May you optimise make my code faster $,$ I am wrting a pyhton function to solve sat problem but I am unable to make it faster $,$ could you help me $?$ Some optimisations you may consider are Instead of looping through all clauses each time in unit propagation, consider using a more efficient data structure like a priority queue or heap to track unit clauses, Ensure that unit propagation is efficiently updating the clauses by removing satisfied literals and clauses, Implement more sophisticated variable selection strategies like VSIDS $($Variable State Independent Decaying Sum$)$ or MOMs $($Maximum Occurrence Heuristic$)$ to choose variables intelligently. Evaluate if copying is truly necessary in certain parts of your code. Unnecessary copying can impact performance, especially for large data structure $,$implement early termination conditions based on heuristics or pre$-$processing techniques to reduce unnecessary exploration of the search space, explore opportunities for parallelizing certain parts of the algorithm, such as branching on different variables concurrently, use profiling tools to identify bottlenecks in your code and prioritize optimization efforts accordingly, implementing additional SAT$-$solving techniques such as clause learning, conflict analysis, and backtracking enhancements. These are some suggestion feel free to implement what you like as long it make the code faster.

Please check your code before submitting as many expert just send a code that is either incorrect or slower than mine. I am not in a rush so take your time to do it properly.

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