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sudoku_vb.vb
' 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*.
Imports System
Imports System.IO
Imports Gurobi
Class sudoku_vb
Shared Sub Main(ByVal args as String())
Dim n As Integer = 9
Dim s As Integer = 3
If args.Length < 1 Then
Console.WriteLine("Usage: sudoku_vb filename")
Return
End If
Try
Dim env As New GRBEnv()
Dim model As New GRBModel(env)
' Create 3-D array of model variables
Dim vars As GRBVar(,,) = New GRBVar(n - 1, n - 1, n - 1) {}
For i As Integer = 0 To n - 1
For j As Integer = 0 To n - 1
For v As Integer = 0 To n - 1
Dim st As String = "G_" & i & "_" & j & "_" & v
vars(i, j, v) = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, st)
Next
Next
Next
' Add constraints
Dim expr As GRBLinExpr
' Each cell must take one value
For i As Integer = 0 To n - 1
For j As Integer = 0 To n - 1
expr = 0
For v As Integer = 0 To n - 1
expr.AddTerm(1.0, vars(i, j, v))
Next
Dim st As String = "V_" & i & "_" & j
model.AddConstr(expr = 1, st)
Next
Next
' Each value appears once per row
For i As Integer = 0 To n - 1
For v As Integer = 0 To n - 1
expr = 0
For j As Integer = 0 To n - 1
expr.AddTerm(1.0, vars(i, j, v))
Next
Dim st As String = "R_" & i & "_" & v
model.AddConstr(expr = 1, st)
Next
Next
' Each value appears once per column
For j As Integer = 0 To n - 1
For v As Integer = 0 To n - 1
expr = 0
For i As Integer = 0 To n - 1
expr.AddTerm(1.0, vars(i, j, v))
Next
Dim st As String = "C_" & j & "_" & v
model.AddConstr(expr = 1, st)
Next
Next
' Each value appears once per sub-grid
For v As Integer = 0 To n - 1
For i0 As Integer = 0 To s - 1
For j0 As Integer = 0 To s - 1
expr = 0
For i1 As Integer = 0 To s - 1
For j1 As Integer = 0 To s - 1
expr.AddTerm(1.0, vars(i0 * s + i1, j0 * s + j1, v))
Next
Next
Dim st As String = "Sub_" & v & "_" & i0 & "_" & j0
model.AddConstr(expr = 1, st)
Next
Next
Next
' Fix variables associated with pre-specified cells
Dim sr As StreamReader = File.OpenText(args(0))
For i As Integer = 0 To n - 1
Dim input As String = sr.ReadLine()
For j As Integer = 0 To n - 1
Dim val As Integer = Microsoft.VisualBasic.Asc(input(j)) - 48 - 1
' 0-based
If val >= 0 Then
vars(i, j, val).LB = 1.0
End If
Next
Next
' Optimize model
model.Optimize()
' Write model to file
model.Write("sudoku.lp")
Dim x As Double(,,) = model.Get(GRB.DoubleAttr.X, vars)
Console.WriteLine()
For i As Integer = 0 To n - 1
For j As Integer = 0 To n - 1
For v As Integer = 0 To n - 1
If x(i, j, v) > 0.5 Then
Console.Write(v + 1)
End If
Next
Next
Console.WriteLine()
Next
' Dispose of model and env
model.Dispose()
env.Dispose()
Catch e As GRBException
Console.WriteLine("Error code: " & e.ErrorCode & ". " & e.Message)
End Try
End Sub
End Class
