May you optimise my code $?$ You may use any advance tecniques like pure elimination $,$ clause learning ect. I will leave the ones you should use to your judge as an expert. Also my code is outpting a dictoniries as an answer could you make a function that before my code return the answer pick the dictonarie and transform it in a list of list where a literal will be an integer, where a negative integer indicates the negation of the variable denotedby the corresponding positive integer. Going back to the optimizations you may take your time I am in not rush for the answer but please give me a correct and fast code $,$ because normally they do not give a accurate answer. Thanks in advance.

my code :

def update$\_$clauses$($clauses$,$ literal$)$:

$"""$

Update the clauses based on the latest assignment.

Parameters:

$-$ clauses: the current set of clauses.

$-$ literal: the literal that has just been assigned a truth value.

Returns:

$-$ The updated set of clauses after considering the assignment, or

$-$ False if a contradiction is found $($an empty clause$).$

$"""$

updated$\_$clauses $=[]$

for clause in clauses:

if literal in clause: # If the clause contains the literal, it is satisfied

continue # So$,$ we skip adding this clause to the updated list

new$\_$clause $=[$x for x in clause if x $!=-$literal$]$ # Remove the negated literal

if not new$\_$clause: # If the clause is empty, we've found a contradiction

return False

updated$\_$clauses.append$($new$\_$clause$)$ # Add the updated clause

return updated$\_$clauses

def dpll$\_$sat$\_$solve$($clauses$,$ assignment$=\{\})$:

$"""$

The main DPLL SAT solver function. It recursively searches for a satisfying assignment

for the clause set under the given partial assignment.

Parameters:

$-$ clauses: a list of sets, where each set represents a clause.

$-$ assignment: a dictionary mapping variables to their assigned boolean values.

Returns:

$-$ A satisfying assignment $($a dictionary$)$ if one exists, or

$-$ False if the clause set is unsatisfiable.

$"""$

clauses, assignment $=$ unit$\_$propagation$($clauses$,$ assignment$)$ # Perform unit propagation

if clauses is False: # Check for a contradiction

return False

if all$($len$($clause$)==0$ for clause in clauses$)$: # Check if all clauses are satisfied

return assignment

# Choose an unassigned variable to branch on

unassigned$\_$vars $=\{$abs$($literal$)$ for clause in clauses for literal in clause if abs$($literal$)$ not in assignment$\}$

if not unassigned$\_$vars: # No variables left to assign, so the current assignment satisfies all clauses

return assignment

var $=$ unassigned$\_$vars.pop$()$ # Select a variable for branching

# Try assigning True to the variable and solve recursively

for value in $[$True$,$ False$]$:

new$\_$assignment $=$ assignment.copy$()$

new$\_$assignment$[$var$]=$ value

result $=$ dpll$\_$sat$\_$solve$($update$\_$clauses$($clauses$,$ var if value else $-$var$),$ new$\_$assignment$)$

if result is not False: # Found a satisfying assignment

return result

return False # No satisfying assignment found