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Added tree height challenge.

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Donne Martin 2015-08-02 10:53:35 -04:00
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README.md
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@ -206,8 +206,8 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
| 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 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 (pre-, in-, post-order) | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_dfs/dfs_solution.ipynb) | | Implement depth-first search (pre-, in-, post-order) | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_dfs/dfs_solution.ipynb) |
| Implement breadth-first search | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_solution.ipynb) | | Implement breadth-first search | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_bfs/bfs_solution.ipynb) |
| Determine the height of a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb) |
| Print a tree using pre-order traversal without recursion | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) | | Print a tree using pre-order traversal without recursion | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
| Determine the height of 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) |
| 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) | | 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) | | 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) | | 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) |

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graphs_trees/tree_height/__init__.py Normal file
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graphs_trees/tree_height/height_challenge.ipynb Normal file
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<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>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Challenge Notebook"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem: Determine the height of a tree.\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 this a binary tree?\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 -> 1\n",
"* 5, 2, 8, 1, 3 -> 3"
]
},
{
"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/tree_height/height_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 height(node):\n",
" # TODO: Implement me"
]
},
{
"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_height.py\n",
"from __future__ import print_function\n",
"from nose.tools import assert_equal\n",
"\n",
"\n",
"class TestHeight(object):\n",
"\n",
" def test_height(self):\n",
" root = Node(5)\n",
" assert_equal(height(root), 1)\n",
" insert(root, 2)\n",
" insert(root, 8)\n",
" insert(root, 1)\n",
" insert(root, 3)\n",
" assert_equal(height(root), 3)\n",
"\n",
" print('Success: test_height')\n",
"\n",
"\n",
"def main():\n",
" test = TestHeight()\n",
" test.test_height()\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/tree_height/height_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
}

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graphs_trees/tree_height/height_solution.ipynb Normal file
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@ -0,0 +1,193 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<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>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solution Notebook"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem: Determine the height of a 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",
"* Is this a binary tree?\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 -> 1\n",
"* 5, 2, 8, 1, 3 -> 3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"We'll use a recursive algorithm.\n",
"\n",
"* If the current node is None, return 0\n",
"* Else, return 1 + the maximum height of the left or right children\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 height(node):\n",
" if node is None:\n",
" return 0\n",
" return 1 + max(height(node.left), \n",
" height(node.right))"
]
},
{
"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_height.py\n"
]
}
],
"source": [
"%%writefile test_height.py\n",
"from __future__ import print_function\n",
"from nose.tools import assert_equal\n",
"\n",
"\n",
"class TestHeight(object):\n",
"\n",
" def test_height(self):\n",
" root = Node(5)\n",
" assert_equal(height(root), 1)\n",
" insert(root, 2)\n",
" insert(root, 8)\n",
" insert(root, 1)\n",
" insert(root, 3)\n",
" assert_equal(height(root), 3)\n",
"\n",
" print('Success: test_height')\n",
"\n",
"\n",
"def main():\n",
" test = TestHeight()\n",
" test.test_height()\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_height\n"
]
}
],
"source": [
"%run -i test_height.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
}

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graphs_trees/tree_height/test_height.py Normal file
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from __future__ import print_function
from nose.tools import assert_equal
class TestHeight(object):
def test_height(self):
root = Node(5)
assert_equal(height(root), 1)
insert(root, 2)
insert(root, 8)
insert(root, 1)
insert(root, 3)
assert_equal(height(root), 3)
print('Success: test_height')
def main():
test = TestHeight()
test.test_height()
if __name__ == '__main__':
main()