195 lines
6.2 KiB
Plaintext
195 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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"metadata": {},
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"source": [
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"##### Copyright 2020 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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"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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"metadata": {},
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"source": [
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"# p_median"
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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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"<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/master/examples/notebook/contrib/p_median.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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/master/examples/contrib/p_median.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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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"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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"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": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com\n",
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"#\n",
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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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"\"\"\"\n",
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"\n",
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" P-median problem in Google CP Solver.\n",
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"\n",
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" Model and data from the OPL Manual, which describes the problem:\n",
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" '''\n",
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" The P-Median problem is a well known problem in Operations Research.\n",
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" The problem can be stated very simply, like this: given a set of customers\n",
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" with known amounts of demand, a set of candidate locations for warehouses,\n",
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" and the distance between each pair of customer-warehouse, choose P\n",
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" warehouses to open that minimize the demand-weighted distance of serving\n",
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" all customers from those P warehouses.\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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" * MiniZinc: http://hakank.org/minizinc/p_median.mzn\n",
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" * Comet: http://hakank.org/comet/p_median.co\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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"\"\"\"\n",
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"from __future__ import print_function\n",
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"import sys\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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"\n",
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"# Create the solver.\n",
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"solver = pywrapcp.Solver('P-median problem')\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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"p = 2\n",
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"\n",
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"num_customers = 4\n",
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"customers = list(range(num_customers))\n",
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"Albert, Bob, Chris, Daniel = customers\n",
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"num_warehouses = 3\n",
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"warehouses = list(range(num_warehouses))\n",
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"Santa_Clara, San_Jose, Berkeley = warehouses\n",
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"\n",
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"demand = [100, 80, 80, 70]\n",
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"distance = [[2, 10, 50], [2, 10, 52], [50, 60, 3], [40, 60, 1]]\n",
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"\n",
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"#\n",
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"# declare variables\n",
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"#\n",
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"open = [solver.IntVar(warehouses, 'open[%i]% % i') for w in warehouses]\n",
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"ship = {}\n",
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"for c in customers:\n",
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" for w in warehouses:\n",
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" ship[c, w] = solver.IntVar(0, 1, 'ship[%i,%i]' % (c, w))\n",
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"ship_flat = [ship[c, w] for c in customers for w in warehouses]\n",
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"\n",
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"z = solver.IntVar(0, 1000, '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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"z_sum = solver.Sum([\n",
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" demand[c] * distance[c][w] * ship[c, w]\n",
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" for c in customers\n",
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" for w in warehouses\n",
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"])\n",
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"solver.Add(z == z_sum)\n",
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"\n",
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"for c in customers:\n",
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" s = solver.Sum([ship[c, w] for w in warehouses])\n",
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" solver.Add(s == 1)\n",
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"\n",
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"solver.Add(solver.Sum(open) == p)\n",
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"\n",
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"for c in customers:\n",
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" for w in warehouses:\n",
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" solver.Add(ship[c, w] <= open[w])\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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"# solution and search\n",
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"#\n",
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"db = solver.Phase(open + ship_flat, solver.INT_VAR_DEFAULT,\n",
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" 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('z:', z.Value())\n",
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" print('open:', [open[w].Value() for w in warehouses])\n",
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" for c in customers:\n",
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" for w in warehouses:\n",
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" print(ship[c, w].Value(), end=' ')\n",
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" print()\n",
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" print()\n",
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"\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(), 'ms')\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": 4
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}
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