mirror of
https://github.com/donnemartin/interactive-coding-challenges
synced 2026-01-07 18:08:01 +00:00
Moved Hanoi challenge from stacks_queues to recursion_dynamic.
This commit is contained in:
Donne Martin
218
recursion_dynamic/hanoi/hanoi_solution.ipynb
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218
recursion_dynamic/hanoi/hanoi_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://github.com/donnemartin/interactive-coding-challenges).</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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"# 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: Implement the [Towers of Hanoi](http://en.wikipedia.org/wiki/Tower_of_Hanoi) with 3 towers and N disks.\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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"* Can we assume we already have a stack class that can be used for this problem?\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 tower(s)\n",
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"* 0 disks\n",
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"* 1 disk\n",
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"* 2 or more disks"
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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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"* Create three stacks to represent each tower\n",
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"* def hanoi(n, src, dest, buffer):\n",
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" * If 0 disks return\n",
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" * hanoi(n-1, src, buffer)\n",
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" * Move remaining element from src to dest\n",
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" * hanoi(n-1, buffer, dest) \n",
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"\n",
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"Complexity:\n",
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"* Time: O(2^n)\n",
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"* Space: O(m) where m is the number of recursion levels"
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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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"%run ../stack/stack.py"
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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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"def hanoi(num_disks, src, dest, buff):\n",
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" if src is None or dest is None or buff is None:\n",
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" return\n",
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" if num_disks > 0:\n",
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" hanoi(num_disks-1, src, buff, dest)\n",
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" data = src.pop()\n",
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" dest.push(data)\n",
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" hanoi(num_disks-1, buff, dest, src)"
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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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]
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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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"Overwriting test_hanoi.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_hanoi.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestHanoi(object):\n",
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"\n",
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" def test_hanoi(self):\n",
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" num_disks = 3\n",
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" src = Stack()\n",
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" buff = Stack()\n",
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" dest = Stack()\n",
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"\n",
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" print('Test: None towers')\n",
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" hanoi(num_disks, None, None, None)\n",
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"\n",
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" print('Test: 0 disks')\n",
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" hanoi(num_disks, src, dest, buff)\n",
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" assert_equal(dest.pop(), None)\n",
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"\n",
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" print('Test: 1 disk')\n",
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" src.push(5)\n",
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" hanoi(num_disks, src, dest, buff)\n",
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" assert_equal(dest.pop(), 5)\n",
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"\n",
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" print('Test: 2 or more disks')\n",
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" for i in range(num_disks, -1, -1):\n",
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" src.push(i)\n",
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" hanoi(num_disks, src, dest, buff)\n",
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" for i in range(0, num_disks):\n",
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" assert_equal(dest.pop(), i)\n",
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"\n",
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" print('Success: test_hanoi')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestHanoi()\n",
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" test.test_hanoi()\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": 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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"Test: None towers\n",
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"Test: 0 disks\n",
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"Test: 1 disk\n",
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"Test: 2 or more disks\n",
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"Success: test_hanoi\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_hanoi.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 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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