interactive-coding-challenges/graphs_trees/bst/bst_solution.ipynb
2017-02-09 05:20:53 -05:00

302 lines
7.2 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 binary search tree with an insert method.\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 insert None values?\n",
" * No\n",
"* Can we assume we are working with valid integers?\n",
" * Yes\n",
"* Can we assume all left descendents <= n < all right descendents?\n",
" * Yes\n",
"* Do we have to keep track of the parent nodes?\n",
" * This is optional\n",
"* Can we assume this fits in memory?\n",
" * Yes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"### Insert\n",
"\n",
"Insert will be tested through the following traversal:\n",
"\n",
"### In-Order Traversal\n",
"\n",
"* 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8\n",
"* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5\n",
"\n",
"If the `root` input is `None`, return a tree with the only element being the new root node.\n",
"\n",
"You do not have to code the in-order traversal, it is part of the unit test."
]
},
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"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"### Insert\n",
"\n",
"* If the root is None, return Node(data)\n",
"* If the data is <= the current node's data\n",
" * If the current node's left child is None, set it to Node(data)\n",
" * Else, recursively call insert on the left child\n",
"* Else\n",
" * If the current node's right child is None, set it to Node(data)\n",
" * Else, recursively call insert on the right child\n",
"\n",
"Complexity:\n",
"\n",
"* Time: O(h), where h is the height of the tree\n",
" * In a balanced tree, the height is O(log(n))\n",
" * In the worst case we have a linked list structure with O(n)\n",
"* Space: O(m), where m is the recursion depth, or O(1) if using an iterative approach"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting bst.py\n"
]
}
],
"source": [
"%%writefile bst.py\n",
"class Node(object):\n",
"\n",
" def __init__(self, data):\n",
" self.data = data\n",
" self.left = None\n",
" self.right = None\n",
" self.parent = None\n",
"\n",
" def __repr__(self):\n",
" return str(self.data)\n",
"\n",
"\n",
"class Bst(object):\n",
"\n",
" def __init__(self, root=None):\n",
" self.root = root\n",
"\n",
" def insert(self, data):\n",
" if data is None:\n",
" raise TypeError('data cannot be None')\n",
" if self.root is None:\n",
" self.root = Node(data)\n",
" return self.root\n",
" else:\n",
" return self._insert(self.root, data)\n",
"\n",
" def _insert(self, node, data):\n",
" if node is None:\n",
" return Node(data)\n",
" if data <= node.data:\n",
" if node.left is None:\n",
" node.left = self._insert(node.left, data)\n",
" node.left.parent = node\n",
" return node.left\n",
" else:\n",
" return self._insert(node.left, data)\n",
" else:\n",
" if node.right is None:\n",
" node.right = self._insert(node.right, data)\n",
" node.right.parent = node\n",
" return node.right\n",
" else:\n",
" return self._insert(node.right, data)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%run bst.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unit Test"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%run dfs.py"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%run ../utils/results.py"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting test_bst.py\n"
]
}
],
"source": [
"%%writefile test_bst.py\n",
"from nose.tools import assert_equal\n",
"\n",
"\n",
"class TestTree(object):\n",
"\n",
" def __init__(self):\n",
" self.results = Results()\n",
"\n",
" def test_tree_one(self):\n",
" bst = Bst()\n",
" bst.insert(5)\n",
" bst.insert(2)\n",
" bst.insert(8)\n",
" bst.insert(1)\n",
" bst.insert(3)\n",
" in_order_traversal(bst.root, self.results.add_result)\n",
" assert_equal(str(self.results), '[1, 2, 3, 5, 8]')\n",
" self.results.clear_results()\n",
"\n",
" def test_tree_two(self):\n",
" bst = Bst()\n",
" bst.insert(1)\n",
" bst.insert(2)\n",
" bst.insert(3)\n",
" bst.insert(4)\n",
" bst.insert(5)\n",
" in_order_traversal(bst.root, self.results.add_result)\n",
" assert_equal(str(self.results), '[1, 2, 3, 4, 5]')\n",
"\n",
" print('Success: test_tree')\n",
"\n",
"\n",
"def main():\n",
" test = TestTree()\n",
" test.test_tree_one()\n",
" test.test_tree_two()\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" main()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Success: test_tree\n"
]
}
],
"source": [
"%run -i test_bst.py"
]
}
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