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Added doctests to Lowest_common_ancestor.py

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Siddhant Jain 2025-01-13 16:41:43 -05:00
parent 4fe50bc1fc
commit 06485a2f01
1 changed files with 104 additions and 4 deletions
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108
data_structures/binary_tree/lowest_common_ancestor.py
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@ -24,7 +24,22 @@ def swap(a: int, b: int) -> tuple[int, 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
Create a sparse table which saves each node's 2^i-th parent.
>>> max_node = 5
>>> parent = [
... [0, 0, 1, 1, 2, 2], # 2^0-th parents
... [0, 0, 0, 0, 1, 1] # 2^1-th parents
... ]
>>> create_sparse(max_node, parent)
[[0, 0, 1, 1, 2, 2], [0, 0, 0, 0, 1, 1]]
>>> max_node = 3
>>> parent = [
... [0, 0, 1, 1], # 2^0-th parents
... [0, 0, 0, 0] # 2^1-th parents
... ]
>>> create_sparse(max_node, parent)
[[0, 0, 1, 1], [0, 0, 0, 0]]
"""
j = 1
while (1 << j) < max_node:
@ -38,6 +53,46 @@ 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:
"""
Return the lowest common ancestor of nodes u and v.
>>> max_node = 13
>>> parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
>>> level = [-1 for _ in range(max_node + 10)]
>>> graph = {
... 1: [2, 3, 4],
... 2: [5],
... 3: [6, 7],
... 4: [8],
... 5: [9, 10],
... 6: [11],
... 7: [],
... 8: [12, 13],
... 9: [],
... 10: [],
... 11: [],
... 12: [],
... 13: [],
... }
>>> level, parent = breadth_first_search(level, parent, max_node, graph, 1)
>>> parent = create_sparse(max_node, parent)
>>> lowest_common_ancestor(1, 3, level, parent)
1
>>> lowest_common_ancestor(5, 6, level, parent)
1
>>> lowest_common_ancestor(7, 11, level, parent)
1
>>> lowest_common_ancestor(6, 7, level, parent)
3
>>> lowest_common_ancestor(4, 12, level, parent)
4
>>> lowest_common_ancestor(8, 8, level, parent)
8
>>> lowest_common_ancestor(9, 10, level, parent)
5
>>> lowest_common_ancestor(12, 13, level, parent)
8
"""
# u must be deeper in the tree than v
if level[u] < level[v]:
u, v = swap(u, v)
@ -65,9 +120,54 @@ def breadth_first_search(
root: int = 1,
) -> tuple[list[int], list[list[int]]]:
"""
sets every nodes direct parent
parent of root node is set to 0
calculates depth of each node from root node
Perform a breadth-first search from the root node of the tree.
Sets every node's direct parent and calculates the depth of each node from the root.
>>> max_node = 5
>>> parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
>>> level = [-1 for _ in range(max_node + 10)]
>>> graph = {
... 1: [2, 3],
... 2: [4],
... 3: [5],
... 4: [],
... 5: []
... }
>>> level, parent = breadth_first_search(level, parent, max_node, graph, 1)
>>> level[:6]
[ -1, 0, 1, 1, 2, 2]
>>> parent[0][1] == 0
True
>>> parent[0][2] == 1
True
>>> parent[0][3] == 1
True
>>> parent[0][4] == 2
True
>>> parent[0][5] == 3
True
>>> # Test with disconnected graph
>>> max_node = 4
>>> parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
>>> level = [-1 for _ in range(max_node + 10)]
>>> graph = {
... 1: [2],
... 2: [],
... 3: [4],
... 4: []
... }
>>> level, parent = breadth_first_search(level, parent, max_node, graph, 1)
>>> level[:5]
[ -1, 0, 1, -1, -1]
>>> parent[0][1] == 0
True
>>> parent[0][2] == 1
True
>>> parent[0][3] == 0
True
>>> parent[0][4] == 3
True
"""
level[root] = 0
q: Queue[int] = Queue(maxsize=max_node)