diff --git a/data_structures/persistent_segment_tree.py b/data_structures/persistent_segment_tree.py new file mode 100644 index 000000000..8963b54a2 --- /dev/null +++ b/data_structures/persistent_segment_tree.py @@ -0,0 +1,80 @@ +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: + 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: + """ + 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: + 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: + """ + Updates the segment tree with a new value at the specified index. + + >>> pst = PersistentSegmentTree([1, 2, 3]) + >>> version_1 = pst.update(0, 1, 5) + >>> pst.query(version_1, 0, 2) # Query sum from index 0 to 2 + 9 + """ + new_root = self._update(self.roots[version], 0, self.n - 1, index, value) + self.roots.append(new_root) + return len(self.roots) - 1 # return the index of the new version + + def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node: + if start == end: + new_node = Node(value) + return new_node + mid = (start + end) // 2 + new_node = Node() + 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) + new_node.value = new_node.left.value + new_node.right.value + return new_node + + def query(self, version: int, left: int, right: int) -> int: + """ + Queries the sum in the given range for the specified version. + + >>> pst = PersistentSegmentTree([1, 2, 3]) + >>> version_1 = pst.update(0, 1, 5) + >>> pst.query(version_1, 0, 1) # Query sum from index 0 to 1 + 6 + >>> pst.query(version_1, 0, 2) # Query sum from index 0 to 2 + 9 + """ + 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: + 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))