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### sudoku_cs.cs

/* Copyright 2023, 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);
}
}
}

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++)
string st = "V_" + i.ToString() + "_" + j.ToString();
}
}

// 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++)
string st = "R_" + i.ToString() + "_" + v.ToString();
}
}

// 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++)
string st = "C_" + j.ToString() + "_" + v.ToString();
}
}

// 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++) {
}
}
string st = "Sub_" + v.ToString() + "_" + i0.ToString()
+ "_" + j0.ToString();
}
}
}

// Fix variables associated with pre-specified cells

for (int i = 0; i < n; i++) {
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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