Could you help me with the following problems :

$1-$ My code only work if the assignment is in dictionary form but he should accept an list of list instrad $,$ where the negation of literal is represent by fora literal will be an integer, where a negative integer indicates the negation of the variable denoted by the corresponding positive integer.

$2-$ My code output two answer one in dictionarie form and the other in a list form $,$ ca you make it to just output the list form

$3-$ after that can you take a look and make it faster $?$ Take your time to analyze it and make sure you code is correct and fast $.$ Most expert either submit soemthing wrong or a code that is slower than mine $.$

My code :

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

updated$\_$clauses $=[]$

for clause in clauses:

if literal in clause:

continue # Skip the clause as it's satisfied

new$\_$clause $=[$x for x in clause if x $!=-$literal$]$

if not new$\_$clause:

return False # Unsatisfiable clause found

updated$\_$clauses.append$($new$\_$clause$)$

return updated$\_$clauses # Always return a list

def choose$\_$variable$($clauses$)$:

literal$\_$count $=\{\}$

for clause in clauses:

for literal in clause:

literal$\_$count$[$abs$($literal$)]=$ literal$\_$count.get$($abs$($literal$),0)+1$

return max$($literal$\_$count, key$=$literal$\_$count.get$)$

def unit$\_$propagation$($clauses$,$ assignment$)$:

while True:

unit$\_$literals $=\{$clause$[0]$ for clause in clauses if len$($clause$)==1\}$

if not unit$\_$literals:

break

for unit$\_$literal in unit$\_$literals:

clauses $=$ update$\_$clauses$($clauses$,$ unit$\_$literal$)$

if clauses is False:

return False, assignment

assignment$[$abs$($unit$\_$literal$)]=$ unit$\_$literal $>0$

return clauses, assignment

def dpll$\_$sat$\_$solve$($clauses$,$ assignment$=$None$)$:

if assignment is None:

assignment $=\{\}$

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

if clauses is False:

return False

if all$($len$($clause$)==0$ for clause in clauses$)$:

return assignment

var $=$ choose$\_$variable$($clauses$)$

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

if not unassigned$\_$vars:

return assignment

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:

return result

return False

def convert$\_$to$\_$list$\_$of$\_$lists$($result$\_$dict$)$:

if result$\_$dict $==$ False:

return False

else:

result$\_$list $=[]$

print$($result$\_$dict$)$

max$\_$var $=$ max$($result$\_$dict, key$=$abs$)$

for i in range$(1,$ max$\_$var $+1)$:

if i in result$\_$dict:

if result$\_$dict$[$i$]$:

result$\_$list.append$($i$)$

else:

result$\_$list.append$(-$i$)$

else:

result$\_$list.append$(-$i$)$

return result$\_$list