diff --git a/README.md b/README.md index 19ca9c7..4ae2272 100644 --- a/README.md +++ b/README.md @@ -208,6 +208,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup | 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) | +| Determine if a tree is a valid binary search tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_validate/bst_validate_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_validate/bst_validate_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) | diff --git a/graphs_trees/bst_validate/__init__.py b/graphs_trees/bst_validate/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/graphs_trees/bst_validate/bst_validate_challenge.ipynb b/graphs_trees/bst_validate/bst_validate_challenge.ipynb new file mode 100644 index 0000000..270b384 --- /dev/null +++ b/graphs_trees/bst_validate/bst_validate_challenge.ipynb @@ -0,0 +1,195 @@ +{ + "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: Determine if a tree is a valid binary search 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", + "* Can the tree have duplicates?\n", + " * Yes\n", + "* Can we assume we already have a Node class?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "
\n",
+    "Valid:\n",
+    "      5\n",
+    "    /   \\\n",
+    "   5     8\n",
+    "  / \\   /\n",
+    " 4   6 7\n",
+    "\n",
+    "Invalid:\n",
+    "      5\n",
+    "    /   \\\n",
+    "   5     8\n",
+    "  / \\   /\n",
+    " 4   9 7\n",
+    "
" + ] + }, + { + "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/bst_validate/bst_validate_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 validate_bst(node):\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_bst_validate.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class TestBstValidate(object):\n", + "\n", + " def test_bst_validate(self):\n", + " node = Node(5)\n", + " insert(node, 8)\n", + " insert(node, 5)\n", + " insert(node, 6)\n", + " insert(node, 4)\n", + " insert(node, 7)\n", + " assert_equal(validate_bst(node), True)\n", + "\n", + " root = Node(5)\n", + " left = Node(5)\n", + " right = Node(8)\n", + " invalid = Node(20)\n", + " root.left = left\n", + " root.right = right\n", + " root.left.right = invalid\n", + " assert_equal(validate_bst(root), False)\n", + " print('Success: test_bst_validate')\n", + "\n", + "\n", + "def main():\n", + " test = TestBstValidate()\n", + " test.test_bst_validate()\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/bst_validate/bst_validate_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/bst_validate/bst_validate_solution.ipynb b/graphs_trees/bst_validate/bst_validate_solution.ipynb new file mode 100644 index 0000000..1ff8045 --- /dev/null +++ b/graphs_trees/bst_validate/bst_validate_solution.ipynb @@ -0,0 +1,228 @@ +{ + "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: Determine if a tree is a valid 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", + "* Can the tree have duplicates?\n", + " * Yes\n", + "* Can we assume we already have a Node class?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "
\n",
+    "Valid:\n",
+    "      5\n",
+    "    /   \\\n",
+    "   5     8\n",
+    "  / \\   /\n",
+    " 4   6 7\n",
+    "\n",
+    "Invalid:\n",
+    "      5\n",
+    "    /   \\\n",
+    "   5     8\n",
+    "    \\   \n",
+    "    20\n",
+    "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We'll use a recursive solution that valides left <= current < right, passing down the min and max values as we do a depth-first traversal.\n", + "\n", + "* If the node is None, return False\n", + "* If min is set and the node's value <= min, return False\n", + "* if max is set and the node's value > max, return False\n", + "* Recursively call the validate function on node.left, updating max\n", + "* Recursively call the validate function on node.right, updating min\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 validate_bst(node):\n", + " return __validate_bst__(node, None, None)\n", + "\n", + "\n", + "def __validate_bst__(node, mininum, maximum):\n", + " if node is None:\n", + " return True\n", + " if mininum is not None and node.data <= mininum:\n", + " return False\n", + " if maximum is not None and node.data > maximum:\n", + " return False\n", + " if not __validate_bst__(node.left, mininum, node.data):\n", + " return False\n", + " if not __validate_bst__(node.right, node.data, maximum):\n", + " return False\n", + " return True" + ] + }, + { + "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_validate.py\n" + ] + } + ], + "source": [ + "%%writefile test_bst_validate.py\n", + "from nose.tools import assert_equal\n", + "\n", + "\n", + "class TestBstValidate(object):\n", + "\n", + " def test_bst_validate(self):\n", + " node = Node(5)\n", + " insert(node, 8)\n", + " insert(node, 5)\n", + " insert(node, 6)\n", + " insert(node, 4)\n", + " insert(node, 7)\n", + " assert_equal(validate_bst(node), True)\n", + "\n", + " root = Node(5)\n", + " left = Node(5)\n", + " right = Node(8)\n", + " invalid = Node(20)\n", + " root.left = left\n", + " root.right = right\n", + " root.left.right = invalid\n", + " assert_equal(validate_bst(root), False)\n", + "\n", + " print('Success: test_bst_validate')\n", + "\n", + "\n", + "def main():\n", + " test = TestBstValidate()\n", + " test.test_bst_validate()\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_validate\n" + ] + } + ], + "source": [ + "%run -i test_bst_validate.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/bst_validate/test_bst_validate.py b/graphs_trees/bst_validate/test_bst_validate.py new file mode 100644 index 0000000..059baed --- /dev/null +++ b/graphs_trees/bst_validate/test_bst_validate.py @@ -0,0 +1,33 @@ +from nose.tools import assert_equal + + +class TestBstValidate(object): + + def test_bst_validate(self): + node = Node(5) + insert(node, 8) + insert(node, 5) + insert(node, 6) + insert(node, 4) + insert(node, 7) + assert_equal(validate_bst(node), True) + + root = Node(5) + left = Node(5) + right = Node(8) + invalid = Node(20) + root.left = left + root.right = right + root.left.right = invalid + assert_equal(validate_bst(root), False) + + print('Success: test_bst_validate') + + +def main(): + test = TestBstValidate() + test.test_bst_validate() + + +if __name__ == '__main__': + main() \ No newline at end of file