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modify doctest

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This commit is contained in:
Siddhant Jain 2025-01-13 17:21:30 -05:00
parent c8ac0429ec
commit 0cd031a685
1 changed files with 26 additions and 27 deletions
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23
data_structures/binary_tree/lowest_common_ancestor.py
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@ -23,11 +23,11 @@ def swap(a: int, b: int) -> tuple[int, int]:
def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
"""
r"""
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:
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]]
@ -40,7 +40,7 @@ def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
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.
>>> parent0 = [0, 0, 1, 1]
>>> parent1 = [0, 0, 0, 0]
>>> parent = [parent0, parent1]
>>> sparse = create_sparse(3, parent)
@ -59,18 +59,17 @@ def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
def lowest_common_ancestor(
u: int, v: int, level: list[int], parent: list[list[int]]
) -> int:
"""
r"""
Return the lowest common ancestor (LCA) of nodes u and v in a tree.
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.
>>> # Consider a simple tree:
>>> # 1
>>> # / \\
>>> # 2 3
>>> # With levels: level[1]=0, level[2]=1, level[3]=1 and parent[0]=[0, 0, 1, 1]
>>> # With levels: level[1]=0, level[2]=1, level[3]=1 and
>>> # parent[0]=[0, 0, 1, 1]
>>> level = [-1, 0, 1, 1] # index 0 is dummy
>>> parent = [[0, 0, 1, 1]] + [[0, 0, 0, 0] for _ in range(19)]
>>> lowest_common_ancestor(2, 3, level, parent)
@ -104,7 +103,7 @@ def breadth_first_search(
graph: dict[int, list[int]],
root: int = 1,
) -> tuple[list[int], list[list[int]]]:
"""
r"""
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
@ -117,7 +116,7 @@ def breadth_first_search(
>>> graph = {1: [2, 3], 2: [], 3: []}
>>> level = [-1] * 4 # index 0 is unused; nodes 1 to 3.
>>> parent = [[0] * 4 for _ in range(20)]
>>> new_level, new_parent = breadth_first_search(level, parent, 3, graph, root=1)
>>> new_level, new_parent=breadth_first_search(level,parent,3,graph,root=1)
>>> new_level[1:4]
[0, 1, 1]
>>> new_parent[0][1:4]
@ -137,7 +136,7 @@ def breadth_first_search(
def main() -> None:
"""
r"""
Run a BFS to set node depths and parents in a sample tree, then create the
sparse table and compute several lowest common ancestors.