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sudoku_solver_csp.py
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sudoku_solver_csp.py
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import sys
def char_range(a, b):
res = []
for i in range(ord(a), ord(b)+1):
res.append(chr(i))
return res
class SudokuSolver:
def __init__(self, sudokuString):
self.domain = {}
self.assignment = {}
self.arcs = {}
self.neighbors = {}
self.initConstraints()
self.initSudoku(sudokuString)
def isSolved(self):
for k, domain in self.domain.items():
if self.assignment[k] == 0:
return False
return True
def initConstraints(self):
constraintMap = {}
# alldiff rows, alldiff(a1, a2 ... a9) as binary arcs:
# a1 != a2, a1 != a3 ..., a1 != a9; ... a9 != a1, a9 != a2 ... a9 != a8
# ...
# i1 != i2, i1 != i3 ..., i1 != i9; ... i9 != i1, i9 != i2 ... i9 != i8
for i in char_range('a', 'i'):
for j in range(1, 10):
for k in range(1, 10):
if k != j:
if not i+str(j)+i+str(k) in constraintMap:
self.appendArc(i+str(j), i+str(k))
constraintMap[i+str(j)+i+str(k)] = 1
# alldiff cols, alldiff(a1, b1 ... b9) as binary arcs:
# a1 != b1, a1 != c1 ..., a1 != i1; ... i1 != a1, i1 != b1 ... i1 != h1
# ...
# a9 != b9, a9 != c9 ..., a9 != i9; ... i9 != a9, i9 != b9 ... i9 != h9
for i in range(1, 10):
for j in char_range('a', 'i'):
for k in char_range('a', 'i'):
if k != j:
if not j+str(i)+k+str(i) in constraintMap:
self.appendArc(j+str(i), k+str(i))
constraintMap[j+str(i)+k+str(i)] = 1
# alldiff blocks, alldiff(a1, b1, c1, a2, b2, c2, a3, b3, c3)
# a1 != b1 ... a1 != c1; ... c1 != a1 ... c1 != b1
# ...
# a3 != b3 ... a3 != c3; ... c3 != a3 ... c3 != b2
for colStride in range(3):
for rowStride in range(3):
for i in char_range(chr(ord('a')+rowStride*3), chr(ord('c')+rowStride*3)):
for j in range(1+colStride*3, 4+colStride*3):
lv = i + str(j)
for k in char_range(chr(ord('a')+rowStride*3), chr(ord('c')+rowStride*3)):
for l in range(1+colStride*3, 4+colStride*3):
rv = k + str(l)
if lv != rv:
if not lv+rv in constraintMap:
self.appendArc(lv, rv)
constraintMap[lv+rv] = 1
def appendArc(self, a, b):
if not a in self.arcs:
self.arcs[a] = []
self.arcs[a].append(b)
if not b in self.neighbors:
self.neighbors[b] = []
inNeighbors = False
if not a in self.neighbors[b]:
self.neighbors[b].append(a)
def getArcs(self):
arcs = []
for a, bs in self.arcs.items():
for b in bs:
arcs.append([a, b])
return arcs
def getNeighbors(self, a, butC):
neighbors = []
if a in self.neighbors:
for b in self.neighbors[a]:
if b != butC:
neighbors.append(b)
return neighbors
def initSudoku(self, sudokuString):
strIndex = 0
for i in char_range('a', 'i'):
for j in range(1, 10):
var = i + str(j)
assignment = int(sudokuString[strIndex])
domain = []
if assignment == 0:
for d in range(1, 10):
domain.append(d)
else:
domain.append(assignment)
self.assignment[var] = assignment
self.domain[var] = domain
strIndex += 1
def getSudokuString(self):
string = ""
for i in char_range('a', 'i'):
for j in range(1, 10):
var = i + str(j)
string = string + str(self.assignment[var])
return string
def ac3(self):
queue = self.getArcs()
infererredDomainReductions = []
assignments = []
while len(queue):
arc = queue.pop(0)
localInfererredDomainReductions = self.revise(arc[0], arc[1])
infererredDomainReductions += localInfererredDomainReductions
if len(localInfererredDomainReductions) > 0:
if len(self.domain[arc[0]]) == 0:
return [False, assignments, infererredDomainReductions]
else:
neighbors = self.getNeighbors(arc[0], arc[1])
for k in neighbors:
queue.append([k, arc[0]])
