diff --git a/examples/dotnet/CoverRectangleSat.cs b/examples/dotnet/CoverRectangleSat.cs new file mode 100644 index 00000000000..20df17bedee --- /dev/null +++ b/examples/dotnet/CoverRectangleSat.cs @@ -0,0 +1,148 @@ +// Copyright 2010-2022 Google LLC +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +using System; +using System.Collections.Generic; +using System.Linq; +using Google.OrTools.Sat; + +/// +/// Fill a 60x50 rectangle exactly using a minimum number of non-overlapping squares.""" +/// +class CoverRectangleSat +{ + static int sizeX = 60; + static int sizeY = 50; + + static bool CoverRectangle(int numSquares) + { + CpModel model = new CpModel(); + + var areas = new List(); + var sizes = new List(); + var xIntervals = new List(); + var yIntervals = new List(); + var xStarts = new List(); + var yStarts = new List(); + + // Creates intervals for the NoOverlap2D and size variables. + foreach (var i in Enumerable.Range(0, numSquares)) + { + var size = model.NewIntVar(1, sizeY, String.Format("size_{0}", i)); + var startX = model.NewIntVar(0, sizeX, String.Format("startX_{0}", i)); + var endX = model.NewIntVar(0, sizeX, String.Format("endX_{0}", i)); + var startY = model.NewIntVar(0, sizeY, String.Format("startY_{0}", i)); + var endY = model.NewIntVar(0, sizeY, String.Format("endY_{0}", i)); + + var intervalX = model.NewIntervalVar(startX, size, endX, String.Format("intervalX_{0}", i)); + var intervalY = model.NewIntervalVar(startY, size, endY, String.Format("intervalY_{0}", i)); + + var area = model.NewIntVar(1, sizeY * sizeY, String.Format("area_{0}", i)); + model.AddMultiplicationEquality(area, size, size); + + areas.Add(area); + xIntervals.Add(intervalX); + yIntervals.Add(intervalY); + sizes.Add(size); + xStarts.Add(startX); + yStarts.Add(startY); + } + + // Main constraint. + NoOverlap2dConstraint noOverlap2d = model.AddNoOverlap2D(); + foreach (var i in Enumerable.Range(0, numSquares)) + { + noOverlap2d.AddRectangle(xIntervals[i], yIntervals[i]); + } + + // Redundant constraints. + model.AddCumulative(sizeY).AddDemands(xIntervals, sizes); + model.AddCumulative(sizeX).AddDemands(yIntervals, sizes); + + // Forces the rectangle to be exactly covered. + model.Add(LinearExpr.Sum(areas) == sizeX * sizeY); + + // Symmetry breaking 1: sizes are ordered. + foreach (var i in Enumerable.Range(0, numSquares - 1)) + { + model.Add(sizes[i] <= sizes[i + 1]); + + // Define same to be true iff sizes[i] == sizes[i + 1] + var same = model.NewBoolVar(""); + model.Add(sizes[i] == sizes[i + 1]).OnlyEnforceIf(same); + model.Add(sizes[i] < sizes[i + 1]).OnlyEnforceIf(same.Not()); + + // Tie break with starts. + model.Add(xStarts[i] <= xStarts[i + 1]).OnlyEnforceIf(same); + } + + // Symmetry breaking 2: first square in one quadrant. + model.Add(xStarts[0] < (sizeX + 1) / 2); + model.Add(yStarts[0] < (sizeY + 1) / 2); + + // Creates a solver and solves. + var solver = new CpSolver(); + solver.StringParameters = "num_search_workers:16, log_search_progress: false, max_time_in_seconds:10"; + var status = solver.Solve(model); + Console.WriteLine(string.Format("{0} found in {1:0.00}s", status, solver.WallTime())); + + // Prints solution. + bool solution_found = status == CpSolverStatus.Optimal || status == CpSolverStatus.Feasible; + if (solution_found) + { + char[][] output = new char[sizeY][]; + foreach (var y in Enumerable.Range(0, sizeY)) + { + + output[y] = new char[sizeX]; + foreach (var x in Enumerable.Range(0, sizeX)) + { + output[y][x] = ' '; + } + } + + foreach (var s in Enumerable.Range(0, numSquares)) + { + int startX = (int)solver.Value(xStarts[s]); + int startY = (int)solver.Value(yStarts[s]); + int size = (int)solver.Value(sizes[s]); + char c = (char)(65 + s); + foreach (var x in Enumerable.Range(startX, size)) + { + foreach (var y in Enumerable.Range(startY, size)) + { + if (output[y][x] != ' ') + { + Console.WriteLine(string.Format("Error at position x={0} y{1}, found {2}", x, y, output[y][x])); + } + output[y][x] = c; + } + } + } + foreach (var y in Enumerable.Range(0, sizeY)) + { + Console.WriteLine(new String(output[y], 0, sizeX)); + } + } + return solution_found; + } + + static void Main() + { + foreach (int numSquares in Enumerable.Range(1, 15)) + { + Console.WriteLine("Trying with size = {0}", numSquares); + if (CoverRectangle(numSquares)) break; + } + } +} diff --git a/ortools/sat/csharp/Constraints.cs b/ortools/sat/csharp/Constraints.cs index 33bc636cc03..b8a45b14402 100644 --- a/ortools/sat/csharp/Constraints.cs +++ b/ortools/sat/csharp/Constraints.cs @@ -400,7 +400,7 @@ public CumulativeConstraint AddDemands(IEnumerable intervals, IE * * * - * This constraint allows adding rectanles to the NoOverlap2D constraint incrementally. + * This constraint allows adding rectangles to the NoOverlap2D constraint incrementally. * */ public class NoOverlap2dConstraint : Constraint