196 lines
6.2 KiB
Plaintext
196 lines
6.2 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "google",
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"metadata": {},
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"source": [
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"##### Copyright 2023 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "apache",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "basename",
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"metadata": {},
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"source": [
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"# ski_assignment"
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]
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},
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{
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"cell_type": "markdown",
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"id": "link",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/ski_assignment.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/ski_assignment.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "doc",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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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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"id": "install",
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"metadata": {},
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"outputs": [],
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"source": [
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"%pip install ortools"
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]
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},
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{
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"cell_type": "markdown",
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"id": "description",
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"metadata": {},
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"source": [
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"\n",
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"\n",
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" Ski assignment in Google CP Solver.\n",
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"\n",
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" From Jeffrey Lee Hellrung, Jr.:\n",
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" PIC 60, Fall 2008 Final Review, December 12, 2008\n",
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" http://www.math.ucla.edu/~jhellrun/course_files/Fall%25202008/PIC%252060%2520-%2520Data%2520Structures%2520and%2520Algorithms/final_review.pdf\n",
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" '''\n",
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" 5. Ski Optimization! Your job at Snapple is pleasant but in the winter\n",
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" you've decided to become a ski bum. You've hooked up with the Mount\n",
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" Baldy Ski Resort. They'll let you ski all winter for free in exchange\n",
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" for helping their ski rental shop with an algorithm to assign skis to\n",
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" skiers. Ideally, each skier should obtain a pair of skis whose height\n",
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" matches his or her own height exactly. Unfortunately, this is generally\n",
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" not possible. We define the disparity between a skier and his or her\n",
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" skis to be the absolute value of the difference between the height of\n",
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" the skier and the pair of skis. Our objective is to find an assignment\n",
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" of skis to skiers that minimizes the sum of the disparities.\n",
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" ...\n",
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" Illustrate your algorithm by explicitly filling out the A[i, j] table\n",
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" for the following sample data:\n",
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" * Ski heights: 1, 2, 5, 7, 13, 21.\n",
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" * Skier heights: 3, 4, 7, 11, 18.\n",
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" '''\n",
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"\n",
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" Compare with the following models:\n",
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" * Comet : http://www.hakank.org/comet/ski_assignment.co\n",
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" * MiniZinc: http://hakank.org/minizinc/ski_assignment.mzn\n",
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" * ECLiPSe : http://www.hakank.org/eclipse/ski_assignment.ecl\n",
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" * SICStus: http://hakank.org/sicstus/ski_assignment.pl\n",
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" * Gecode: http://hakank.org/gecode/ski_assignment.cpp\n",
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"\n",
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" This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
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" Also see my other Google CP Solver models:\n",
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" http://www.hakank.org/google_or_tools/\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": null,
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"id": "code",
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"metadata": {},
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"outputs": [],
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"source": [
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"import sys\n",
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"\n",
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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"\n",
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"def main():\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver('Ski assignment')\n",
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"\n",
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" #\n",
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" # data\n",
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" #\n",
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" num_skis = 6\n",
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" num_skiers = 5\n",
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" ski_heights = [1, 2, 5, 7, 13, 21]\n",
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" skier_heights = [3, 4, 7, 11, 18]\n",
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"\n",
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" #\n",
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" # variables\n",
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" #\n",
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"\n",
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" # which ski to choose for each skier\n",
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" x = [solver.IntVar(0, num_skis - 1, 'x[%i]' % i) for i in range(num_skiers)]\n",
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" z = solver.IntVar(0, sum(ski_heights), 'z')\n",
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"\n",
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" #\n",
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" # constraints\n",
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" #\n",
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" solver.Add(solver.AllDifferent(x))\n",
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"\n",
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" z_tmp = [\n",
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" abs(solver.Element(ski_heights, x[i]) - skier_heights[i])\n",
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" for i in range(num_skiers)\n",
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" ]\n",
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" solver.Add(z == sum(z_tmp))\n",
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"\n",
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" # objective\n",
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" objective = solver.Minimize(z, 1)\n",
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"\n",
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" #\n",
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" # search and result\n",
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" #\n",
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" db = solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)\n",
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"\n",
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" solver.NewSearch(db, [objective])\n",
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"\n",
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" num_solutions = 0\n",
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" while solver.NextSolution():\n",
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" num_solutions += 1\n",
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" print('total differences:', z.Value())\n",
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" for i in range(num_skiers):\n",
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" x_val = x[i].Value()\n",
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" ski_height = ski_heights[x[i].Value()]\n",
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" diff = ski_height - skier_heights[i]\n",
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" print('Skier %i: Ski %i with length %2i (diff: %2i)' %\\\n",
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" (i, x_val, ski_height, diff))\n",
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" print()\n",
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"\n",
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" solver.EndSearch()\n",
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"\n",
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" print()\n",
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" print('num_solutions:', num_solutions)\n",
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" print('failures:', solver.Failures())\n",
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" print('branches:', solver.Branches())\n",
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" print('WallTime:', solver.WallTime())\n",
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"\n",
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"\n",
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"main()\n",
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"\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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