219 lines
6.7 KiB
Plaintext
219 lines
6.7 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 2025 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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"# sicherman_dice"
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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/sicherman_dice.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/sicherman_dice.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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" Sicherman Dice in Google CP Solver.\n",
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"\n",
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" From http://en.wikipedia.org/wiki/Sicherman_dice\n",
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" \"\"\n",
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" Sicherman dice are the only pair of 6-sided dice which are not normal dice,\n",
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" bear only positive integers, and have the same probability distribution for\n",
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" the sum as normal dice.\n",
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"\n",
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" The faces on the dice are numbered 1, 2, 2, 3, 3, 4 and 1, 3, 4, 5, 6, 8.\n",
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" \"\"\n",
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"\n",
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" I read about this problem in a book/column by Martin Gardner long\n",
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" time ago, and got inspired to model it now by the WolframBlog post\n",
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" \"Sicherman Dice\": http://blog.wolfram.com/2010/07/13/sicherman-dice/\n",
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"\n",
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" This model gets the two different ways, first the standard way and\n",
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" then the Sicherman dice:\n",
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"\n",
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" x1 = [1, 2, 3, 4, 5, 6]\n",
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" x2 = [1, 2, 3, 4, 5, 6]\n",
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" ----------\n",
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" x1 = [1, 2, 2, 3, 3, 4]\n",
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" x2 = [1, 3, 4, 5, 6, 8]\n",
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"\n",
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"\n",
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" Extra: If we also allow 0 (zero) as a valid value then the\n",
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" following two solutions are also valid:\n",
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"\n",
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" x1 = [0, 1, 1, 2, 2, 3]\n",
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" x2 = [2, 4, 5, 6, 7, 9]\n",
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" ----------\n",
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" x1 = [0, 1, 2, 3, 4, 5]\n",
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" x2 = [2, 3, 4, 5, 6, 7]\n",
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"\n",
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" These two extra cases are mentioned here:\n",
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" http://mathworld.wolfram.com/SichermanDice.html\n",
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"\n",
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" Compare with these models:\n",
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" * MiniZinc: http://hakank.org/minizinc/sicherman_dice.mzn\n",
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" * Gecode: http://hakank.org/gecode/sicherman_dice.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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"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(\"Sicherman dice\")\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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" n = 6\n",
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" m = 10\n",
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"\n",
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" # standard distribution\n",
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" standard_dist = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 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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"\n",
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" # the two dice\n",
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" x1 = [solver.IntVar(0, m, \"x1(%i)\" % i) for i in range(n)]\n",
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" x2 = [solver.IntVar(0, m, \"x2(%i)\" % i) for i in range(n)]\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(standard_dist[k] == solver.Sum([x1[i] + x2[j] == k+2 for i in range(n) for j in range(n)]))\n",
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" # for k in range(len(standard_dist))]\n",
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" for k in range(len(standard_dist)):\n",
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" tmp = [solver.BoolVar() for i in range(n) for j in range(n)]\n",
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" for i in range(n):\n",
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" for j in range(n):\n",
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" solver.Add(tmp[i * n + j] == solver.IsEqualCstVar(x1[i] + x2[j], k + 2))\n",
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" solver.Add(standard_dist[k] == solver.Sum(tmp))\n",
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"\n",
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" # symmetry breaking\n",
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" [solver.Add(x1[i] <= x1[i + 1]) for i in range(n - 1)],\n",
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" [solver.Add(x2[i] <= x2[i + 1]) for i in range(n - 1)],\n",
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" [solver.Add(x1[i] <= x2[i]) for i in range(n - 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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" solution = solver.Assignment()\n",
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" solution.Add(x1)\n",
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" solution.Add(x2)\n",
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"\n",
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" # db: DecisionBuilder\n",
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" db = solver.Phase(x1 + x2, solver.INT_VAR_SIMPLE, solver.ASSIGN_MIN_VALUE)\n",
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"\n",
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" solver.NewSearch(db)\n",
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" num_solutions = 0\n",
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" while solver.NextSolution():\n",
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" print(\"x1:\", [x1[i].Value() for i in range(n)])\n",
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" print(\"x2:\", [x2[i].Value() for i in range(n)])\n",
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" print()\n",
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"\n",
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" num_solutions += 1\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, \"solver.solutions:\",\n",
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" solver.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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" print(\"MemoryUsage:\", solver.MemoryUsage())\n",
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" print(\"SearchDepth:\", solver.SearchDepth())\n",
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" print(\"SolveDepth:\", solver.SolveDepth())\n",
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" print(\"stamp:\", solver.Stamp())\n",
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" print(\"solver\", solver)\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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"language_info": {
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"name": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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