245 lines
7.9 KiB
Plaintext
245 lines
7.9 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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"# costas_array"
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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/costas_array.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/costas_array.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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" Costas array in Google CP Solver.\n",
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"\n",
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" From http://mathworld.wolfram.com/CostasArray.html:\n",
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" '''\n",
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" An order-n Costas array is a permutation on {1,...,n} such\n",
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" that the distances in each row of the triangular difference\n",
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" table are distinct. For example, the permutation {1,3,4,2,5}\n",
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" has triangular difference table {2,1,-2,3}, {3,-1,1}, {1,2},\n",
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" and {4}. Since each row contains no duplications, the permutation\n",
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" is therefore a Costas array.\n",
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" '''\n",
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"\n",
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" Also see\n",
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" http://en.wikipedia.org/wiki/Costas_array\n",
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"\n",
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" About this model:\n",
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" This model is based on Barry O'Sullivan's model:\n",
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" http://www.g12.cs.mu.oz.au/mzn/costas_array/CostasArray.mzn\n",
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"\n",
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" and my small changes in\n",
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" http://hakank.org/minizinc/costas_array.mzn\n",
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"\n",
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" Since there is no symmetry breaking of the order of the Costas\n",
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" array it gives all the solutions for a specific length of\n",
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" the array, e.g. those listed in\n",
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" http://mathworld.wolfram.com/CostasArray.html\n",
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"\n",
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" 1 1 (1)\n",
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" 2 2 (1, 2), (2,1)\n",
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" 3 4 (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2)\n",
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" 4 12 (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 2, 3), (2, 1, 3, 4),\n",
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" (2, 3, 1, 4), (2, 4, 3, 1), (3, 1, 2, 4), (3, 2, 4, 1),\n",
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" (3, 4, 2, 1), (4, 1, 3, 2), (4, 2, 1, 3), (4, 3, 1, 2)\n",
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" ....\n",
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"\n",
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" See http://www.research.att.com/~njas/sequences/A008404\n",
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" for the number of solutions for n=1..\n",
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" 1, 2, 4, 12, 40, 116, 200, 444, 760, 2160, 4368, 7852, 12828,\n",
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" 17252, 19612, 21104, 18276, 15096, 10240, 6464, 3536, 2052,\n",
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" 872, 200, 88, 56, 204,...\n",
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"\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=6):\n",
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"\n",
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" # Create the solver.\n",
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" solver = pywrapcp.Solver(\"Costas array\")\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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" print(\"n:\", n)\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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" costas = [solver.IntVar(1, n, \"costas[%i]\" % i) for i in range(n)]\n",
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" differences = {}\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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" differences[(i, j)] = solver.IntVar(-n + 1, n - 1,\n",
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" \"differences[%i,%i]\" % (i, j))\n",
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" differences_flat = [differences[i, j] for i in range(n) for j 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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"\n",
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" # Fix the values in the lower triangle in the\n",
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" # difference matrix to -n+1. This removes variants\n",
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" # of the difference matrix for the same Costas array.\n",
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" for i in range(n):\n",
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" for j in range(i + 1):\n",
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" solver.Add(differences[i, j] == -n + 1)\n",
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"\n",
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" # hakank: All the following constraints are from\n",
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" # Barry O'Sullivans's original model.\n",
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" #\n",
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" solver.Add(solver.AllDifferent(costas))\n",
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"\n",
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" # \"How do the positions in the Costas array relate\n",
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" # to the elements of the distance triangle.\"\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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" if i < j:\n",
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" solver.Add(differences[(i, j)] == costas[j] - costas[j - i - 1])\n",
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"\n",
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" # \"All entries in a particular row of the difference\n",
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" # triangle must be distint.\"\n",
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" for i in range(n - 2):\n",
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" solver.Add(\n",
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" solver.AllDifferent([differences[i, j] for j in range(n) if j > i]))\n",
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"\n",
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" #\n",
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" # \"All the following are redundant - only here to speed up search.\"\n",
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" #\n",
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"\n",
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" # \"We can never place a 'token' in the same row as any other.\"\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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" if i < j:\n",
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" solver.Add(differences[i, j] != 0)\n",
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"\n",
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" for k in range(2, n):\n",
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" for l in range(2, n):\n",
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" if k < l:\n",
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" solver.Add(differences[k - 2, l - 1] + differences[k, l] ==\n",
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" differences[k - 1, l - 1] + differences[k - 1, l])\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(costas + differences_flat, solver.CHOOSE_FIRST_UNBOUND,\n",
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" 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(\"costas:\", [costas[i].Value() for i in range(n)])\n",
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" print(\"differences:\")\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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" v = differences[i, j].Value()\n",
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" if v == -n + 1:\n",
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" print(\" \", end=\" \")\n",
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" else:\n",
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" print(\"%2d\" % v, end=\" \")\n",
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" print()\n",
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" print()\n",
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" num_solutions += 1\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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"n = 6\n",
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"if len(sys.argv) > 1:\n",
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" n = int(sys.argv[1])\n",
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"main(n)\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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