Pyupgrade to Python 3.9 (#4718)

* Pyupgrade to Python 3.9

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

project_euler/problem_077/sol1.py

@@ -12,10 +12,10 @@ It is possible to write ten as the sum of primes in exactly five different ways:
 What is the first value which can be written as the sum of primes in over
 five thousand different ways?
 """
+from __future__ import annotations
 
 from functools import lru_cache
 from math import ceil
-from typing import Optional, Set
 
 NUM_PRIMES = 100
 
@@ -30,7 +30,7 @@ for prime in range(3, ceil(NUM_PRIMES ** 0.5), 2):
 
 
 @lru_cache(maxsize=100)
-def partition(number_to_partition: int) -> Set[int]:
+def partition(number_to_partition: int) -> set[int]:
     """
     Return a set of integers corresponding to unique prime partitions of n.
     The unique prime partitions can be represented as unique prime decompositions,
@@ -47,7 +47,7 @@ def partition(number_to_partition: int) -> Set[int]:
     elif number_to_partition == 0:
         return {1}
 
-    ret: Set[int] = set()
+    ret: set[int] = set()
     prime: int
     sub: int
 
@@ -60,7 +60,7 @@ def partition(number_to_partition: int) -> Set[int]:
     return ret
 
 
-def solution(number_unique_partitions: int = 5000) -> Optional[int]:
+def solution(number_unique_partitions: int = 5000) -> int | None:
     """
     Return the smallest integer that can be written as the sum of primes in over
     m unique ways.