mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add steps challenge
This commit is contained in:
Donne Martin
parent
abc982d360
commit
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0
recursion_dynamic/steps/__init__.py
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0
recursion_dynamic/steps/__init__.py
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172
recursion_dynamic/steps/steps_challenge.ipynb
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172
recursion_dynamic/steps/steps_challenge.ipynb
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@ -0,0 +1,172 @@
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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: You are running up n steps. If you can take a single, double, or triple step, how many possible ways are there to run up to the nth step?\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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"* If n == 0, what should the result be?\n",
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" * Go with 1, but discuss different approaches\n",
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"* Can we assume the inputs are valid?\n",
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" * No\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 or negative input -> Exception\n",
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"* n == 0 -> 1\n",
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"* n == 1 -> 1\n",
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"* n == 2 -> 2\n",
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"* n == 3 -> 4\n",
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"* n == 4 -> 7\n",
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"* n == 10 -> 274"
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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 Steps(object):\n",
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"\n",
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" def count_ways(self, num_steps):\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_steps.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 TestSteps(object):\n",
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"\n",
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" def test_steps(self):\n",
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" steps = Steps()\n",
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" assert_raises(TypeError, steps.count_ways, None)\n",
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" assert_raises(TypeError, steps.count_ways, -1)\n",
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" assert_equal(steps.count_ways(0), 1)\n",
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" assert_equal(steps.count_ways(1), 1)\n",
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" assert_equal(steps.count_ways(2), 2)\n",
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" assert_equal(steps.count_ways(3), 4)\n",
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" assert_equal(steps.count_ways(4), 7)\n",
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" assert_equal(steps.count_ways(10), 274)\n",
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" print('Success: test_steps')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestSteps()\n",
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" test.test_steps()\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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228
recursion_dynamic/steps/steps_solution.ipynb
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recursion_dynamic/steps/steps_solution.ipynb
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@ -0,0 +1,228 @@
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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: You are running up n steps. If you can take a single, double, or triple step, how many possible ways are there to run up to the nth step?\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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"* If n == 0, what should the result be?\n",
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" * Go with 1, but discuss different approaches\n",
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"* Can we assume the inputs are valid?\n",
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" * No\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 or negative input -> Exception\n",
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"* n == 0 -> 1\n",
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"* n == 1 -> 1\n",
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"* n == 2 -> 2\n",
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"* n == 3 -> 4\n",
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"* n == 4 -> 7\n",
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"* n == 10 -> 274"
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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 get to step n, we will need to have gone:\n",
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"\n",
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"* One step from n-1\n",
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"* Two steps from n-2\n",
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"* Three steps from n-3\n",
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"\n",
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"If we go the one step route above, we'll be at n-1 before taking the last step. To get to step n-1, we will need to have gone:\n",
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"\n",
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"* One step from n-1-1\n",
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"* Two steps from n-1-2\n",
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"* Three steps from n-1-2\n",
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"\n",
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"Continue this process until we reach the start.\n",
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"\n",
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"Base case:\n",
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"\n",
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"* If n < 0: return 0\n",
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"* If n == 0: return 1\n",
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"\n",
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"Note, if we had chosen n == 0 to return 0 instead, we would need to add additional base cases. Otherwise we'd be adding multiple 0's once we hit the base cases and not get any result > 0.\n",
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"\n",
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"Recursive case:\n",
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"\n",
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"We'll memoize the solution to improve performance.\n",
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"\n",
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"* Use the memo if we've already processed the current step.\n",
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"* Update the memo by adding the recursive calls to step(n-1), step(n-2), step(n-3)\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n), if using memoization\n",
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"* Space: O(n), where n is the recursion depth\n",
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"\n",
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"Note: The number of ways will quickly overflow the bounds of an integer."
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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 Steps(object):\n",
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"\n",
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" def count_ways(self, num_steps):\n",
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" if num_steps is None or num_steps < 0:\n",
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" raise TypeError('num_steps cannot be None or negative')\n",
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" cache = {}\n",
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" return self._count_ways(num_steps, cache)\n",
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"\n",
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" def _count_ways(self, num_steps, cache):\n",
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" if num_steps < 0:\n",
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" return 0\n",
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" if num_steps == 0:\n",
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" return 1\n",
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" if num_steps in cache:\n",
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" return cache[num_steps]\n",
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" cache[num_steps] = (self._count_ways(num_steps-1, cache) +\n",
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" self._count_ways(num_steps-2, cache) +\n",
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" self._count_ways(num_steps-3, cache))\n",
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" return cache[num_steps]"
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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_steps.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_steps.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 TestSteps(object):\n",
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"\n",
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" def test_steps(self):\n",
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" steps = Steps()\n",
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" assert_raises(TypeError, steps.count_ways, None)\n",
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" assert_raises(TypeError, steps.count_ways, -1)\n",
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" assert_equal(steps.count_ways(0), 1)\n",
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" assert_equal(steps.count_ways(1), 1)\n",
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" assert_equal(steps.count_ways(2), 2)\n",
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" assert_equal(steps.count_ways(3), 4)\n",
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" assert_equal(steps.count_ways(4), 7)\n",
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" assert_equal(steps.count_ways(10), 274)\n",
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" print('Success: test_steps')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestSteps()\n",
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" test.test_steps()\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_steps\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_steps.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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25
recursion_dynamic/steps/test_steps.py
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25
recursion_dynamic/steps/test_steps.py
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@ -0,0 +1,25 @@
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from nose.tools import assert_equal, assert_raises
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class TestSteps(object):
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def test_steps(self):
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steps = Steps()
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assert_raises(TypeError, steps.count_ways, None)
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assert_raises(TypeError, steps.count_ways, -1)
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assert_equal(steps.count_ways(0), 1)
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assert_equal(steps.count_ways(1), 1)
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assert_equal(steps.count_ways(2), 2)
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assert_equal(steps.count_ways(3), 4)
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assert_equal(steps.count_ways(4), 7)
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assert_equal(steps.count_ways(10), 274)
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print('Success: test_steps')
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def main():
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test = TestSteps()
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test.test_steps()
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if __name__ == '__main__':
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main()
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