for k, domain in self.domain.items():
if self.assignment[k] == 0 and len(domain) == 1:
self.assignment[k] = domain[0]
assignments.append([k, domain[0]])
return [True, assignments, infererredDomainReductions]
def revise(self, i, j):
excludedFromDomain = {}
infererredDomainReductions = []
for x in self.domain[i]:
compatible = False
for y in self.domain[j]:
if x != y:
compatible = True
if not compatible:
excludedFromDomain[x] = 1
infererredDomainReductions.append([i, x])
if len(excludedFromDomain) > 0:
newDomain = []
for x in self.domain[i]:
if not x in excludedFromDomain:
newDomain.append(x)
self.domain[i] = newDomain
return infererredDomainReductions
def bts(self):
if self.isSolved():
return True
var = self.selectUnassignedVariable()
for value in self.domain[var]:
assignments = [] # backtracking assignments info
domainReductions = [] # backtracking domain substractions info
if self.checkCompatibleAssignment(var, value):
domainReductions += self.assignVarAndGetDomainReductions(var, value)
assignments.append([var, value])
inferences = self.ac3()
assignments += inferences[1]
domainReductions += inferences[2]
if inferences[0] != False:
if self.bts():
return True
# backtrack domain changes and assignments
for assignment in assignments:
self.assignment[assignment[0]] = 0
for domainReduction in domainReductions:
self.domain[domainReduction[0]].append(domainReduction[1])
return False
def selectUnassignedVariable(self):
minVariable = 'a1'
minDomain = 11
for var, domain in self.domain.items():
ld = len(domain)
if ld > 1 and ld < minDomain:
minVariable = var
minDomain = ld
return minVariable
def checkCompatibleAssignment(self, var, value):
affectedVars = self.arcs[var]
for affectedVar in affectedVars:
anyCompatibleAssignment = False
for valueInDomain in self.domain[affectedVar]:
if valueInDomain != value:
anyCompatibleAssignment = True
break
if not anyCompatibleAssignment:
return False
# NOTE: Since sudoku has symmetrical arcs, neighbors are not checked, but we should
return True
def assignVarAndGetDomainReductions(self, var, value):
domainReductions = []
for valueInDomain in self.domain[var]:
if valueInDomain != value:
domainReductions.append([var, valueInDomain])
self.domain[var] = [value]
self.assignment[var] = value
return domainReductions
def dumpSudokuWithDomains(self):
layout = []
layout.append(list(" 1 2 3 4 5 6 7 8 9 "))
for i in char_range('a', 'i'):
layoutI = 1+(ord(i)-ord('a'))*4
layout.append(list( " +---+---+---++---+---+---||---+---+---+"))
layout.append(list(i+"| | | || | | || | | |"))
layout.append(list( " | | | || | | || | | |"))
layout.append(list( " | | | || | | || | | |"))
for j in range(1, 10):
layoutJ = 1+(j-1)*4+j//4+j//7+1-j//8
v = i+str(j)
domain = self.domain[v]
k = len(domain)
for l in range(0, k):
layout[layoutI+1+l%3][layoutJ+l//3] = chr(ord('0')+domain[l])
layout.append(list(" +---+---+---++---+---+---||---+---+---+"))
for line in layout:
print("".join(line))
def main():
if len(sys.argv) != 2:
print "Usage:",sys.argv[0],"<sudoku string>"
print " sudoku_string: for instance 094000130000000000000076002080010000032000000000200060000050400000008007006304008"
exit()
inputSudokuString = sys.argv[1]
sudokuSolver = SudokuSolver(inputSudokuString)
sudokuSolver.ac3()
if sudokuSolver.isSolved():
print "Easy sudoku: solved just with constraint satisfaction"
print sudokuSolver.dumpSudokuWithDomains()
else:
sudokuSolver.bts()
print "Advanced sudoku: solved with constraint satisfaction + backtracking"
print sudokuSolver.dumpSudokuWithDomains()
if __name__ == '__main__':
main()