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 = value
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self.left = None
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self.right = None
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class PersistentSegmentTree:
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def __init__(self, arr: list[int]) -> None:
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2024-10-19 16:16:21 +05:30
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self.n = 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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2024-10-19 16:19:23 +05:30
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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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2024-10-19 15:58:29 +05:30
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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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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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2024-10-19 16:16:21 +05:30
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return len(self.roots) - 1
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2024-10-19 15:58:29 +05:30
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def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node:
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2024-10-19 16:19:23 +05:30
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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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>>> pst = PersistentSegmentTree([1, 2, 3, 4])
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>>> old_root = pst.roots[0]
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>>> new_root = pst._update(old_root, 0, 3, 1, 5) # Update index 1 to 5
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>>> new_root.value # New sum after update
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13
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>>> old_root.value # Old root remains unchanged
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10
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>>> new_root.left.value # Updated left child
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6
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>>> new_root.right.value # Right child remains the same
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7
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"""
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2024-10-19 15:58:29 +05:30
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if start == end:
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2024-10-19 16:16:21 +05:30
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return Node(value)
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2024-10-19 15:58:29 +05:30
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mid = (start + end) // 2
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new_node = Node()
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2024-10-19 16:16:21 +05:30
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2024-10-19 15:58:29 +05:30
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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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2024-10-19 16:16:21 +05:30
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2024-10-19 15:58:29 +05:30
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new_node.value = new_node.left.value + new_node.right.value
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2024-10-19 16:16:21 +05:30
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2024-10-19 15:58:29 +05:30
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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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return self._query(self.roots[version], 0, self.n - 1, left, right)
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def _query(self, node: Node, start: int, end: int, left: int, right: int) -> int:
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2024-10-19 16:19:23 +05:30
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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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>>> pst = PersistentSegmentTree([1, 2, 3, 4])
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>>> root = pst.roots[0]
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>>> pst._query(root, 0, 3, 1, 2) # Sum of elements at index 1 and 2
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5
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>>> pst._query(root, 0, 3, 0, 3) # Sum of all elements
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10
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>>> pst._query(root, 0, 3, 2, 3) # Sum of elements at index 2 and 3
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7
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"""
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2024-10-19 15:58:29 +05:30
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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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2024-10-19 10:50:37 +00:00
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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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2024-10-19 16:16:21 +05:30
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2024-10-19 16:19:23 +05:30
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# Running the doctests
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2024-10-19 16:16:21 +05:30
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if __name__ == "__main__":
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import doctest
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2024-10-19 10:50:37 +00:00
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2024-10-19 16:16:21 +05:30
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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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