flat-tree/flat_tree/accessor.py

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"""An accessor for navigating flat trees."""
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__all__ = ["FlatTreeAccessor"]
from typing import List, Optional
class FlatTreeAccessor:
"""A flat tree accessor."""
def index(self, depth: int, offset: int) -> int:
"""The tree index specified by the depth and offset.
:param depth: The depth of the tree
:param offset: The offset from left hand side of the tree
"""
return ((1 + (2 * offset)) * (2 ** depth)) - 1
def offset(self, index: int, depth: Optional[int] = None) -> int:
"""The offset of given index from the left hand side of the tree.
:param index: The tree index
:param depth: The depth of the tree
"""
if not (index & 1):
return int(index / 2)
if depth is None:
depth = self.depth(index)
return int((((index + 1) / (2 ** depth)) - 1) / 2)
def depth(self, index: int) -> int:
"""The depth of the given index in the tree.
:param index: The tree index
"""
depth = 0
index += 1
while not (index & 1):
depth += 1
index = index >> 1
return depth
def parent(self, index: int, depth: Optional[int] = None) -> int:
"""The index of the parent relative to the given index.
:param index: The index relative to the parent
:param depth: The depth of the index
"""
if depth is None:
depth = self.depth(index)
offset = self.offset(index, depth)
return self.index(depth + 1, int((offset - (offset & 1)) / 2))
def sibling(self, index: int, depth: Optional[int] = None) -> int:
"""The index of the sibling relative to the given index.
:param index: The index relative to the sibling
:param depth: The depth of the index
"""
if depth is None:
depth = self.depth(index)
offset = self.offset(index, depth)
offset = offset - 1 if (offset & 1) else offset + 1
return self.index(depth, offset)
def children(self, index: int, depth: Optional[int] = None) -> List[int]:
"""All children relative to the given index.
:param index: The parent index
:param depth: The depth of the index
"""
if not (index & 1):
return []
if not depth:
depth = self.depth(index)
offset = self.offset(index, depth) * 2
return [
self.index((depth - 1), offset),
self.index((depth - 1), (offset + 1)),
]
def spans(self, index: int, depth: Optional[int] = None) -> List[int]:
"""The span of the tree.
:param index: The index of the root
:param depth: The depth of the index
"""
if not (index & 1):
return [index, index]
if not depth:
depth = self.depth(index)
offset = self.offset(index, depth)
width = 2 ** (depth + 1)
return [(offset * width), ((offset + 1) * width) - 2]
def left_span(self, index: int, depth: Optional[int] = None) -> int:
"""The leftmost span of the tree.
:param index: The index of the tree root
:param depth: The depth of the index
"""
if not (index & 1):
return index
if not depth:
depth = self.depth(index)
return self.offset(index, depth) * (2 ** (depth + 1))
def right_span(self, index: int, depth: Optional[int] = None) -> int:
"""The rightmost span of the tree.
:param index: The index of the tree root
:param depth: The depth of the index
"""
if not (index & 1):
return index
if not depth:
depth = self.depth(index)
return (self.offset(index, depth) + 1) * (2 ** (depth + 1)) - 2
def count(self, index: int, depth: Optional[int] = None) -> int:
"""The number of nodes a tree contains.
:param index: The index of the root of the tree
:param depth: The depth of the root of the tree
"""
if not (index & 1):
return 1
if not depth:
depth = self.depth(index)
return (2 ** (depth + 1)) - 1
def full_roots(self, index: int) -> List[int]:
"""All full roots within the tree.
:param index: The index of the root of the tree
"""
if index & 1:
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message = "Roots only available for tree depth 0"
raise ValueError(message)
roots: List[int] = []
index = int(index / 2)
offset, factor = 0, 1
while True:
if not index:
return roots
while (factor * 2) <= index:
factor = factor * 2
roots.append((offset + factor) - 1)
offset = (offset + 2) * factor
index = index - factor
factor = 1
def left_child(self, index: int, depth: Optional[int] = None) -> int:
"""The left child of the given index.
:param index: The index of the tree
:param depth: The depth of the tree
"""
if not (index & 1):
return -1
if not depth:
depth = self.depth(index)
return self.index((depth - 1), (self.offset(index, depth) * 2))
def right_child(self, index: int, depth: Optional[int] = None) -> int:
"""The right child of the given index.
:param index: The index of the tree
:param depth: The depth of the tree
"""
if not (index & 1):
return -1
if not depth:
depth = self.depth(index)
return self.index((depth - 1), (1 + (self.offset(index, depth) * 2)))