
" print('Test: Remove a')\n",
" trie.remove('a')\n",
" words_removed = ['a', 'me', 'mens']\n",
" words = ['at', 'has', 'hat', 'he',\n",
" 'men', 'met']\n",
" for word in words:\n",
" assert_true(trie.find(word) is not None)\n",
" for word in words_removed:\n",
" assert_true(trie.find(word) is None)\n",
"\n",
" print('Test: Remove has')\n",
" trie.remove('has')\n",
" words_removed = ['a', 'has', 'me', 'mens']\n",
" words = ['at', 'hat', 'he',\n",
" 'men', 'met']\n",
" for word in words:\n",
" assert_true(trie.find(word) is not None)\n",
" for word in words_removed:\n",
" assert_true(trie.find(word) is None)\n",
"\n",
" print('Success: test_trie')\n",
"\n",
" @raises(Exception)\n",
" def test_trie_remove_invalid(self):\n",
" print('Test: Remove from empty trie')\n",
" trie = Trie()\n",
" assert_true(trie.remove('foo') is None) \n",
"\n",
"\n",
"def main():\n",
" test = TestTrie()\n",
" test.test_trie()\n",
" test.test_trie_remove_invalid()\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" main()"
]
},
{
"cell_type": "code",
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{
"name": "stdout",
"output_type": "stream",
"text": [
"Test: Insert\n",
"Test: Remove me\n",
"Test: Remove mens\n",
"Test: Remove a\n",
"Test: Remove has\n",
"Success: test_trie\n",
"Test: Remove from empty trie\n"
]
}
],
"source": [
"%run -i test_trie.py"
]
}
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