def add_pair(index,value,temp,unassigned,order,tried):
domain_want = []
for i,j in temp.items():
if index in unassigned[i].relations:
j.relations.append(index)
if value in unassigned[i].domain:
domain_want.append(i)
#restore the value to the cells that should have it if index was the only one constraining it
for wanting in domain_want:
give = True
for history in order:
if history[0] in unassigned[wanting].relations:
if history[1]==value:
give = False
break
if give:
temp[wanting].domain.append(value)
#restore the index back into the unassigned dictionary
temp[index] = Cell(index,".")
temp[index].domain = [val for val in unassigned[index].domain]
for history in order:
if history[0] in temp[index].relations:
if history[1] in temp[index].domain:
temp[index].domain.remove(history[1])
for already in tried[index]:
if already in temp[index].domain:
temp[index].domain.remove(already)
temp[index].relations = [relate for relate in unassigned[index].relations if relate in temp.keys()]
return temp
def backtracking_search(board):
unassigned = {}
indices = []
tried ={}
#Put all the remaining cells in the CSP into these structures
for i,j in board.items():
if len(j.domain)>1:
unassigned[i] = Cell(i,".")
unassigned[i].domain = j.domain.copy()
indices.append(i)
tried[i]=[]
for i,j in unassigned.items():
unassigned[i].relations = remove_relations(unassigned[i].relations,indices)
order = []
i = 0
other_dict = deepcopy(unassigned)
temp = {key:val for key,val in sorted(other_dict.items(),key = sorting_key)}
#Backtrack search for a valid solution.
#Uses the Minimum Remaining Values, Degree, and the Least Constraining Value heuristics
while i>=0 and i<len(indices):
#Check the best variable to choose
first_key = next(iter(temp))
first_value = best_value(first_key,temp)
#If there are no valid domain values
if first_value==0:
if len(order)==0:
print("Invalid Puzzle!!!")
return
#Backtrack one cell and variable pair
old_key,old_value = order.pop()
#Reset the current tried values and add the backtracked value into the tried values
tried[first_key] = []
tried[old_key].append(old_value)
#Add the backtracked index back into the CSP and reset the domain of the current variable
temp = add_pair(old_key,old_value,temp,unassigned,order,tried)
temp[first_key].domain = restore_domain(first_key,order,unassigned)
i-=1
else:
#Add the current best value and cell pair into the history, remove the value from affected cells and remove the chosen cell from the CSP
order.append([first_key,first_value])
temp = remove_pair(first_key,first_value,temp)
del temp[first_key]
i+=1
#Sort the remaining values to find the next best value to choose
temp = {key:val for key,val in sorted(temp.items(),key = sorting_key)}
#Set the variables chosen from backtracking to the main board
for i,j in order:
board[i].domain = [j]
return board
