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generateDIMACS.py
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#!/usr/bin/python
import sys
def literal(i, j, k, n2):
return fit(i, n2) + fit(j, n2) + fit(k, n2)
def fit(n, n2):
diff = len(str(n2)) - len(str(n))
zeros = ["0" for i in range(0, diff)]
fitn = ''.join(zeros)
fitn += str(n)
return fitn
def readInitial(n, fname):
dimacs = ""
dimacs += "c Adding random values for first row, first column and main diagonal\n"
lines = [word[:-1].split(',') for line in open(fname, 'r') for word in line.split()]
literals = [ (literal(i+1, j+1, lines[i][j], n*n) + " 0\n") for i in range(0, len(lines)) for j in range(0, len(lines[i])) if lines[i][j] != '' ]
literals = ''.join(literals)
dimacs += literals
return dimacs
def reduction1(n, initial):
n2 = n * n
atoms = n2 * n2 * n2
clauses = 0
dimacs = initial
digits = len(str(n2))
dimacs += "c There is at most one number in each cell\n"
for i in range(1, n2 + 1):
for j in range(1, n2 + 1):
for k in range(1, n2):
for h in range(k + 1, n2 + 1):
dimacs += "-" + literal(i, j, k, n2) + " -" + literal(i, j, h, n2) + " 0\n"
clauses += 1
dimacs += "c There is at least one number in each cell\n"
for i in range(1, n2 + 1):
for j in range(1, n2 + 1):
for k in range(1, n2 + 1):
dimacs += literal(i, j, k, n2) + " "
dimacs += "0\n"
clauses += 1
dimacs += "c Each number appears at most once in each row\n"
for j in range(1, n2 + 1):
for k in range(1, n2 + 1):
for i in range(1, n2):
for h in range(i + 1, n2 + 1):
dimacs += "-" + literal(i, j, k, n2) + " -" + literal(h, j, k, n2) + " 0\n"
clauses += 1
dimacs += "c Each number appears at least once in each row\n"
for j in range(1, n2 + 1):
for k in range(1, n2 + 1):
for i in range(1, n2 + 1):
dimacs += literal(i, j, k, n2) + " "
dimacs += "0\n"
clauses += 1
dimacs += "c Each number appears at most once in each column\n"
for i in range(1, n2 + 1):
for k in range(1, n2 + 1):
for j in range(1, n2):
for h in range(j + 1, n2 + 1):
dimacs += "-" + literal(i, j, k, n2) + " -" + literal(i, h, k, n2) + " 0\n"
clauses += 1
dimacs += "c Each number appears at least once in each column\n"
for i in range(1, n2 + 1):
for k in range(1, n2 + 1):
for j in range(1, n2 + 1):
dimacs += literal(i, j, k, n2) + " "
dimacs += "0\n"
clauses += 1
dimacs += "c Each number appears at most once in each " + str(n) + "*" + str(n) + " sub-matrix\n"
for k in range(1, n2 + 1):
for x in range(0, n):
for y in range(0, n):
for i in range(1, n + 1):
for j in range(1, n + 1):
for z in range(j + 1, n + 1):
dimacs += "-" + literal(n*x + i, n*y + j, k, n2) + " -" + literal(n*x + i, n*y + z, k, n2) + " 0\n"
clauses += 1
for k in range(1, n2 + 1):
for x in range(0, n):
for y in range(0, n):
for i in range(1, n + 1):
for j in range(1, n + 1):
for z in range(i + 1, n + 1):
for w in range(1, n + 1):
dimacs += "-" + literal(n*x + i, n*y + j, k, n2) + " -" + literal(n*x + z, n*y + w, k, n2) + " 0\n"
clauses += 1
dimacs += "c Each number appears at least once in each " + str(n) + "*" + str(n) + " sub-matrix\n"
for k in range(1, n2 + 1):
for x in range(0, n):
for y in range(0, n):
for i in range(1, n + 1):
for j in range(1, n + 1):
dimacs += literal(n*x + i, n*y + j, k, n2) + " "
dimacs += "0\n"
clauses += 1
dimacs = "c Created by Sudoku Dimacs Creator\n" + dimacs
dimacs = "p cnf " + str(atoms) + " " + str(clauses) + "\n" + dimacs
print(dimacs),
def reduction2(n, initial):
n2 = n * n
atoms = n2 * n2 * n2
clauses = 0
dimacs = initial
digits = len(str(n2))
dimacs += "c At least one number in each entry\n"
for i in range(1, n2 + 1):
for j in range(1, n2 + 1):
for k in range(1, n2 + 1):
dimacs += literal(i, j, k, n2) + " "
dimacs += "0\n"
clauses += 1
dimacs += "c A number is not repeated in a row\n"
for i in range(1, n2 + 1):
for j in range(1, n2 + 1):
for k in range(1, n2 + 1):
for j_s in range(j+1, n2 + 1):
dimacs += "-" + literal(i, j, k, n2) + " -" + literal(i, j_s, k, n2) + " 0\n"
clauses += 1
dimacs += "c A number is not repeated in a column\n"
for i in range(1, n2 + 1):
for j in range(1, n2 + 1):
for k in range(1, n2 + 1):
for i_s in range(i+1, n2 + 1):
dimacs += "-" + literal(i, j, k, n2) + " -" + literal(i_s, j, k, n2) + " 0\n"
clauses += 1
dimacs += "c A number is not repeated in a " + str(n) + "*" + str(n) + " sub-matrix\n"
for k in range(1, n2+1):
for x in range(0, n):
for y in range(0, n):
for i in range(1, n+1):
for j in range(1, n+1):
for z in range(j+1, n+1):
dimacs += "-" + literal(n*x + i, n*y + j, k, n2) + " -" + literal(n*x + i, n*y + z, k, n2) + " 0\n"
clauses += 1
for k in range(1, n2+1):
for x in range(0, n):
for y in range(0, n):
for i in range(1, n+1):
for j in range(1, n+1):
for z in range(i+1, n+1):
for w in range(1, n+1):
dimacs += "-" + literal(n*x + i, n*y + j, k, n2) + " -" + literal(n*x + z, n*y + w, k, n2) + " 0\n"
clauses += 1
dimacs = "c Created by Sudoku Dimacs Creator\n" + dimacs
dimacs = "p cnf " + str(atoms) + " " + str(clauses) + "\n" + dimacs
print(dimacs),
def main():
n = int(sys.argv[1])
reduction = int(sys.argv[2])
initial = sys.argv[3]
initialClauses = readInitial(n, initial)
if reduction == 1:
reduction1(n, initialClauses)
elif reduction == 2:
reduction2(n, initialClauses)
if __name__ == '__main__':
main()