from __future__ import annotations (#2464)

* from __future__ import annotations

* fixup! from __future__ import annotations

* fixup! from __future__ import annotations

* fixup! Format Python code with psf/black push

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

data_structures/binary_tree/lowest_common_ancestor.py

@@ -1,11 +1,12 @@
 # https://en.wikipedia.org/wiki/Lowest_common_ancestor
 # https://en.wikipedia.org/wiki/Breadth-first_search
 
+from __future__ import annotations
+
 import queue
-from typing import Dict, List, Tuple
 
 
-def swap(a: int, b: int) -> Tuple[int, int]:
+def swap(a: int, b: int) -> tuple[int, int]:
     """
     Return a tuple (b, a) when given two integers a and b
     >>> swap(2,3)
@@ -21,7 +22,7 @@ def swap(a: int, b: int) -> Tuple[int, int]:
     return a, b
 
 
-def create_sparse(max_node: int, parent: List[List[int]]) -> List[List[int]]:
+def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
     """
     creating sparse table which saves each nodes 2^i-th parent
     """
@@ -35,8 +36,8 @@ def create_sparse(max_node: int, parent: List[List[int]]) -> List[List[int]]:
 
 # returns lca of node u,v
 def lowest_common_ancestor(
-    u: int, v: int, level: List[int], parent: List[List[int]]
-) -> List[List[int]]:
+    u: int, v: int, level: list[int], parent: list[list[int]]
+) -> list[list[int]]:
     # u must be deeper in the tree than v
     if level[u] < level[v]:
         u, v = swap(u, v)
@@ -57,12 +58,12 @@ def lowest_common_ancestor(
 
 # runs a breadth first search from root node of the tree
 def breadth_first_search(
-    level: List[int],
-    parent: List[List[int]],
+    level: list[int],
+    parent: list[list[int]],
     max_node: int,
-    graph: Dict[int, int],
+    graph: dict[int, int],
     root=1,
-) -> Tuple[List[int], List[List[int]]]:
+) -> tuple[list[int], list[list[int]]]:
     """
     sets every nodes direct parent
     parent of root node is set to 0