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Add check prime challenge (#226)
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Donne Martin
GitHub
207
math_probability/check_prime/check_prime_solution.ipynb
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207
math_probability/check_prime/check_prime_solution.ipynb
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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: Check if a number is prime.\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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"* Is it correct that 1 is not considered a prime number?\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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"* 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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"* Not an int -> Exception\n",
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"* Less than 2 -> False\n",
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"* General case"
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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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"For a number to be prime, it must be 2 or greater and cannot be divisible by another number other than itself (and 1).\n",
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"\n",
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"We'll check by dividing all numbers from 2 to the input number to determine if the number is prime.\n",
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"\n",
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"As an optimization, we can divide from 2 to the square root of the input number. For each value that divides the input number evenly, there is a complement b where a * b = n. If a > sqrt(n) then b < sqrt(n) because sqrt(n^2) = n.\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n) where n is the value of the input number\n",
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"* Space: O(1)\n",
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"\n",
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"### Sieve of Eratosthenes\n",
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"\n",
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"The Sieve of Eratosthenes provides a more efficient way of computing and generating primes. See the challenge [\"Generate a list of primes\"]() for more details."
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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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"import math\n",
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"\n",
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"\n",
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"class Math(object):\n",
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"\n",
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" def check_prime(self, num):\n",
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" if num is None:\n",
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" raise TypeError('num cannot be None')\n",
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" if num < 2:\n",
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" return False\n",
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" for i in range(2, num):\n",
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" if num % i == 0:\n",
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" return False\n",
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" return True\n",
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"\n",
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" def check_prime_optimized(self, num):\n",
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" if num is None:\n",
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" raise TypeError('num cannot be None')\n",
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" if num < 2:\n",
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" return False\n",
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" for i in range(2, int(math.sqrt(num)+1)):\n",
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" if num % i == 0:\n",
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" return False\n",
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" return True"
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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_check_prime.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_check_prime.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 TestMath(object):\n",
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"\n",
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" def test_check_prime(self):\n",
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" math = Math()\n",
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" assert_raises(TypeError, math.check_prime, None)\n",
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" assert_raises(TypeError, math.check_prime, 98.6)\n",
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" assert_equal(math.check_prime(0), False)\n",
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" assert_equal(math.check_prime(1), False)\n",
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" assert_equal(math.check_prime(97), True)\n",
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" print('Success: test_check_prime')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestMath()\n",
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" test.test_check_prime()\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_check_prime\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_check_prime.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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