diff --git a/data_structures/binary_tree/lowest_common_ancestor.py b/data_structures/binary_tree/lowest_common_ancestor.py index 2a729414d..6ba53b0af 100644 --- a/data_structures/binary_tree/lowest_common_ancestor.py +++ b/data_structures/binary_tree/lowest_common_ancestor.py @@ -22,21 +22,21 @@ def swap(a: int, b: int) -> tuple[int, int]: def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]: """ Create a sparse table that saves each node's 2^i-th parent. - + The given ``parent`` table should have the direct parent of each node in row 0. This function fills in: - + parent[j][i] = parent[j - 1][parent[j - 1][i]] - + for each j where 2^j is less than max_node. - + For example, consider a small tree where: - Node 1 is the root (its parent is 0), - Nodes 2 and 3 have parent 1. We set up the parent table for only two levels (row 0 and row 1) for max_node = 3. (Note that in practice the table has many rows.) - + >>> parent0 = [0, 0, 1, 1] # 0 is unused; node1's parent=0, nodes 2 and 3's parent=1. >>> parent1 = [0, 0, 0, 0] >>> parent = [parent0, parent1] @@ -58,11 +58,11 @@ def lowest_common_ancestor( """ Return the lowest common ancestor (LCA) of nodes u and v in a tree. <<<<<<< HEAD - + The lists ``level`` and ``parent`` must be precomputed. ``level[i]`` is the depth of node i, and ``parent`` is a sparse table where parent[0][i] is the direct parent of node i. - + ======= The lists `level` and `parent` must be precomputed. `level[i]` is the depth of node i, @@ -107,10 +107,10 @@ def breadth_first_search( ) -> tuple[list[int], list[list[int]]]: """ Run a breadth-first search (BFS) from the root node of the tree. - + This sets each node's direct parent (stored in parent[0]) and calculates the depth (level) of each node from the root. - + >>> # Consider a simple tree: >>> # 1 >>> # / \\ @@ -141,18 +141,18 @@ def main() -> None: """ Run a BFS to set node depths and parents in a sample tree, then create the sparse table and compute several lowest common ancestors. - + The sample tree used is: <<<<<<< HEAD - + 1 - / | \ + / | \ 2 3 4 / / \\ \\ 5 6 7 8 / \\ | / \\ 9 10 11 12 13 - + ======= 1 @@ -171,7 +171,7 @@ def main() -> None: - LCA(6, 7) --> 3 - LCA(4, 12) --> 4 - LCA(8, 8) --> 8 - + To test main() without it printing to the console, we capture the output. >>> import sys