# SUDOKU, Number Placement Puzzle
from __future__ import print_function
"""Sudoku, also known as Number Place, is a logic-based placement
puzzle. The aim of the canonical puzzle is to enter a numerical
digit from 1 through 9 in each cell of a 9x9 grid made up of 3x3
subgrids (called "regions"), starting with various digits given in
some cells (the "givens"). Each row, column, and region must contain
only one instance of each numeral.
Example:
+-------+-------+-------+
| 5 3 . | . 7 . | . . . |
| 6 . . | 1 9 5 | . . . |
| . 9 8 | . . . | . 6 . |
+-------+-------+-------+
| 8 . . | . 6 . | . . 3 |
| 4 . . | 8 . 3 | . . 1 |
| 7 . . | . 2 . | . . 6 |
+-------+-------+-------+
| . 6 . | . . . | 2 8 . |
| . . . | 4 1 9 | . . 5 |
| . . . | . 8 . | . 7 9 |
+-------+-------+-------+
(From Wikipedia, the free encyclopedia.)"""
# the "givens"
g =(
(5,3,0,0,7,0,0,0,0),
(6,0,0,1,9,5,0,0,0),
(0,9,8,0,0,0,0,6,0),
(8,0,0,0,6,0,0,0,3),
(4,0,0,8,0,3,0,0,1),
(7,0,0,0,2,0,0,0,6),
(0,6,0,0,0,0,2,8,0),
(0,0,0,4,1,9,0,0,5),
(0,0,0,0,8,0,0,7,9))
from pymprog import model, iprod
p = model("sudoku")
I = range(1,10)
J = range(1,10)
K = range(1,10)
T = iprod(I,J,K) #create Indice tuples
x = p.var('x', T, bool)
#x[i,j,k] = 1 means cell [i,j] is assigned number k
#assign pre-defined numbers using the "givens"
[x[i,j,k] == (1 if g[i-1][j-1] == k else 0)
for (i,j,k) in T if g[i-1][j-1] > 0 ]
#each cell must be assigned exactly one number
[sum(x[i,j,k] for k in K)==1 for i in I for j in J]
#cells in the same row must be assigned distinct numbers
[sum(x[i,j,k] for j in J)==1 for i in I for k in K]
#cells in the same column must be assigned distinct numbers
[sum(x[i,j,k] for i in I)==1 for j in J for k in K]
#cells in \-diagonal
#p.st([sum(x[i,i,k] for i in I)==1 for k in K])
#cells in /-diagonal
#p.st([sum(x[i,10-i,k] for i in I)==1 for k in K])
#cells in the same region must be assigned distinct numbers
[sum(x[i,j,k] for i in range(r,r+3) for j in range(c, c+3))==1
for r in range(1,10,3) for c in range(1,10,3) for k in K]
#there is no need for an objective function here
p.solve()
for i in I:
if i in range(1,10,3):
print(" +-------+-------+-------+")
print('', end=' ')
for j in J:
if j in range(1,10,3): print("|", end=' ')
print("%g"%sum(x[i,j,k].primal*k for k in K), end=' ')
if j==9: print("|")
if i == 9:
print(" +-------+-------+-------+")
p.end()
