"""
The Looping Sudoku Problem Formulation for the PuLP Modeller
Authors: Antony Phillips, Dr Stuart Mitchell
edited by Dr Nathan Sudermann-Merx
"""
# Import PuLP modeler functions
from pulp import *
# All rows, columns and values within a Sudoku take values from 1 to 9
VALS = ROWS = COLS = range(1, 10)
# The boxes list is created, with the row and column index of each square in each box
Boxes = [
[(3 * i + k + 1, 3 * j + l + 1) for k in range(3) for l in range(3)]
for i in range(3)
for j in range(3)
]
# The prob variable is created to contain the problem data
prob = LpProblem("Sudoku Problem")
# The decision variables are created
choices = LpVariable.dicts("Choice", (VALS, ROWS, COLS), cat="Binary")
# We do not define an objective function since none is needed
# A constraint ensuring that only one value can be in each square is created
for r in ROWS:
for c in COLS:
prob += lpSum([choices[v][r][c] for v in VALS]) == 1
# The row, column and box constraints are added for each value
for v in VALS:
for r in ROWS:
prob += lpSum([choices[v][r][c] for c in COLS]) == 1
for c in COLS:
prob += lpSum([choices[v][r][c] for r in ROWS]) == 1
for b in Boxes:
prob += lpSum([choices[v][r][c] for (r, c) in b]) == 1
# The starting numbers are entered as constraints
input_data = [
(5, 1, 1),
(6, 2, 1),
(8, 4, 1),
(4, 5, 1),
(7, 6, 1),
(3, 1, 2),
(9, 3, 2),
(6, 7, 2),
(8, 3, 3),
(1, 2, 4),
(8, 5, 4),
(4, 8, 4),
(7, 1, 5),
(9, 2, 5),
(6, 4, 5),
(2, 6, 5),
(1, 8, 5),
(8, 9, 5),
(5, 2, 6),
(3, 5, 6),
(9, 8, 6),
(2, 7, 7),
(6, 3, 8),
(8, 7, 8),
(7, 9, 8),
(3, 4, 9),
# Since the previous Sudoku contains only one unique solution, we remove some numers from the board to obtain a
# Sudoku with multiple solutions
# (1, 5, 9),
# (6, 6, 9),
# (5, 8, 9)
]
for v, r, c in input_data:
prob += choices[v][r][c] == 1
# The problem data is written to an .lp file
prob.writeLP("Sudoku.lp")
# A file called sudokuout.txt is created/overwritten for writing to
sudokuout = open("sudokuout.txt", "w")
while True:
prob.solve()
# The status of the solution is printed to the screen
print("Status:", LpStatus[prob.status])
# The solution is printed if it was deemed "optimal" i.e met the constraints
if LpStatus[prob.status] == "Optimal":
# The solution is written to the sudokuout.txt file
for r in ROWS:
if r in [1, 4, 7]:
sudokuout.write("+-------+-------+-------+\n")
for c in COLS:
for v in VALS:
if value(choices[v][r][c]) == 1:
if c in [1, 4, 7]:
sudokuout.write("| ")
sudokuout.write(str(v) + " ")
if c == 9:
sudokuout.write("|\n")
sudokuout.write("+-------+-------+-------+\n\n")
# The constraint is added that the same solution cannot be returned again
prob += (
lpSum(
[
choices[v][r][c]
for v in VALS
for r in ROWS
for c in COLS
if value(choices[v][r][c]) == 1
]
)
<= 80
)
# If a new optimal solution cannot be found, we end the program
else:
break
sudokuout.close()
# The location of the solutions is give to the user
print("Solutions Written to sudokuout.txt")