mirror of
https://github.com/TheAlgorithms/Python.git
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95 lines
3.1 KiB
Python
95 lines
3.1 KiB
Python
from __future__ import annotations
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class Node:
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def __init__(self, value: int = 0) -> None:
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self.value: int = value
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self.left: Node | None = None
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self.right: Node | None = None
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class PersistentSegmentTree:
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def __init__(self, arr: list[int]) -> None:
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self.n: int = len(arr)
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self.roots: list[Node] = []
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self.roots.append(self._build(arr, 0, self.n - 1))
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def _build(self, arr: list[int], start: int, end: int) -> Node:
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"""
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Builds a segment tree from the provided array.
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"""
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if start == end:
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return Node(arr[start])
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mid = (start + end) // 2
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node = Node()
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node.left = self._build(arr, start, mid)
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node.right = self._build(arr, mid + 1, end)
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node.value = node.left.value + node.right.value
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return node
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def update(self, version: int, index: int, value: int) -> int:
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"""
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Updates the value at the given index and returns the new version.
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"""
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new_root = self._update(self.roots[version], 0, self.n - 1, index, value)
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self.roots.append(new_root)
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return len(self.roots) - 1
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def _update(
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self, node: Node | None, start: int, end: int, index: int, value: int
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) -> Node:
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"""
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Updates the node for the specified index and value and returns the new node.
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"""
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if node is None: # Handle the None case
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node = Node() # Create a new node if None
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if start == end:
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return Node(value)
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mid = (start + end) // 2
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new_node = Node()
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if index <= mid:
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new_node.left = self._update(node.left, start, mid, index, value)
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new_node.right = node.right # Ensure right node is the same as the original
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else:
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new_node.left = node.left # Ensure left node is the same as the original
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new_node.right = self._update(node.right, mid + 1, end, index, value)
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new_node.value = new_node.left.value + (
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new_node.right.value if new_node.right else 0
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)
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return new_node
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def query(self, version: int, left: int, right: int) -> int:
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"""
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Queries the sum in the given range for the specified version.
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"""
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return self._query(self.roots[version], 0, self.n - 1, left, right)
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def _query(
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self, node: Node | None, start: int, end: int, left: int, right: int
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) -> int:
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"""
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Queries the sum of values in the range [left, right] for the given node.
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"""
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if node is None or left > end or right < start:
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return 0
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if left <= start and right >= end:
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return node.value
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mid = (start + end) // 2
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return self._query(node.left, start, mid, left, right) + self._query(
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node.right, mid + 1, end, left, right
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)
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# Running the doctests
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if __name__ == "__main__":
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import doctest
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print("Running doctests...")
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result = doctest.testmod()
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print(f"Ran {result.attempted} tests, {result.failed} failed.")
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