Try our new documentation site.


sudoku_c++.cpp


/* Copyright 2019, 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*.
*/

#include "gurobi_c++.h"
#include <sstream>
using namespace std;

#define sd 3
#define n (sd*sd)

string itos(int i) {stringstream s; s << i; return s.str(); }

int
main(int   argc,
     char *argv[])
{
  try {
    GRBEnv env = GRBEnv();
    GRBModel model = GRBModel(env);

    GRBVar vars[n][n][n];
    int i, j, v;

    // Create 3-D array of model variables

    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        for (v = 0; v < n; v++) {
          string s = "G_" + itos(i) + "_" + itos(j) + "_" + itos(v);
          vars[i][j][v] = model.addVar(0.0, 1.0, 0.0, GRB_BINARY, s);
        }
      }
    }

    // Add constraints

    // Each cell must take one value

    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        GRBLinExpr expr = 0;
        for (v = 0; v < n; v++)
          expr += vars[i][j][v];
        string s = "V_" + itos(i) + "_" + itos(j);
        model.addConstr(expr, GRB_EQUAL, 1.0, s);
      }
    }

    // Each value appears once per row

    for (i = 0; i < n; i++) {
      for (v = 0; v < n; v++) {
        GRBLinExpr expr = 0;
        for (j = 0; j < n; j++)
          expr += vars[i][j][v];
        string s = "R_" + itos(i) + "_" + itos(v);
        model.addConstr(expr == 1.0, s);
      }
    }

    // Each value appears once per column

    for (j = 0; j < n; j++) {
      for (v = 0; v < n; v++) {
        GRBLinExpr expr = 0;
        for (i = 0; i < n; i++)
          expr += vars[i][j][v];
        string s = "C_" + itos(j) + "_" + itos(v);
        model.addConstr(expr == 1.0, s);
      }
    }

    // Each value appears once per sub-grid

    for (v = 0; v < n; v++) {
      for (int i0 = 0; i0 < sd; i0++) {
        for (int j0 = 0; j0 < sd; j0++) {
          GRBLinExpr expr = 0;
          for (int i1 = 0; i1 < sd; i1++) {
            for (int j1 = 0; j1 < sd; j1++) {
              expr += vars[i0*sd+i1][j0*sd+j1][v];
            }
          }

          string s = "Sub_" + itos(v) + "_" + itos(i0) + "_" + itos(j0);
          model.addConstr(expr == 1.0, s);
        }
      }
    }

    // Fix variables associated with pre-specified cells

    char input[10];
    for (i = 0; i < n; i++) {
      cin >> input;
      for (j = 0; j < n; j++) {
        int val = (int) input[j] - 48 - 1; // 0-based

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

    // Optimize model

    model.optimize();

    // Write model to file

    model.write("sudoku.lp");

    cout << endl;
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        for (v = 0; v < n; v++) {
          if (vars[i][j][v].get(GRB_DoubleAttr_X) > 0.5)
            cout << v+1;
        }
      }
      cout << endl;
    }
    cout << endl;
  } catch(GRBException e) {
    cout << "Error code = " << e.getErrorCode() << endl;
    cout << e.getMessage() << endl;
  } catch (...) {
    cout << "Error during optimization" << endl;
  }

  return 0;
}

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search