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https://github.com/donnemartin/interactive-coding-challenges
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Moved fibonacci to its own folder. Appended _solution to current notebooks to prepare for challenge and solution notebooks.
This commit is contained in:
Donne Martin
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recursion_dynamic/fibonacci/fibonacci_solution.ipynb
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201
recursion_dynamic/fibonacci/fibonacci_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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"<small><i>This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://bit.ly/code-notes).</i></small>"
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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: Implement fibonacci recursively, dynamically, and iteratively.\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: Recursive](#Code:-Recursive)\n",
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"* [Code: Dynamic](#Code:-Dynamic)\n",
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"* [Code: Iterative](#Code:-Iterative)\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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"*Problem statements are often intentionally ambiguous. Identifying constraints and stating assumptions can help to ensure you code the intended solution.*\n",
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"\n",
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"* 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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"## Test Cases\n",
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"\n",
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"* n = 0\n",
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"* n = 1\n",
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"* n > 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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"## Algorithm\n",
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"\n",
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"* Fibonacci is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34...\n",
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"* If n = 0 or 1, return n\n",
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"* Else return fib(n-1) + fib(n+2)\n",
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"\n",
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"Complexity:\n",
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"* Time: O(2^n) if recursive or iterative, O(n) if dynamic\n",
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"* Space: O(n) if recursive, O(1) if iterative, O(1) if dynamic"
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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: Recursive"
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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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"def fib_recursive(n):\n",
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" if n == 0 or n == 1:\n",
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" return n\n",
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" else:\n",
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" return fib_recursive(n-1) + fib_recursive(n-2)"
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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: Dynamic"
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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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"source": [
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"num_items = 10\n",
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"cache = [None] * (num_items + 1)\n",
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"\n",
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"def fib_dynamic(n):\n",
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" if n == 0 or n == 1:\n",
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" return n\n",
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" if cache[n] != None:\n",
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" return cache[n]\n",
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" cache[n] = fib_dynamic(n-1) + fib_dynamic(n-2)\n",
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" return cache[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: Iterative"
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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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"source": [
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"def fib_iterative(n):\n",
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" a = 0 \n",
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" b = 1\n",
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" for _ in xrange(n):\n",
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" a, b = b, a + b\n",
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" return a"
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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\n",
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"\n",
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"*It is important to identify and run through general and edge cases from the [Test Cases](#Test-Cases) section by hand. You generally will not be asked to write a unit test like what is shown below.*"
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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": 4,
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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_fib\n",
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"Success: test_fib\n",
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"Success: test_fib\n"
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]
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}
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],
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"source": [
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"from nose.tools import assert_equal\n",
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"\n",
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"class Test(object):\n",
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" def test_fib(self, func):\n",
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" result = []\n",
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" for i in xrange(num_items):\n",
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" result.append(func(i))\n",
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" fib_seq = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]\n",
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" assert_equal(result, fib_seq)\n",
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" print('Success: test_fib')\n",
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"\n",
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"if __name__ == '__main__':\n",
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" test = Test()\n",
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" test.test_fib(fib_recursive)\n",
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" test.test_fib(fib_dynamic)\n",
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" test.test_fib(fib_iterative)"
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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 2",
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"language": "python",
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"name": "python2"
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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": 2
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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": "ipython2",
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"version": "2.7.10"
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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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