mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add power two challenge
This commit is contained in:
Donne Martin
parent
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commit
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0
math_probability/power_two/__init__.py
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0
math_probability/power_two/__init__.py
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171
math_probability/power_two/power_two_challenge.ipynb
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math_probability/power_two/power_two_challenge.ipynb
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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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"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)."
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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: Determine if a number is a power of two.\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 input number an int?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Is the output a boolean?\n",
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" * Yes\n",
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"* Can we assume this fits memory?\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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"* None -> TypeError\n",
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"* 0 -> False\n",
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"* 1 -> True\n",
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"* 2 -> True\n",
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"* 15 -> False\n",
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"* 16 -> True"
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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](). 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": false
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},
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"outputs": [],
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"source": [
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"class Solution(object):\n",
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"\n",
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" def is_power_of_two(self, val):\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": false
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},
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"outputs": [],
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"source": [
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"# %load test_is_power_of_two.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestSolution(object):\n",
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"\n",
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" def test_is_power_of_two(self):\n",
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" solution = Solution()\n",
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" assert_raises(TypeError, solution.is_power_of_two, None)\n",
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" assert_equal(solution.is_power_of_two(0), False)\n",
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" assert_equal(solution.is_power_of_two(1), True)\n",
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" assert_equal(solution.is_power_of_two(2), True)\n",
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" assert_equal(solution.is_power_of_two(15), False)\n",
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" assert_equal(solution.is_power_of_two(16), True)\n",
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" print('Success: test_is_power_of_two')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestSolution()\n",
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" test.test_is_power_of_two()\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]() 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 3",
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"language": "python",
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"name": "python3"
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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": 3
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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": "ipython3",
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"version": "3.5.0"
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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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206
math_probability/power_two/power_two_solution.ipynb
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math_probability/power_two/power_two_solution.ipynb
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@ -0,0 +1,206 @@
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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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"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)."
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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: Determine if a number is a power of two.\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 input number an int?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Is the output a boolean?\n",
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" * Yes\n",
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"* Can we assume this fits memory?\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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"* None -> TypeError\n",
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"* 0 -> False\n",
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"* 1 -> True\n",
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"* 2 -> True\n",
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"* 15 -> False\n",
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"* 16 -> True"
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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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"We can use bit manipulation to determine if a number is a power of two. \n",
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"\n",
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"For a number to be a power of two, there must only be one bit that is a `1`. \n",
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"\n",
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"We can use the following bit manipulation trick to determine this:\n",
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"\n",
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"`n & (n - 1)`\n",
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"\n",
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"Here's an example why:\n",
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"\n",
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"<pre>\n",
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"0000 1000 = n\n",
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"0000 0001 = 1\n",
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"0000 0111 = n-1\n",
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"\n",
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"0000 1000 = n\n",
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"0000 0111 = n-1\n",
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"0000 0000 = n & n-1, result = 0\n",
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"</pre>\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": false
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},
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"outputs": [],
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"source": [
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"class Solution(object):\n",
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"\n",
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" def is_power_of_two(self, n):\n",
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" if n is None:\n",
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" raise TypeError('n cannot be None')\n",
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" if n <= 0:\n",
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" return False\n",
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" return (n & (n - 1)) == 0"
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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": 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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_is_power_of_two.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_is_power_of_two.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestSolution(object):\n",
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"\n",
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" def test_is_power_of_two(self):\n",
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" solution = Solution()\n",
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" assert_raises(TypeError, solution.is_power_of_two, None)\n",
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" assert_equal(solution.is_power_of_two(0), False)\n",
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" assert_equal(solution.is_power_of_two(1), True)\n",
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" assert_equal(solution.is_power_of_two(2), True)\n",
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" assert_equal(solution.is_power_of_two(15), False)\n",
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" assert_equal(solution.is_power_of_two(16), True)\n",
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" print('Success: test_is_power_of_two')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestSolution()\n",
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" test.test_is_power_of_two()\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": 3,
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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_is_power_of_two\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_is_power_of_two.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 3",
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"language": "python",
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"name": "python3"
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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": 3
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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": "ipython3",
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"version": "3.5.0"
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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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23
math_probability/power_two/test_is_power_of_two.py
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math_probability/power_two/test_is_power_of_two.py
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@ -0,0 +1,23 @@
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from nose.tools import assert_equal, assert_raises
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class TestSolution(object):
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def test_is_power_of_two(self):
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solution = Solution()
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assert_raises(TypeError, solution.is_power_of_two, None)
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assert_equal(solution.is_power_of_two(0), False)
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assert_equal(solution.is_power_of_two(1), True)
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assert_equal(solution.is_power_of_two(2), True)
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assert_equal(solution.is_power_of_two(15), False)
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assert_equal(solution.is_power_of_two(16), True)
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print('Success: test_is_power_of_two')
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def main():
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test = TestSolution()
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test.test_is_power_of_two()
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if __name__ == '__main__':
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main()
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