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sudoku.py

#!/usr/bin/env python3.11

# 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*.

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)

---

Next: tsp.py Up: Python Examples Previous: sos.py