Python/data_structures/persistent_segment_tree.py

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class Node:
def __init__(self, value: int = 0) -> None:
self.value = value
self.left = None
self.right = None
class PersistentSegmentTree:
def __init__(self, arr: list[int]) -> None:
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self.n = len(arr)
self.roots: list[Node] = []
self.roots.append(self._build(arr, 0, self.n - 1))
def _build(self, arr: list[int], start: int, end: int) -> Node:
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"""
Builds a segment tree from the provided array.
>>> pst = PersistentSegmentTree([1, 2, 3, 4])
>>> root = pst._build([1, 2, 3, 4], 0, 3)
>>> root.value # Sum of the whole array
10
>>> root.left.value # Sum of the left half
3
>>> root.right.value # Sum of the right half
7
"""
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if start == end:
return Node(arr[start])
mid = (start + end) // 2
node = Node()
node.left = self._build(arr, start, mid)
node.right = self._build(arr, mid + 1, end)
node.value = node.left.value + node.right.value
return node
def update(self, version: int, index: int, value: int) -> int:
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"""
Updates the value at the given index and returns the new version.
>>> pst = PersistentSegmentTree([1, 2, 3, 4])
>>> version_1 = pst.update(0, 1, 5) # Update index 1 to 5
>>> pst.query(version_1, 0, 3) # Query sum of all elements in new version
13
>>> pst.query(0, 0, 3) # Original version remains unchanged
10
>>> version_2 = pst.update(version_1, 3, 6) # Update index 3 to 6 in version_1
>>> pst.query(version_2, 0, 3) # Query sum of all elements in newest version
15
"""
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new_root = self._update(self.roots[version], 0, self.n - 1, index, value)
self.roots.append(new_root)
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return len(self.roots) - 1
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def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node:
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"""
Updates the node for the specified index and value and returns the new node.
>>> pst = PersistentSegmentTree([1, 2, 3, 4])
>>> old_root = pst.roots[0]
>>> new_root = pst._update(old_root, 0, 3, 1, 5) # Update index 1 to 5
>>> new_root.value # New sum after update
13
>>> old_root.value # Old root remains unchanged
10
>>> new_root.left.value # Updated left child
6
>>> new_root.right.value # Right child remains the same
7
"""
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if start == end:
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return Node(value)
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mid = (start + end) // 2
new_node = Node()
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if index <= mid:
new_node.left = self._update(node.left, start, mid, index, value)
new_node.right = node.right
else:
new_node.left = node.left
new_node.right = self._update(node.right, mid + 1, end, index, value)
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new_node.value = new_node.left.value + new_node.right.value
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return new_node
def query(self, version: int, left: int, right: int) -> int:
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"""
Queries the sum in the given range for the specified version.
>>> pst = PersistentSegmentTree([1, 2, 3, 4])
>>> pst.query(0, 0, 3) # Sum of all elements in original version
10
>>> pst.query(0, 1, 2) # Sum of elements at index 1 and 2 in original version
5
>>> version_1 = pst.update(0, 1, 5) # Update index 1 to 5
>>> pst.query(version_1, 0, 3) # Sum of all elements in new version
13
>>> pst.query(version_1, 1, 2) # Sum of elements at index 1 and 2 in new version
8
"""
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return self._query(self.roots[version], 0, self.n - 1, left, right)
def _query(self, node: Node, start: int, end: int, left: int, right: int) -> int:
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"""
Queries the sum of values in the range [left, right] for the given node.
>>> pst = PersistentSegmentTree([1, 2, 3, 4])
>>> root = pst.roots[0]
>>> pst._query(root, 0, 3, 1, 2) # Sum of elements at index 1 and 2
5
>>> pst._query(root, 0, 3, 0, 3) # Sum of all elements
10
>>> pst._query(root, 0, 3, 2, 3) # Sum of elements at index 2 and 3
7
"""
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if left > end or right < start:
return 0
if left <= start and right >= end:
return node.value
mid = (start + end) // 2
return self._query(node.left, start, mid, left, right) + self._query(
node.right, mid + 1, end, left, right
)
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# Running the doctests
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if __name__ == "__main__":
import doctest
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print("Running doctests...")
result = doctest.testmod()
print(f"Ran {result.attempted} tests, {result.failed} failed.")