mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add longest increasing subseq challenge
This commit is contained in:
Donne Martin
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0
recursion_dynamic/longest_inc_subseq/__init__.py
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0
recursion_dynamic/longest_inc_subseq/__init__.py
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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: Find the longest increasing subsequence.\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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"* Are duplicates possible?\n",
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" * Yes\n",
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"* Can we assume the inputs are integers?\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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"* Do we expect the result to be an array of the longest increasing subsequence?\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 -> Exception\n",
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"* [] -> []\n",
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"* [3, 4, -1, 0, 6, 2, 3] -> [-1, 0, 2, 3]"
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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 Subsequence(object):\n",
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"\n",
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" def longest_inc_subseq(self, seq):\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_longest_increasing_subseq.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 TestLongestIncreasingSubseq(object):\n",
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"\n",
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" def test_longest_increasing_subseq(self):\n",
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" subseq = Subsequence()\n",
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" assert_raises(TypeError, subseq.longest_inc_subseq, None)\n",
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" assert_equal(subseq.longest_inc_subseq([]), [])\n",
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" seq = [3, 4, -1, 0, 6, 2, 3]\n",
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" expected = [-1, 0, 2, 3]\n",
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" assert_equal(subseq.longest_inc_subseq(seq), expected)\n",
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" print('Success: test_longest_increasing_subseq')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestLongestIncreasingSubseq()\n",
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" test.test_longest_increasing_subseq()\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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@ -0,0 +1,231 @@
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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: Find the longest increasing subsequence.\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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"* Are duplicates possible?\n",
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" * Yes\n",
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"* Can we assume the inputs are integers?\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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"* Do we expect the result to be an array of the longest increasing subsequence?\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 -> Exception\n",
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"* [] -> []\n",
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"* [3, 4, -1, 0, 6, 2, 3] -> [-1, 0, 2, 3]"
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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'll use bottom up dynamic programming to build a table.\n",
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"\n",
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"<pre>\n",
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"Init a temp array of size len(input) to 1. \n",
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"We'll use l and r to iterate through the input.\n",
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"Array prev will hold the index of the prior smaller value, used to reconstruct the final sequence.\n",
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"\n",
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"if input[l] < input[r]:\n",
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" if temp[r] < temp[l] + 1:\n",
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" temp[r] = temp[l] + 1\n",
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" prev[r] = l\n",
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"\n",
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" l r\n",
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"index: 0 1 2 3 4 5 6\n",
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"---------------------------\n",
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"input: 3 4 -1 0 6 2 3\n",
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"temp: 1 2 1 1 1 1 1\n",
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"prev: x x x x x x x\n",
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"\n",
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"End result:\n",
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"\n",
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"index: 0 1 2 3 4 5 6\n",
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"---------------------------\n",
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"input: 3 4 -1 0 6 2 3\n",
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"temp: 1 2 1 2 3 3 4\n",
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"prev: x 0 x 2 1 3 5\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n^2)\n",
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"* Space: O(n)"
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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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"class Subsequence(object):\n",
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"\n",
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" def longest_inc_subseq(self, seq):\n",
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" if seq is None:\n",
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" raise TypeError('seq cannot be None')\n",
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" if not seq:\n",
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" return []\n",
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" temp = [1] * len(seq)\n",
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" prev = [None] * len(seq)\n",
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" for r in range(1, len(seq)):\n",
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" for l in range(r):\n",
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" if seq[l] < seq[r]:\n",
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" if temp[r] < temp[l] + 1:\n",
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" temp[r] = temp[l] + 1\n",
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" prev[r] = l\n",
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" max_val = 0\n",
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" max_index = -1\n",
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" results = []\n",
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" for index, value in enumerate(temp):\n",
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" if value > max_val:\n",
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" max_val = value\n",
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" max_index = index\n",
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" curr_index = max_index\n",
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" while curr_index is not None:\n",
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" results.append(seq[curr_index])\n",
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" curr_index = prev[curr_index]\n",
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" return results[::-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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"## 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_longest_increasing_subseq.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_longest_increasing_subseq.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 TestLongestIncreasingSubseq(object):\n",
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"\n",
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" def test_longest_increasing_subseq(self):\n",
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" subseq = Subsequence()\n",
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" assert_raises(TypeError, subseq.longest_inc_subseq, None)\n",
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" assert_equal(subseq.longest_inc_subseq([]), [])\n",
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" seq = [3, 4, -1, 0, 6, 2, 3]\n",
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" expected = [-1, 0, 2, 3]\n",
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" assert_equal(subseq.longest_inc_subseq(seq), expected)\n",
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" print('Success: test_longest_increasing_subseq')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestLongestIncreasingSubseq()\n",
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" test.test_longest_increasing_subseq()\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_longest_increasing_subseq\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_longest_increasing_subseq.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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@ -0,0 +1,22 @@
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from nose.tools import assert_equal, assert_raises
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class TestLongestIncreasingSubseq(object):
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def test_longest_increasing_subseq(self):
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subseq = Subsequence()
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assert_raises(TypeError, subseq.longest_inc_subseq, None)
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assert_equal(subseq.longest_inc_subseq([]), [])
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seq = [3, 4, -1, 0, 6, 2, 3]
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expected = [-1, 0, 2, 3]
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assert_equal(subseq.longest_inc_subseq(seq), expected)
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print('Success: test_longest_increasing_subseq')
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def main():
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test = TestLongestIncreasingSubseq()
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test.test_longest_increasing_subseq()
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if __name__ == '__main__':
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main()
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