mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
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Add new int challenge
This commit is contained in:
Donne Martin
parent
c915ea69f5
commit
d9edf2fa15
0
sorting_searching/new_int/__init__.py
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0
sorting_searching/new_int/__init__.py
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174
sorting_searching/new_int/new_int_challenge.ipynb
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174
sorting_searching/new_int/new_int_challenge.ipynb
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@ -0,0 +1,174 @@
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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: Given an array of 32 integers, find an int not in the input. Use a minimal amount of memory.\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 we working with non-negative ints?\n",
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" * Yes\n",
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"* What is the range of the integers?\n",
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" * Discuss the approach for 4 billion integers\n",
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" * Implement for 32 integers\n",
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"* Can we assume the inputs are valid?\n",
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" * No"
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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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"* [] -> Exception\n",
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"* General case\n",
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" * There is an int excluded from the input -> int\n",
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" * There isn't an int excluded from the input -> None"
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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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"from bitstring import BitArray # run pip install bitstring\n",
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"\n",
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"\n",
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"class Bits(object):\n",
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"\n",
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" def new_int(self, array, max_size):\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_new_int.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 TestBits(object):\n",
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"\n",
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" def test_new_int(self):\n",
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" bits = Bits()\n",
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" max_size = 32\n",
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" assert_raises(TypeError, bits.new_int, None, max_size)\n",
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" assert_raises(TypeError, bits.new_int, [], max_size)\n",
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" data = [item for item in range(30)]\n",
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" data.append(31)\n",
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" assert_equal(bits.new_int(data, max_size), 30)\n",
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" data = [item for item in range(32)]\n",
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" assert_equal(bits.new_int(data, max_size), None)\n",
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" print('Success: test_find_int_excluded_from_input')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestBits()\n",
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" test.test_new_int()\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": "3.4.3"
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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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214
sorting_searching/new_int/new_int_solution.ipynb
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214
sorting_searching/new_int/new_int_solution.ipynb
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@ -0,0 +1,214 @@
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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: Given an array of n integers, find an int not in the input. Use a minimal amount of memory.\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 we working with non-negative ints?\n",
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" * Yes\n",
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"* What is the range of the integers?\n",
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" * Discuss the approach for 4 billion integers\n",
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" * Implement for 32 integers\n",
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"* Can we assume the inputs are valid?\n",
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" * No"
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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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"* [] -> Exception\n",
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"* General case\n",
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" * There is an int excluded from the input -> int\n",
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" * There isn't an int excluded from the input -> None"
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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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"The problem states to use a minimal amount of memory. We'll use a bit vector to keep track of the inputs.\n",
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"\n",
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"Say we are given 4 billion integers, which is 2^32 integers. The number of non-negative integers would be 2^31. With a bit vector, we'll need 4 billion bits to map each integer to a bit. Say we had only 1 GB of memory or 2^32 bytes. This would leave us with 8 billion bits.\n",
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"\n",
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"To simplify this exercise, we'll work with an input of up to 32 ints that we'll map to a bit vector of 32 bits.\n",
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"\n",
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"<pre>\n",
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"\n",
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"input = [0, 1, 2, 3, 4...28, 29, 31]\n",
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"\n",
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"bytes [ 1 ] [ 2 ] [ 3 ] [ 4 ]\n",
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"index = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31\n",
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"bit_vector = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1\n",
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"\n",
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"result = 30\n",
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"\n",
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"* Loop through each item in the input, setting bit_vector[item] = True.\n",
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"* Loop through the bit_vector, return the first index where bit_vector[item] == False.\n",
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"\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(b), where b is the number of bits\n",
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"* Space: O(b)"
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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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"from bitstring import BitArray # Run pip install bitstring\n",
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"\n",
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"\n",
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"class Bits(object):\n",
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"\n",
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" def new_int(self, array, max_size):\n",
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" if not array:\n",
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" raise TypeError('array cannot be None or empty')\n",
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" bit_vector = BitArray(max_size)\n",
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" for item in array:\n",
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" bit_vector[item] = True\n",
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" for index, item in enumerate(bit_vector):\n",
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" if not item:\n",
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" return index\n",
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" return None"
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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_new_int.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_new_int.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 TestBits(object):\n",
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"\n",
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" def test_new_int(self):\n",
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" bits = Bits()\n",
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" max_size = 32\n",
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" assert_raises(TypeError, bits.new_int, None, max_size)\n",
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" assert_raises(TypeError, bits.new_int, [], max_size)\n",
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" data = [item for item in range(30)]\n",
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" data.append(31)\n",
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" assert_equal(bits.new_int(data, max_size), 30)\n",
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" data = [item for item in range(32)]\n",
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" assert_equal(bits.new_int(data, max_size), None)\n",
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" print('Success: test_find_int_excluded_from_input')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestBits()\n",
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" test.test_new_int()\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_find_int_excluded_from_input\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_new_int.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": "3.4.3"
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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
sorting_searching/new_int/test_new_int.py
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25
sorting_searching/new_int/test_new_int.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 TestBits(object):
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def test_new_int(self):
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bits = Bits()
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max_size = 32
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assert_raises(TypeError, bits.new_int, None, max_size)
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assert_raises(TypeError, bits.new_int, [], max_size)
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data = [item for item in range(30)]
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data.append(31)
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assert_equal(bits.new_int(data, max_size), 30)
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data = [item for item in range(32)]
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assert_equal(bits.new_int(data, max_size), None)
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print('Success: test_find_int_excluded_from_input')
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def main():
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test = TestBits()
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test.test_new_int()
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if __name__ == '__main__':
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main()
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