diff --git a/math_probability/power_two/__init__.py b/math_probability/power_two/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/math_probability/power_two/power_two_challenge.ipynb b/math_probability/power_two/power_two_challenge.ipynb new file mode 100644 index 0000000..4815a68 --- /dev/null +++ b/math_probability/power_two/power_two_challenge.ipynb @@ -0,0 +1,171 @@ +{ + "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 number is a power of two.\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 the input number an int?\n", + " * Yes\n", + "* Can we assume the inputs are valid?\n", + " * No\n", + "* Is the output a boolean?\n", + " * Yes\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* None -> TypeError\n", + "* 0 -> False\n", + "* 1 -> True\n", + "* 2 -> True\n", + "* 15 -> False\n", + "* 16 -> True" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "Refer to the [Solution Notebook](). 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": false + }, + "outputs": [], + "source": [ + "class Solution(object):\n", + "\n", + " def is_power_of_two(self, val):\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_is_power_of_two.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestSolution(object):\n", + "\n", + " def test_is_power_of_two(self):\n", + " solution = Solution()\n", + " assert_raises(TypeError, solution.is_power_of_two, None)\n", + " assert_equal(solution.is_power_of_two(0), False)\n", + " assert_equal(solution.is_power_of_two(1), True)\n", + " assert_equal(solution.is_power_of_two(2), True)\n", + " assert_equal(solution.is_power_of_two(15), False)\n", + " assert_equal(solution.is_power_of_two(16), True)\n", + " print('Success: test_is_power_of_two')\n", + "\n", + "\n", + "def main():\n", + " test = TestSolution()\n", + " test.test_is_power_of_two()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "Review the [Solution Notebook]() for a discussion on algorithms and code solutions." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/math_probability/power_two/power_two_solution.ipynb b/math_probability/power_two/power_two_solution.ipynb new file mode 100644 index 0000000..9e67bf4 --- /dev/null +++ b/math_probability/power_two/power_two_solution.ipynb @@ -0,0 +1,206 @@ +{ + "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 number is a power of two.\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 the input number an int?\n", + " * Yes\n", + "* Can we assume the inputs are valid?\n", + " * No\n", + "* Is the output a boolean?\n", + " * Yes\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* None -> TypeError\n", + "* 0 -> False\n", + "* 1 -> True\n", + "* 2 -> True\n", + "* 15 -> False\n", + "* 16 -> True" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We can use bit manipulation to determine if a number is a power of two. \n", + "\n", + "For a number to be a power of two, there must only be one bit that is a `1`. \n", + "\n", + "We can use the following bit manipulation trick to determine this:\n", + "\n", + "`n & (n - 1)`\n", + "\n", + "Here's an example why:\n", + "\n", + "
\n",
+    "0000 1000 = n\n",
+    "0000 0001 = 1\n",
+    "0000 0111 = n-1\n",
+    "\n",
+    "0000 1000 = n\n",
+    "0000 0111 = n-1\n",
+    "0000 0000 = n & n-1, result = 0\n",
+    "
\n", + "\n", + "Complexity:\n", + "* Time: O(1)\n", + "* Space: O(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Solution(object):\n", + "\n", + " def is_power_of_two(self, n):\n", + " if n is None:\n", + " raise TypeError('n cannot be None')\n", + " if n <= 0:\n", + " return False\n", + " return (n & (n - 1)) == 0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting test_is_power_of_two.py\n" + ] + } + ], + "source": [ + "%%writefile test_is_power_of_two.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestSolution(object):\n", + "\n", + " def test_is_power_of_two(self):\n", + " solution = Solution()\n", + " assert_raises(TypeError, solution.is_power_of_two, None)\n", + " assert_equal(solution.is_power_of_two(0), False)\n", + " assert_equal(solution.is_power_of_two(1), True)\n", + " assert_equal(solution.is_power_of_two(2), True)\n", + " assert_equal(solution.is_power_of_two(15), False)\n", + " assert_equal(solution.is_power_of_two(16), True)\n", + " print('Success: test_is_power_of_two')\n", + "\n", + "\n", + "def main():\n", + " test = TestSolution()\n", + " test.test_is_power_of_two()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Success: test_is_power_of_two\n" + ] + } + ], + "source": [ + "%run -i test_is_power_of_two.py" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/math_probability/power_two/test_is_power_of_two.py b/math_probability/power_two/test_is_power_of_two.py new file mode 100644 index 0000000..bdc3ab2 --- /dev/null +++ b/math_probability/power_two/test_is_power_of_two.py @@ -0,0 +1,23 @@ +from nose.tools import assert_equal, assert_raises + + +class TestSolution(object): + + def test_is_power_of_two(self): + solution = Solution() + assert_raises(TypeError, solution.is_power_of_two, None) + assert_equal(solution.is_power_of_two(0), False) + assert_equal(solution.is_power_of_two(1), True) + assert_equal(solution.is_power_of_two(2), True) + assert_equal(solution.is_power_of_two(15), False) + assert_equal(solution.is_power_of_two(16), True) + print('Success: test_is_power_of_two') + + +def main(): + test = TestSolution() + test.test_is_power_of_two() + + +if __name__ == '__main__': + main() \ No newline at end of file