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# sudoku_cs.cs

    /* Copyright 2025, Gurobi Optimization, LLC */

    /*
      Sudoku example.

      The Sudoku board is a 9x9 grid, which is further divided into a 3x3 grid
      of 3x3 grids.  Each cell in the grid must take a value from 0 to 9.
      No two grid cells in the same row, column, or 3x3 subgrid may take the
      same value.

      In the MIP formulation, binary variables x[i,j,v] indicate whether
      cell <i,j> takes value 'v'.  The constraints are as follows:
        1. Each cell must take exactly one value (sum_v x[i,j,v] = 1)
        2. Each value is used exactly once per row (sum_i x[i,j,v] = 1)
        3. Each value is used exactly once per column (sum_j x[i,j,v] = 1)
        4. Each value is used exactly once per 3x3 subgrid (sum_grid x[i,j,v] = 1)

      Input datasets for this example can be found in examples/data/sudoku*.
    */

    using System;
    using System.IO;
    using Gurobi;

    class sudoku_cs
    {
      static void Main(string[] args)
      {
        int n = 9;
        int s = 3;

        if (args.Length < 1) {
          Console.Out.WriteLine("Usage: sudoku_cs filename");
          return;
        }

        try {
          GRBEnv env = new GRBEnv();
          GRBModel model = new GRBModel(env);

          // Create 3-D array of model variables

          GRBVar[,,] vars = new GRBVar[n,n,n];

          for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
              for (int v = 0; v < n; v++) {
                string st = "G_" + i.ToString() + "_" + j.ToString()
                                 + "_" + v.ToString();
                vars[i,j,v] = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, st);
              }
            }
          }

          // Add constraints

          GRBLinExpr expr;

          // Each cell must take one value

          for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
              expr = 0.0;
              for (int v = 0; v < n; v++)
                expr.AddTerm(1.0, vars[i,j,v]);
              string st = "V_" + i.ToString() + "_" + j.ToString();
              model.AddConstr(expr == 1.0, st);
            }
          }

          // Each value appears once per row

          for (int i = 0; i < n; i++) {
            for (int v = 0; v < n; v++) {
              expr = 0.0;
              for (int j = 0; j < n; j++)
                expr.AddTerm(1.0, vars[i,j,v]);
              string st = "R_" + i.ToString() + "_" + v.ToString();
              model.AddConstr(expr == 1.0, st);
            }
          }

          // Each value appears once per column

          for (int j = 0; j < n; j++) {
            for (int v = 0; v < n; v++) {
              expr = 0.0;
              for (int i = 0; i < n; i++)
                expr.AddTerm(1.0, vars[i,j,v]);
              string st = "C_" + j.ToString() + "_" + v.ToString();
              model.AddConstr(expr == 1.0, st);
            }
          }

          // Each value appears once per sub-grid

          for (int v = 0; v < n; v++) {
            for (int i0 = 0; i0 < s; i0++) {
              for (int j0 = 0; j0 < s; j0++) {
                expr = 0.0;
                for (int i1 = 0; i1 < s; i1++) {
                  for (int j1 = 0; j1 < s; j1++) {
                    expr.AddTerm(1.0, vars[i0*s+i1,j0*s+j1,v]);
                  }
                }
                string st = "Sub_" + v.ToString() + "_" + i0.ToString()
                                   + "_" + j0.ToString();
                model.AddConstr(expr == 1.0, st);
              }
            }
          }

          // Fix variables associated with pre-specified cells

          StreamReader sr = File.OpenText(args[0]);

          for (int i = 0; i < n; i++) {
            string input = sr.ReadLine();
            for (int j = 0; j < n; j++) {
              int val = (int) input[j] - 48 - 1; // 0-based

              if (val >= 0)
                vars[i,j,val].LB = 1.0;
            }
          }

          // Optimize model

          model.Optimize();

          // Write model to file
          model.Write("sudoku.lp");

          double[,,] x = model.Get(GRB.DoubleAttr.X, vars);

          Console.WriteLine();
          for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
              for (int v = 0; v < n; v++) {
                if (x[i,j,v] > 0.5) {
                  Console.Write(v+1);
                }
              }
            }
            Console.WriteLine();
          }

          // Dispose of model and env
          model.Dispose();
          env.Dispose();

        } catch (GRBException e) {
          Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message);
        }
      }
    }

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