There is a problem in my code $,$ my unit$\_$propagation fuction does work because i am trying to call the attribute starwith in a intenger but i dont know how to solve withou ruin my code $.$ Could you help me please $?$ Also if you could can you optmize it and instead of returning a dictionary return a list of list $.$ If the number is false should return the negation of the number for example if $1$: False it should appear as $-1$ in the list $.$ Thank you in advance $.$ Here is my code :

def dpll$\_$sat$\_$solve$($clause$\_$set, partial$\_$assignment$=$None$)$:

if partial$\_$assignment is None:

partial$\_$assignment $=\{\}$

# Unit propagation

clause$\_$set $=\_$unit$\_$propagate$($clause$\_$set, partial$\_$assignment.copy$())$

if not clause$\_$set:

return partial$\_$assignment # All clauses are satisfied

# Check for empty clause after unit propagation $($UNSAT$)$

for clause in clause$\_$set:

if not clause:

return False

# Choose a variable to branch on $($heuristics can be applied here$)$

unassigned$\_$vars $=[$var for var in set.union$(*$clause$\_$set$)$ if var not in partial$\_$assignment$]$

var $=$ unassigned$\_$vars$[0]$ # Simple heuristic: choose the first unassigned variable

# Try both truth assignments for the chosen variable

result $=$ dpll$\_$sat$\_$solve$($clause$\_$set.copy$(),$ dict$($partial$\_$assignment, $**\{$var: True$\}))$

if result:

return result

result $=$ dpll$\_$sat$\_$solve$($clause$\_$set.copy$(),$ dict$($partial$\_$assignment, $**\{$var: False$\}))$

return result

def $\_$unit$\_$propagate$($clause$\_$set, partial$\_$assignment$)$:

simplified$\_$clauses $=[]$

for clause in clause$\_$set:

# Check for unit clauses $($only one unassigned literal$)$

unassigned$\_$literals $=[$lit for lit in clause if lit not in partial$\_$assignment$]$

if len$($unassigned$\_$literals$)==1$:

literal $=$ unassigned$\_$literals$[0]$

# Imply the assignment based on the remaining literal

partial$\_$assignment$[$literal$]=$ not literal.startswith$("-")$

else:

simplified$\_$clauses.append$($clause$)$

# Return the simplified clause set after removing unit clauses

return simplified$\_$clauses