diff --git a/README.md b/README.md index 2d3d96b..e76b099 100644 --- a/README.md +++ b/README.md @@ -208,6 +208,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup | Determine the height of a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb) | | Create a binary search tree with minimal height from a sorted array | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_min/bst_min_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_min/bst_min_solution.ipynb) | | Create a linked list for each level of a binary tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_level_lists/tree_level_lists_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_level_lists/tree_level_lists_solution.ipynb) | +| Check if a binary tree is balanced | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_solution.ipynb) | | Implement a binary search tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_solution.ipynb) | | Implement depth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_solution.ipynb) | | Implement breadth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_bfs/bfs_solution.ipynb) | @@ -217,7 +218,6 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup | Determine the lowest common ancestor of two nodes | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Transform a binary tree into a heap | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Implement a right and left rotation on a tree | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | -| Check if a binary tree is balanced | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Check if a binary tree is binary search tree | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Add a challenge | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | diff --git a/graphs_trees/check_balance/__init__.py b/graphs_trees/check_balance/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/graphs_trees/check_balance/check_balance_challenge.ipynb b/graphs_trees/check_balance/check_balance_challenge.ipynb new file mode 100644 index 0000000..3f13284 --- /dev/null +++ b/graphs_trees/check_balance/check_balance_challenge.ipynb @@ -0,0 +1,180 @@ +{ + "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": [ + "# Challenge Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Check if a binary tree is balanced.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)\n", + "* [Solution Notebook](#Solution-Notebook)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?\n", + " * Yes\n", + "* Can we assume we already have a Node class with an insert method?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* 5, 3, 8, 1, 4 -> Yes\n", + "* 5, 3, 8, 9, 10 -> No" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_solution.ipynb). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run ../bst/bst.py\n", + "%load ../bst/bst.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def check_balance(root):\n", + " # TODO: Implement me\n", + " pass" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**The following unit test is expected to fail until you solve the challenge.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# %load test_check_balance.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class TestCheckBalance(object):\n", + "\n", + " def test_check_balance(self):\n", + " node = Node(5)\n", + " insert(node, 3)\n", + " insert(node, 8)\n", + " insert(node, 1)\n", + " insert(node, 4)\n", + " assert_equal(check_balance(node), True)\n", + "\n", + " node = Node(5)\n", + " insert(node, 3)\n", + " insert(node, 8)\n", + " insert(node, 9)\n", + " insert(node, 10)\n", + " assert_equal(check_balance(node), False)\n", + "\n", + " print('Success: test_check_balance')\n", + "\n", + "\n", + "def main():\n", + " test = TestCheckBalance()\n", + " test.test_check_balance()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_solution.ipynb) for a discussion on algorithms and code solutions." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/graphs_trees/check_balance/check_balance_solution.ipynb b/graphs_trees/check_balance/check_balance_solution.ipynb new file mode 100644 index 0000000..5c91c88 --- /dev/null +++ b/graphs_trees/check_balance/check_balance_solution.ipynb @@ -0,0 +1,218 @@ +{ + "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: Check if a binary tree is balanced.\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", + "* Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?\n", + " * Yes\n", + "* Can we assume we already have a Node class with an insert method?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* 5, 3, 8, 1, 4 -> Yes\n", + "* 5, 3, 8, 9, 10 -> No" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "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", + "\n", + "However, we could check whether the tree is balanced while also checking for the heights.\n", + "\n", + "* Base case: If the root is None, return 0\n", + "* Check the height of `root.left`, if -1, return -1\n", + "* Check the height of `root.right`, if -1, return -1\n", + "* If the height differences is greater than 1, return -1\n", + "* Otherwise, return 1 + max(left height, right height)\n", + " \n", + "Complexity:\n", + "* Time: O(n)\n", + "* Space: O(log n)" + ] + }, + { + "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 check_balance(root):\n", + " if check_height(root) == -1:\n", + " return False\n", + " else:\n", + " return True\n", + "\n", + "def check_height(root):\n", + " if root is None:\n", + " return 0\n", + " left_height = check_height(root.left)\n", + " if left_height == -1:\n", + " return -1\n", + " right_height = check_height(root.right)\n", + " if right_height == -1:\n", + " return -1\n", + " diff_height = left_height - right_height\n", + " if abs(diff_height) > 1:\n", + " return -1\n", + " else:\n", + " return 1 + max(left_height, right_height)" + ] + }, + { + "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_check_balance.py\n" + ] + } + ], + "source": [ + "%%writefile test_check_balance.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class TestCheckBalance(object):\n", + "\n", + " def test_check_balance(self):\n", + " node = Node(5)\n", + " insert(node, 3)\n", + " insert(node, 8)\n", + " insert(node, 1)\n", + " insert(node, 4)\n", + " assert_equal(check_balance(node), True)\n", + "\n", + " node = Node(5)\n", + " insert(node, 3)\n", + " insert(node, 8)\n", + " insert(node, 9)\n", + " insert(node, 10)\n", + " assert_equal(check_balance(node), False)\n", + "\n", + " print('Success: test_check_balance')\n", + "\n", + "\n", + "def main():\n", + " test = TestCheckBalance()\n", + " test.test_check_balance()\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_check_balance\n" + ] + } + ], + "source": [ + "%run -i test_check_balance.py" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/graphs_trees/check_balance/test_check_balance.py b/graphs_trees/check_balance/test_check_balance.py new file mode 100644 index 0000000..b63de5c --- /dev/null +++ b/graphs_trees/check_balance/test_check_balance.py @@ -0,0 +1,30 @@ +from nose.tools import assert_equal + + +class TestCheckBalance(object): + + def test_check_balance(self): + node = Node(5) + insert(node, 3) + insert(node, 8) + insert(node, 1) + insert(node, 4) + assert_equal(check_balance(node), True) + + node = Node(5) + insert(node, 3) + insert(node, 8) + insert(node, 9) + insert(node, 10) + assert_equal(check_balance(node), False) + + print('Success: test_check_balance') + + +def main(): + test = TestCheckBalance() + test.test_check_balance() + + +if __name__ == '__main__': + main() \ No newline at end of file