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Add new int challenge

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Donne Martin 2017-03-27 05:15:40 -04:00
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0
sorting_searching/new_int/__init__.py Normal file
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sorting_searching/new_int/new_int_challenge.ipynb Normal file
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{
"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: Given an array of 32 integers, find an int not in the input. Use a minimal amount of memory.\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 we working with non-negative ints?\n",
" * Yes\n",
"* What is the range of the integers?\n",
" * Discuss the approach for 4 billion integers\n",
" * Implement for 32 integers\n",
"* Can we assume the inputs are valid?\n",
" * No"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"* None -> Exception\n",
"* [] -> Exception\n",
"* General case\n",
" * There is an int excluded from the input -> int\n",
" * There isn't an int excluded from the input -> None"
]
},
{
"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": [
"from bitstring import BitArray # run pip install bitstring\n",
"\n",
"\n",
"class Bits(object):\n",
"\n",
" def new_int(self, array, max_size):\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_new_int.py\n",
"from nose.tools import assert_equal, assert_raises\n",
"\n",
"\n",
"class TestBits(object):\n",
"\n",
" def test_new_int(self):\n",
" bits = Bits()\n",
" max_size = 32\n",
" assert_raises(TypeError, bits.new_int, None, max_size)\n",
" assert_raises(TypeError, bits.new_int, [], max_size)\n",
" data = [item for item in range(30)]\n",
" data.append(31)\n",
" assert_equal(bits.new_int(data, max_size), 30)\n",
" data = [item for item in range(32)]\n",
" assert_equal(bits.new_int(data, max_size), None)\n",
" print('Success: test_find_int_excluded_from_input')\n",
"\n",
"\n",
"def main():\n",
" test = TestBits()\n",
" test.test_new_int()\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": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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sorting_searching/new_int/new_int_solution.ipynb Normal file
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{
"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: Given an array of n integers, find an int not in the input. Use a minimal amount of memory.\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 we working with non-negative ints?\n",
" * Yes\n",
"* What is the range of the integers?\n",
" * Discuss the approach for 4 billion integers\n",
" * Implement for 32 integers\n",
"* Can we assume the inputs are valid?\n",
" * No"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"* None -> Exception\n",
"* [] -> Exception\n",
"* General case\n",
" * There is an int excluded from the input -> int\n",
" * There isn't an int excluded from the input -> None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"The problem states to use a minimal amount of memory. We'll use a bit vector to keep track of the inputs.\n",
"\n",
"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",
"\n",
"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",
"\n",
"<pre>\n",
"\n",
"input = [0, 1, 2, 3, 4...28, 29, 31]\n",
"\n",
"bytes [ 1 ] [ 2 ] [ 3 ] [ 4 ]\n",
"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",
"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",
"\n",
"result = 30\n",
"\n",
"* Loop through each item in the input, setting bit_vector[item] = True.\n",
"* Loop through the bit_vector, return the first index where bit_vector[item] == False.\n",
"\n",
"</pre>\n",
"\n",
"Complexity:\n",
"* Time: O(b), where b is the number of bits\n",
"* Space: O(b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from bitstring import BitArray # Run pip install bitstring\n",
"\n",
"\n",
"class Bits(object):\n",
"\n",
" def new_int(self, array, max_size):\n",
" if not array:\n",
" raise TypeError('array cannot be None or empty')\n",
" bit_vector = BitArray(max_size)\n",
" for item in array:\n",
" bit_vector[item] = True\n",
" for index, item in enumerate(bit_vector):\n",
" if not item:\n",
" return index\n",
" return None"
]
},
{
"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_new_int.py\n"
]
}
],
"source": [
"%%writefile test_new_int.py\n",
"from nose.tools import assert_equal, assert_raises\n",
"\n",
"\n",
"class TestBits(object):\n",
"\n",
" def test_new_int(self):\n",
" bits = Bits()\n",
" max_size = 32\n",
" assert_raises(TypeError, bits.new_int, None, max_size)\n",
" assert_raises(TypeError, bits.new_int, [], max_size)\n",
" data = [item for item in range(30)]\n",
" data.append(31)\n",
" assert_equal(bits.new_int(data, max_size), 30)\n",
" data = [item for item in range(32)]\n",
" assert_equal(bits.new_int(data, max_size), None)\n",
" print('Success: test_find_int_excluded_from_input')\n",
"\n",
"\n",
"def main():\n",
" test = TestBits()\n",
" test.test_new_int()\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_find_int_excluded_from_input\n"
]
}
],
"source": [
"%run -i test_new_int.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": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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sorting_searching/new_int/test_new_int.py Normal file
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from nose.tools import assert_equal, assert_raises
class TestBits(object):
def test_new_int(self):
bits = Bits()
max_size = 32
assert_raises(TypeError, bits.new_int, None, max_size)
assert_raises(TypeError, bits.new_int, [], max_size)
data = [item for item in range(30)]
data.append(31)
assert_equal(bits.new_int(data, max_size), 30)
data = [item for item in range(32)]
assert_equal(bits.new_int(data, max_size), None)
print('Success: test_find_int_excluded_from_input')
def main():
test = TestBits()
test.test_new_int()
if __name__ == '__main__':
main()