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Update persistent_segment_tree.py

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Putul Singh 2024-10-19 16:16:21 +05:30 committed by GitHub
parent f5d380aafb
commit 819fdc8836
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1 changed files with 30 additions and 20 deletions
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data_structures/persistent_segment_tree.py
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@ -7,19 +7,18 @@ class Node:
class PersistentSegmentTree: class PersistentSegmentTree:
def __init__(self, arr: list[int]) -> None: def __init__(self, arr: list[int]) -> None:
"""
Initialize the Persistent Segment Tree with the given array.
>>> pst = PersistentSegmentTree([1, 2, 3])
>>> pst.query(0, 0, 2)
6
"""
self.n = len(arr) self.n = len(arr)
self.roots: list[Node] = [] self.roots: list[Node] = []
self.roots.append(self._build(arr, 0, self.n - 1)) self.roots.append(self._build(arr, 0, self.n - 1))
def _build(self, arr: list[int], start: int, end: int) -> Node: def _build(self, arr: list[int], start: int, end: int) -> Node:
"""
Builds a segment tree from the provided array.
>>> pst = PersistentSegmentTree([1, 2, 3])
>>> root = pst._build([1, 2, 3], 0, 2)
>>> root.value # Sum of the whole array
6
"""
if start == end: if start == end:
return Node(arr[start]) return Node(arr[start])
mid = (start + end) // 2 mid = (start + end) // 2
@ -31,41 +30,46 @@ class PersistentSegmentTree:
def update(self, version: int, index: int, value: int) -> int: def update(self, version: int, index: int, value: int) -> int:
""" """
Updates the segment tree with a new value at the specified index. Update the value at the given index and return the new version.
>>> pst = PersistentSegmentTree([1, 2, 3]) >>> pst = PersistentSegmentTree([1, 2, 3])
>>> version_1 = pst.update(0, 1, 5) >>> version_1 = pst.update(0, 1, 5)
>>> pst.query(version_1, 0, 2) # Query sum from index 0 to 2 >>> pst.query(version_1, 0, 2)
9 9
""" """
new_root = self._update(self.roots[version], 0, self.n - 1, index, value) new_root = self._update(self.roots[version], 0, self.n - 1, index, value)
self.roots.append(new_root) self.roots.append(new_root)
return len(self.roots) - 1 # return the index of the new version return len(self.roots) - 1
def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node: def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node:
if start == end: if start == end:
new_node = Node(value) return Node(value)
return new_node
mid = (start + end) // 2 mid = (start + end) // 2
new_node = Node() new_node = Node()
if index <= mid: if index <= mid:
new_node.left = self._update(node.left, start, mid, index, value) new_node.left = self._update(node.left, start, mid, index, value)
new_node.right = node.right new_node.right = node.right
else: else:
new_node.left = node.left new_node.left = node.left
new_node.right = self._update(node.right, mid + 1, end, index, value) new_node.right = self._update(node.right, mid + 1, end, index, value)
new_node.value = new_node.left.value + new_node.right.value new_node.value = new_node.left.value + new_node.right.value
return new_node return new_node
def query(self, version: int, left: int, right: int) -> int: def query(self, version: int, left: int, right: int) -> int:
""" """
Queries the sum in the given range for the specified version. Query the sum in the given range for the specified version.
>>> pst = PersistentSegmentTree([1, 2, 3]) >>> pst = PersistentSegmentTree([1, 2, 3])
>>> version_1 = pst.update(0, 1, 5) >>> pst.query(0, 0, 2)
>>> pst.query(version_1, 0, 1) # Query sum from index 0 to 1
6 6
>>> pst.query(version_1, 0, 2) # Query sum from index 0 to 2 >>> version_1 = pst.update(0, 1, 5)
>>> pst.query(version_1, 0, 1)
6
>>> pst.query(version_1, 0, 2)
9 9
""" """
return self._query(self.roots[version], 0, self.n - 1, left, right) return self._query(self.roots[version], 0, self.n - 1, left, right)
@ -76,6 +80,12 @@ class PersistentSegmentTree:
if left <= start and right >= end: if left <= start and right >= end:
return node.value return node.value
mid = (start + end) // 2 mid = (start + end) // 2
return self._query(node.left, start, mid, left, right) + self._query( return (self._query(node.left, start, mid, left, right) +
node.right, mid + 1, end, left, right self._query(node.right, mid + 1, end, left, right))
)
if __name__ == "__main__":
import doctest
print("Running doctests...")
result = doctest.testmod()
print(f"Ran {result.attempted} tests, {result.failed} failed.")