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### sudoku.R

#  Copyright 2024, 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*.
#

library(Matrix)
library(gurobi)

args <- commandArgs(trailingOnly = TRUE)
if (length(args) < 1) {
stop('Usage: Rscript sudoku.R filename\n')
}

conn <- file(args[1], open='r')
if(!isOpen(conn)) {
stop('Stop now\n')
}
close(conn)

# Ensure that all lines have the same length as the number of lines, and
# that the character set is the correct one.
# Load fixed positions in board
Dim    <- length(linn)
board  <- matrix(0, Dim, Dim, byrow = TRUE)
if (Dim != 9) {
stop('Stop now\n')
}
for (i in 1:Dim) {
line <- strsplit(linn[[i]],split='')[[1]]
if (length(line) != Dim) {
cat('Input line',i,'has',length(line),'characters, expected',Dim,'\n')
stop('Stop now\n')
}
for (j in 1:Dim) {
if (line[[j]] != '.') {
k <- as.numeric(line[[j]])
if (k < 1 || k > Dim) {
cat('Unexpected character in Input line',i,'character',j,'\n')
stop('Stop now\n')
} else {
board[i,j] = k
}
}
}
}

# Map X[i,j,k] into an index variable in the model
nVars  <- Dim * Dim * Dim
varIdx <- function(i,j,k) {i + (j-1) * Dim + (k-1) * Dim * Dim}

cat('Dataset grid:',Dim,'x',Dim,'\n')

# Set up parameters
params <- list()
params$logfile <- 'sudoku.log' # Build model model <- list() model$modelname  <- 'sudoku'
model$modelsense <- 'min' # Create variable names, types, and bounds model$vtype    <- 'B'
model$lb <- rep(0, nVars) model$ub       <- rep(1,  nVars)
model$varnames <- rep('', nVars) for (i in 1:Dim) { for (j in 1:Dim) { for (k in 1:Dim) { if (board[i,j] == k) model$lb[varIdx(i,j,k)] = 1
model$varnames[varIdx(i,j,k)] = paste0('X',i,j,k) } } } # Create (empty) constraints: model$A           <- spMatrix(0,nVars)
model$rhs <- c() model$sense       <- c()
model$constrnames <- c() # Each cell gets a value: for (i in 1:Dim) { for (j in 1:Dim) { B <- spMatrix(1, nVars, i = rep(1,Dim), j = varIdx(i,j,1:Dim), x = rep(1,Dim)) model$A           <- rbind(model$A, B) model$rhs         <- c(model$rhs, 1) model$sense       <- c(model$sense, '=') model$constrnames <- c(model$constrnames, paste0('OneValInCell',i,j)) } } # Each value must appear once in each column for (i in 1:Dim) { for (k in 1:Dim) { B <- spMatrix(1, nVars, i = rep(1,Dim), j = varIdx(i,1:Dim,k), x = rep(1,Dim)) model$A           <- rbind(model$A, B) model$rhs         <- c(model$rhs, 1) model$sense       <- c(model$sense, '=') model$constrnames <- c(model$constrnames, paste0('OnceValueInRow',i,k)) } } #Each value must appear once in each row for (j in 1:Dim) { for (k in 1:Dim) { B <- spMatrix(1, nVars, i = rep(1,Dim), j = varIdx(1:Dim,j,k), x = rep(1,Dim)) model$A           <- rbind(model$A, B) model$rhs         <- c(model$rhs, 1) model$sense       <- c(model$sense, '=') model$constrnames <- c(model$constrnames, paste0('OnceValueInColumn',j,k)) } } # Each value must appear once in each subgrid SubDim <- 3 for (k in 1:Dim) { for (g1 in 1:SubDim) { for (g2 in 1:SubDim) { B <- spMatrix(1, nVars, i = rep(1,Dim), j = c(varIdx(1+(g1-1)*SubDim,(g2-1)*SubDim + 1:SubDim, k), varIdx(2+(g1-1)*SubDim,(g2-1)*SubDim + 1:SubDim, k), varIdx(3+(g1-1)*SubDim,(g2-1)*SubDim + 1:SubDim, k)), x = rep(1,Dim)) model$A           <- rbind(model$A, B) model$rhs         <- c(model$rhs, 1) model$sense       <- c(model$sense, '=') model$constrnames <- c(model$constrnames, paste0('OnceValueInSubGrid',g1,g2,k)) } } } # Save model gurobi_write(model, 'sudoku.lp', params) # Optimize model result <- gurobi(model, params = params) if (result$status == 'OPTIMAL') {
cat('Solution:\n')
cat('----------------------------------\n')
for (i in 1:Dim) {
for (j in 1:Dim) {
if (j %% SubDim == 1) cat('| ')
for (k in 1:Dim) {
if (result\$x[varIdx(i,j,k)] > 0.99) {
cat(k,' ')
}
}
}
cat('|\n')
if (i %% SubDim == 0) cat('----------------------------------\n')
}
} else {
cat('Problem was infeasible\n')
}

# Clear space
rm(result, model, board, linn, params)


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