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data_structures/binary_tree/lowest_common_ancestor.py
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@ -32,7 +32,7 @@ def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
For example, consider a small tree where: For example, consider a small tree where:
- Node 1 is the root (its parent is 0), - Node 1 is the root (its parent is 0),
- Nodes 2 and 3 have parent 1. - Nodes 2 and 3 have parent 1.
We set up the parent table for only two levels (row 0 and row 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.) for max_node = 3. (Note that in practice the table has many rows.)
@ -65,7 +65,7 @@ def lowest_common_ancestor(
The lists `level` and `parent` must be precomputed. `level[i]` is the depth of node i, 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. and `parent` is a sparse table where parent[0][i] is the direct parent of node i.
>>> # Consider a simple tree: >>> # Consider a simple tree:
>>> # 1 >>> # 1
>>> # / \\ >>> # / \\
@ -142,9 +142,9 @@ def main() -> None:
then create the sparse table and compute several lowest common ancestors. then create the sparse table and compute several lowest common ancestors.
The sample tree used is: The sample tree used is:
1 1
/ | \ / | \
2 3 4 2 3 4
/ / \\ \\ / / \\ \\
5 6 7 8 5 6 7 8
@ -160,7 +160,7 @@ def main() -> None:
- LCA(8, 8) --> 8 - LCA(8, 8) --> 8
To test main() without it printing to the console, we capture the output. To test main() without it printing to the console, we capture the output.
>>> import sys >>> import sys
>>> from io import StringIO >>> from io import StringIO
>>> backup = sys.stdout >>> backup = sys.stdout