mirror of
https://github.com/donnemartin/interactive-coding-challenges
synced 2026-01-05 08:58:02 +00:00
Add bst successor challenge.
This commit is contained in:
Donne Martin
234
graphs_trees/bst_successor/bst_successor_solution.ipynb
Normal file
234
graphs_trees/bst_successor/bst_successor_solution.ipynb
Normal file
@@ -0,0 +1,234 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"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: Find the in-order successor of a given node in a binary search tree.\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",
|
||||
"* If there is no successor, do we return None?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume we already have a Node class that keeps track of parents?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"<pre>\n",
|
||||
" _5_\n",
|
||||
" / \\\n",
|
||||
" 3 8\n",
|
||||
" / \\ / \\\n",
|
||||
" 2 4 6 12\n",
|
||||
" / \\ / \\\n",
|
||||
" 1 7 10 15\n",
|
||||
" /\n",
|
||||
" 9\n",
|
||||
"\n",
|
||||
"In: 4 Out: 5\n",
|
||||
"In: 5 Out: 6\n",
|
||||
"In: 8 Out: 9\n",
|
||||
"In: 15 Out: None\n",
|
||||
"</pre>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Algorithm\n",
|
||||
"\n",
|
||||
"* If the node has a right subtree, return the left-most node in the right subtree\n",
|
||||
"* Else, go up until you find a node that is its parent's left node\n",
|
||||
" * If you get to the root (ie node.parent is None), return None\n",
|
||||
" * Else, return the parent\n",
|
||||
" \n",
|
||||
"Complexity:\n",
|
||||
"* Time: O(n)\n",
|
||||
"* Space: O(h), where h is the height of the tree"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Code"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%run ../bst/bst.py"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def left_most_node(node):\n",
|
||||
" if node is None:\n",
|
||||
" return\n",
|
||||
" if node.left is None:\n",
|
||||
" return node.data\n",
|
||||
" return left_most_node(node.left)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def bst_successor(node):\n",
|
||||
" if node is None:\n",
|
||||
" return\n",
|
||||
" if node.right is not None:\n",
|
||||
" return left_most_node(node.right)\n",
|
||||
" else:\n",
|
||||
" parent = node.parent\n",
|
||||
" while parent is not None and parent.left is not node:\n",
|
||||
" node = node.parent\n",
|
||||
" parent = node.parent\n",
|
||||
" if parent is None:\n",
|
||||
" return\n",
|
||||
" return parent.data"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Unit Test"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Overwriting test_bst_successor.py\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%%writefile test_bst_successor.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestBstSuccessor(object):\n",
|
||||
"\n",
|
||||
" def test_bst_successor(self):\n",
|
||||
" nodes = {}\n",
|
||||
" node = Node(5)\n",
|
||||
" nodes[5] = node\n",
|
||||
" nodes[3] = insert(node, 3)\n",
|
||||
" nodes[8] = insert(node, 8)\n",
|
||||
" nodes[2] = insert(node, 2)\n",
|
||||
" nodes[4] = insert(node, 4)\n",
|
||||
" nodes[6] = insert(node, 6)\n",
|
||||
" nodes[12] = insert(node, 12)\n",
|
||||
" nodes[1] = insert(node, 1)\n",
|
||||
" nodes[7] = insert(node, 7)\n",
|
||||
" nodes[10] = insert(node, 10)\n",
|
||||
" nodes[15] = insert(node, 15)\n",
|
||||
" nodes[9] = insert(node, 9)\n",
|
||||
"\n",
|
||||
" assert_equal(bst_successor(nodes[4]), 5)\n",
|
||||
" assert_equal(bst_successor(nodes[5]), 6)\n",
|
||||
" assert_equal(bst_successor(nodes[8]), 9)\n",
|
||||
" assert_equal(bst_successor(nodes[15]), None)\n",
|
||||
"\n",
|
||||
" print('Success: test_bst_successor')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestBstSuccessor()\n",
|
||||
" test.test_bst_successor()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
" main()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Success: test_bst_successor\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%run -i test_bst_successor.py"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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
|
||||
}
|
||||
Reference in New Issue
Block a user