2024-10-19 16:43:40 +05:30
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from __future__ import annotations
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2024-10-19 10:58:52 +00:00
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2024-10-19 11:25:59 +00:00
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2024-10-19 15:58:29 +05:30
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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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2024-10-19 11:25:59 +00:00
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2024-10-19 15:58:29 +05:30
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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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>>> pst = PersistentSegmentTree([1, 2, 3, 4])
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>>> root = pst._build([1, 2, 3, 4], 0, 3)
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>>> root.value # Sum of the whole array
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10
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>>> root.left.value # Sum of the left half
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3
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>>> root.right.value # Sum of the right half
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7
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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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>>> pst = PersistentSegmentTree([1, 2, 3, 4])
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>>> version_1 = pst.update(0, 1, 5) # Update index 1 to 5
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>>> pst.query(version_1, 0, 3) # Query sum of all elements in new version
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13
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>>> pst.query(0, 0, 3) # Original version remains unchanged
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10
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>>> version_2 = pst.update(version_1, 3, 6) # Update index 3 to 6 in version_1
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>>> pst.query(version_2, 0, 3) # Query sum of all elements in newest version
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15
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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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if node is None:
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raise ValueError("Cannot update a None node")
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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
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else:
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new_node.left = node.left
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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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>>> pst = PersistentSegmentTree([1, 2, 3, 4])
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>>> pst.query(0, 0, 3) # Sum of all elements in original version
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10
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>>> pst.query(0, 1, 2) # Sum of elements at index 1 and 2 in original version
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5
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>>> version_1 = pst.update(0, 1, 5) # Update index 1 to 5
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>>> pst.query(version_1, 0, 3) # Sum of all elements in new version
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13
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>>> pst.query(version_1, 1, 2) # Sum of elements at index 1 and 2 in new version
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8
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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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if node is None:
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return 0
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if 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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