May you fill in my code function and make it optimal and fast.

My code:

def dpll$\_$sat$\_$solve$($clause$\_$set, partial$\_$assignment$)$:

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

# Implement unit propagation

pass

def pure$\_$literal$\_$elimination$($clauses$,$ assignment$)$:

# Implement pure literal elimination

pass

def choose$\_$literal$($clauses$,$ assignment$)$:

# Implement advanced heuristic for choosing the next literal

pass

def clause$\_$learning$($clauses$,$ assignment$)$:

# Implement clause learning

pass

def backtrack$($assignment$)$:

# Implement non$-$chronological backtracking

pass

def is$\_$satisfied$($clauses$,$ assignment$)$:

# Check if the clauses are satisfied by the assignment

pass

def is$\_$unsatisfiable$($clauses$)$:

# Check if the clauses are unsatisfiable

pass

# Main DPLL algorithm

if not clause$\_$set:

return partial$\_$assignment

# Apply unit propagation

clause$\_$set $=$ unit$\_$propagation$($clause$\_$set, partial$\_$assignment$)$

# Apply pure literal elimination

clause$\_$set $=$ pure$\_$literal$\_$elimination$($clause$\_$set, partial$\_$assignment$)$

if is$\_$satisfied$($clause$\_$set, partial$\_$assignment$)$:

return partial$\_$assignment

if is$\_$unsatisfiable$($clause$\_$set$)$:

return False

literal $=$ choose$\_$literal$($clause$\_$set, partial$\_$assignment$)$

# Try assigning true to the literal

new$\_$assignment $=$ partial$\_$assignment $+[$literal$]$

result $=$ dpll$\_$sat$\_$solve$($clause$\_$set, new$\_$assignment$)$

if result $!=$ False:

return result

# If assigning true fails, try assigning false

new$\_$assignment $=$ partial$\_$assignment $+[-$literal$]$

result $=$ dpll$\_$sat$\_$solve$($clause$\_$set, new$\_$assignment$)$

return result if result $!=$ False else backtrack$($partial$\_$assignment$)$