mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
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Added min height bst challenge.
This commit is contained in:
Donne Martin
parent
d098e67ffd
commit
0c0ea408ee
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@ -206,6 +206,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
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| Implement depth-first search (pre-, in-, post-order) on a tree | [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) |
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| Implement breadth-first search on a tree | [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) |
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| 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) |
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| 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) |
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| 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) |
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| 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) |
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| 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) |
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0
graphs_trees/bst_min/__init__.py
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0
graphs_trees/bst_min/__init__.py
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193
graphs_trees/bst_min/bst_min_challenge.ipynb
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193
graphs_trees/bst_min/bst_min_challenge.ipynb
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@ -0,0 +1,193 @@
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{
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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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"# Challenge 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: Create a binary search tree with minimal height from a sorted array.\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)\n",
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"* [Solution Notebook](#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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"## Constraints\n",
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"\n",
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"* Is the array in increasing order?\n",
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" * Yes\n",
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"* Are the array elements unique?\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"
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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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"* 0, 1, 2, 3, 4, 5, 6 -> height 3\n",
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"* 0, 1, 2, 3, 4, 5, 6, 7 -> height 4"
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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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"Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_min/bst_min_solution.ipynb). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
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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": null,
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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\n",
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"%load ../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": null,
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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 create_min_bst(array):\n",
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" # TODO: Implement me\n",
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" # Calls __create_min_bst__\n",
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" pass \n",
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"\n",
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"\n",
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"def __create_min_bst__(array, start, end):\n",
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" # TODO: Implement me\n",
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" pass"
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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": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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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": null,
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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 ../tree_height/height.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": null,
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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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"# %load test_bst_min.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 TestBstMin(object):\n",
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"\n",
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" def test_bst_min(self):\n",
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" array = [0, 1, 2, 3, 4, 5, 6]\n",
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" root = create_min_bst(array)\n",
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" assert_equal(height(root), 3)\n",
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"\n",
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" array = [0, 1, 2, 3, 4, 5, 6, 7]\n",
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" root = create_min_bst(array)\n",
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" assert_equal(height(root), 4)\n",
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"\n",
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" print('Success: test_bst_min')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestBstMin()\n",
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" test.test_bst_min()\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": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_min/bst_min_solution.ipynb) for a discussion on algorithms and code solutions."
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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 2",
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"language": "python",
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"name": "python2"
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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": 2
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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": "ipython2",
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"version": "2.7.10"
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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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221
graphs_trees/bst_min/bst_min_solution.ipynb
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221
graphs_trees/bst_min/bst_min_solution.ipynb
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@ -0,0 +1,221 @@
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{
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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: Create a binary search tree with minimal height from a sorted array.\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 the array in increasing order?\n",
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" * Yes\n",
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"* Are the array elements unique?\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"
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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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"* 0, 1, 2, 3, 4, 5, 6 -> height 3\n",
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"* 0, 1, 2, 3, 4, 5, 6, 7 -> height 4"
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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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"To create a bst with minimum height, we need to use the middle element as the root. We'll use recursion to divide the array in half and continue to pick the middle element from the left and right halves as the nodes to insert in the tree.\n",
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"\n",
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"* create_min_bst(array, start, end)\n",
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"* Base case: Stop when end < start\n",
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"* Create a node with the mid element\n",
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"* Recursively build node.left by calling create_min_bst using the left sub array\n",
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"* Recursively build node.right by calling create_min_bst using the right sub array\n",
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"* Return the node\n",
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" \n",
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"Complexity:\n",
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"* Time: O(1)\n",
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"* Space: O(1)"
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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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"from __future__ import division\n",
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"\n",
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"\n",
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"def create_min_bst(array):\n",
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" if array is None:\n",
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" return\n",
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" return __create_min_bst__(array, 0, len(array) - 1)\n",
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"\n",
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"\n",
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"def __create_min_bst__(array, start, end):\n",
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" if end < start:\n",
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" return\n",
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" mid = (start + end) // 2\n",
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" node = Node(array[mid])\n",
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" node.left = __create_min_bst__(array, start, mid-1)\n",
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" node.right = __create_min_bst__(array, mid+1, end)\n",
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" return node"
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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": true
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},
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"outputs": [],
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"source": [
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"%run ../tree_height/height.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": 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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"Overwriting test_bst_min.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_bst_min.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 TestBstMin(object):\n",
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"\n",
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" def test_bst_min(self):\n",
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" array = [0, 1, 2, 3, 4, 5, 6]\n",
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" root = create_min_bst(array)\n",
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" assert_equal(height(root), 3)\n",
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"\n",
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" array = [0, 1, 2, 3, 4, 5, 6, 7]\n",
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" root = create_min_bst(array)\n",
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" assert_equal(height(root), 4)\n",
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"\n",
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" print('Success: test_bst_min')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestBstMin()\n",
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" test.test_bst_min()\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": 5,
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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_bst_min\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_bst_min.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 2",
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"language": "python",
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"name": "python2"
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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": 2
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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": "ipython2",
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"version": "2.7.10"
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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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24
graphs_trees/bst_min/test_bst_min.py
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24
graphs_trees/bst_min/test_bst_min.py
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@ -0,0 +1,24 @@
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from nose.tools import assert_equal
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class TestBstMin(object):
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def test_bst_min(self):
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array = [0, 1, 2, 3, 4, 5, 6]
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root = create_min_bst(array)
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assert_equal(height(root), 3)
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array = [0, 1, 2, 3, 4, 5, 6, 7]
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root = create_min_bst(array)
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assert_equal(height(root), 4)
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print('Success: test_bst_min')
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def main():
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test = TestBstMin()
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test.test_bst_min()
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if __name__ == '__main__':
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main()
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