mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
234 lines
6.0 KiB
Python
234 lines
6.0 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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"<small><i>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).</i></small>"
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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: Check if a binary tree is balanced.\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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"* Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?\n",
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" * Yes\n",
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"* If this is called on a None input, should we return False?\n",
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" * Yes\n",
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"* Can we assume we already have a Node class with an insert method?\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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"* None -> No\n",
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"* 1 -> Yes\n",
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"* 5, 3, 8, 1, 4 -> Yes\n",
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"* 5, 3, 8, 9, 10 -> No"
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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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"The algorithm will be similar to where we get the height of a tree as seen in [here](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb).\n",
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"\n",
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"However, we could check whether the tree is balanced while also checking for the heights.\n",
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"\n",
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"* Base case: If the root is None, return 0\n",
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"* Recursively check whether the left sub tree is balanced, and get its maximum and minimum height\n",
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"* Recursively Check whether the right sub tree is balanced, and get its maximum and minimum height\n",
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"* Calculate the maximum height and minimum height of the current tree\n",
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"* If both sub-trees are balanced, and the maximum and minimum height of the current tree doesn't differ by more than 1, then the current tree is balanced. Otherwise, it is not\n",
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"* Return whether the current tree is balanced, and the maximum height and minimum height of the current tree\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), where h is the height of the tree"
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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": true
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},
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"outputs": [],
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"source": [
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"%run ../bst/bst.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": 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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"def _check_balance(root):\n",
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" if not root:\n",
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" return (True, 0, 0)\n",
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" left_balanced, left_min_h, left_max_h = _check_balance(root.left)\n",
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" right_balanced, right_min_h, right_max_h = _check_balance(root.right)\n",
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" min_h = 1 + min(left_min_h, right_min_h)\n",
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" max_h = 1 + max(left_max_h, right_max_h)\n",
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" balanced = left_balanced and right_balanced and abs(max_h-min_h) <= 1\n",
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" return (balanced, min_h, max_h)\n",
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"\n",
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"def check_balance(root):\n",
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" if root is None:\n",
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" return False\n",
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" balanced, _, _ = _check_balance(root)\n",
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" return balanced"
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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_check_balance.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_check_balance.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 TestCheckBalance(object):\n",
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"\n",
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" def test_check_balance(self):\n",
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" assert_equal(check_balance(None), False)\n",
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"\n",
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" node = Node(5)\n",
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" assert_equal(check_balance(node), True)\n",
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"\n",
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" insert(node, 3)\n",
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" insert(node, 8)\n",
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" insert(node, 1)\n",
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" insert(node, 4)\n",
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" assert_equal(check_balance(node), True)\n",
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"\n",
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" node = Node(5)\n",
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" insert(node, 3)\n",
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" insert(node, 8)\n",
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" insert(node, 9)\n",
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" insert(node, 10)\n",
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" assert_equal(check_balance(node), False)\n",
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"\n",
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" node = Node(3)\n",
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" insert(node, 2)\n",
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" insert(node, 1)\n",
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" insert(node, 5)\n",
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" insert(node, 4)\n",
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" insert(node, 6)\n",
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" insert(node, 7)\n",
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" assert_equal(check_balance(node), False)\n",
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"\n",
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" print('Success: test_check_balance')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestCheckBalance()\n",
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" test.test_check_balance()\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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"Success: test_check_balance\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_check_balance.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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