Filter Content By
Version

### sudoku.py

#!/usr/bin/env python3.7

# 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*.

import sys
import math
import gurobipy as gp
from gurobipy import GRB

if len(sys.argv) < 2:
print('Usage: sudoku.py filename')
sys.exit(0)

f = open(sys.argv[1])

grid = f.read().split()

n = len(grid[0])
s = int(math.sqrt(n))

# Create our 3-D array of model variables

model = gp.Model('sudoku')

vars = model.addVars(n, n, n, vtype=GRB.BINARY, name='G')

# Fix variables associated with cells whose values are pre-specified

for i in range(n):
for j in range(n):
if grid[i][j] != '.':
v = int(grid[i][j]) - 1
vars[i, j, v].LB = 1

# Each cell must take one value

model.addConstrs((vars.sum(i, j, '*') == 1
for i in range(n)
for j in range(n)), name='V')

# Each value appears once per row

model.addConstrs((vars.sum(i, '*', v) == 1
for i in range(n)
for v in range(n)), name='R')

# Each value appears once per column

model.addConstrs((vars.sum('*', j, v) == 1
for j in range(n)
for v in range(n)), name='C')

# Each value appears once per subgrid

model.addConstrs((
gp.quicksum(vars[i, j, v] for i in range(i0*s, (i0+1)*s)
for j in range(j0*s, (j0+1)*s)) == 1
for v in range(n)
for i0 in range(s)
for j0 in range(s)), name='Sub')

model.optimize()

model.write('sudoku.lp')

print('')
print('Solution:')
print('')

# Retrieve optimization result

solution = model.getAttr('X', vars)

for i in range(n):
sol = ''
for j in range(n):
for v in range(n):
if solution[i, j, v] > 0.5:
sol += str(v+1)
print(sol)


#### 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.