diff --git a/recursion_dynamic/longest_inc_subseq/__init__.py b/recursion_dynamic/longest_inc_subseq/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_challenge.ipynb b/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_challenge.ipynb new file mode 100644 index 0000000..dfe8d4d --- /dev/null +++ b/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_challenge.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Challenge Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Find the longest increasing subsequence.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)\n", + "* [Solution Notebook](#Solution-Notebook)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Are duplicates possible?\n", + " * Yes\n", + "* Can we assume the inputs are integers?\n", + " * Yes\n", + "* Can we assume the inputs are valid?\n", + " * No\n", + "* Do we expect the result to be an array of the longest increasing subsequence?\n", + " * Yes\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* None -> Exception\n", + "* [] -> []\n", + "* [3, 4, -1, 0, 6, 2, 3] -> [-1, 0, 2, 3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "Refer to the [Solution Notebook](). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Subsequence(object):\n", + "\n", + " def longest_inc_subseq(self, seq):\n", + " # TODO: Implement me\n", + " pass" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**The following unit test is expected to fail until you solve the challenge.**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# %load test_longest_increasing_subseq.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestLongestIncreasingSubseq(object):\n", + "\n", + " def test_longest_increasing_subseq(self):\n", + " subseq = Subsequence()\n", + " assert_raises(TypeError, subseq.longest_inc_subseq, None)\n", + " assert_equal(subseq.longest_inc_subseq([]), [])\n", + " seq = [3, 4, -1, 0, 6, 2, 3]\n", + " expected = [-1, 0, 2, 3]\n", + " assert_equal(subseq.longest_inc_subseq(seq), expected)\n", + " print('Success: test_longest_increasing_subseq')\n", + "\n", + "\n", + "def main():\n", + " test = TestLongestIncreasingSubseq()\n", + " test.test_longest_increasing_subseq()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Notebook\n", + "\n", + "Review the [Solution Notebook]() for a discussion on algorithms and code solutions." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_solution.ipynb b/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_solution.ipynb new file mode 100644 index 0000000..a46c896 --- /dev/null +++ b/recursion_dynamic/longest_inc_subseq/longest_inc_subseq_solution.ipynb @@ -0,0 +1,231 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solution Notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Find the longest increasing subsequence.\n", + "\n", + "* [Constraints](#Constraints)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Unit Test](#Unit-Test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constraints\n", + "\n", + "* Are duplicates possible?\n", + " * Yes\n", + "* Can we assume the inputs are integers?\n", + " * Yes\n", + "* Can we assume the inputs are valid?\n", + " * No\n", + "* Do we expect the result to be an array of the longest increasing subsequence?\n", + " * Yes\n", + "* Can we assume this fits memory?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* None -> Exception\n", + "* [] -> []\n", + "* [3, 4, -1, 0, 6, 2, 3] -> [-1, 0, 2, 3]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We'll use bottom up dynamic programming to build a table.\n", + "\n", + "
\n", + "Init a temp array of size len(input) to 1. \n", + "We'll use l and r to iterate through the input.\n", + "Array prev will hold the index of the prior smaller value, used to reconstruct the final sequence.\n", + "\n", + "if input[l] < input[r]:\n", + " if temp[r] < temp[l] + 1:\n", + " temp[r] = temp[l] + 1\n", + " prev[r] = l\n", + "\n", + " l r\n", + "index: 0 1 2 3 4 5 6\n", + "---------------------------\n", + "input: 3 4 -1 0 6 2 3\n", + "temp: 1 2 1 1 1 1 1\n", + "prev: x x x x x x x\n", + "\n", + "End result:\n", + "\n", + "index: 0 1 2 3 4 5 6\n", + "---------------------------\n", + "input: 3 4 -1 0 6 2 3\n", + "temp: 1 2 1 2 3 3 4\n", + "prev: x 0 x 2 1 3 5\n", + "\n", + "\n", + "Complexity:\n", + "* Time: O(n^2)\n", + "* Space: O(n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Subsequence(object):\n", + "\n", + " def longest_inc_subseq(self, seq):\n", + " if seq is None:\n", + " raise TypeError('seq cannot be None')\n", + " if not seq:\n", + " return []\n", + " temp = [1] * len(seq)\n", + " prev = [None] * len(seq)\n", + " for r in range(1, len(seq)):\n", + " for l in range(r):\n", + " if seq[l] < seq[r]:\n", + " if temp[r] < temp[l] + 1:\n", + " temp[r] = temp[l] + 1\n", + " prev[r] = l\n", + " max_val = 0\n", + " max_index = -1\n", + " results = []\n", + " for index, value in enumerate(temp):\n", + " if value > max_val:\n", + " max_val = value\n", + " max_index = index\n", + " curr_index = max_index\n", + " while curr_index is not None:\n", + " results.append(seq[curr_index])\n", + " curr_index = prev[curr_index]\n", + " return results[::-1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting test_longest_increasing_subseq.py\n" + ] + } + ], + "source": [ + "%%writefile test_longest_increasing_subseq.py\n", + "from nose.tools import assert_equal, assert_raises\n", + "\n", + "\n", + "class TestLongestIncreasingSubseq(object):\n", + "\n", + " def test_longest_increasing_subseq(self):\n", + " subseq = Subsequence()\n", + " assert_raises(TypeError, subseq.longest_inc_subseq, None)\n", + " assert_equal(subseq.longest_inc_subseq([]), [])\n", + " seq = [3, 4, -1, 0, 6, 2, 3]\n", + " expected = [-1, 0, 2, 3]\n", + " assert_equal(subseq.longest_inc_subseq(seq), expected)\n", + " print('Success: test_longest_increasing_subseq')\n", + "\n", + "\n", + "def main():\n", + " test = TestLongestIncreasingSubseq()\n", + " test.test_longest_increasing_subseq()\n", + "\n", + "\n", + "if __name__ == '__main__':\n", + " main()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Success: test_longest_increasing_subseq\n" + ] + } + ], + "source": [ + "%run -i test_longest_increasing_subseq.py" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/recursion_dynamic/longest_inc_subseq/test_longest_increasing_subseq.py b/recursion_dynamic/longest_inc_subseq/test_longest_increasing_subseq.py new file mode 100644 index 0000000..7a0f9c0 --- /dev/null +++ b/recursion_dynamic/longest_inc_subseq/test_longest_increasing_subseq.py @@ -0,0 +1,22 @@ +from nose.tools import assert_equal, assert_raises + + +class TestLongestIncreasingSubseq(object): + + def test_longest_increasing_subseq(self): + subseq = Subsequence() + assert_raises(TypeError, subseq.longest_inc_subseq, None) + assert_equal(subseq.longest_inc_subseq([]), []) + seq = [3, 4, -1, 0, 6, 2, 3] + expected = [-1, 0, 2, 3] + assert_equal(subseq.longest_inc_subseq(seq), expected) + print('Success: test_longest_increasing_subseq') + + +def main(): + test = TestLongestIncreasingSubseq() + test.test_longest_increasing_subseq() + + +if __name__ == '__main__': + main() \ No newline at end of file