diff --git a/data_structures/persistent_segment_tree.py b/data_structures/persistent_segment_tree.py index 7d7851071..5bcf1f64d 100644 --- a/data_structures/persistent_segment_tree.py +++ b/data_structures/persistent_segment_tree.py @@ -7,19 +7,18 @@ class Node: class PersistentSegmentTree: def __init__(self, arr: list[int]) -> None: + """ + Initialize the Persistent Segment Tree with the given array. + + >>> pst = PersistentSegmentTree([1, 2, 3]) + >>> pst.query(0, 0, 2) + 6 + """ 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 @@ -31,41 +30,46 @@ class PersistentSegmentTree: def update(self, version: int, index: int, value: int) -> int: """ - Updates the segment tree with a new value at the specified index. + Update the value at the given index and return the new version. >>> 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 + >>> pst.query(version_1, 0, 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 + return len(self.roots) - 1 def _update(self, node: Node, start: int, end: int, index: int, value: int) -> Node: if start == end: - new_node = Node(value) - return new_node + return Node(value) + 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. + Query 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 + >>> pst.query(0, 0, 2) 6 - >>> pst.query(version_1, 0, 2) # Query sum from index 0 to 2 + >>> version_1 = pst.update(0, 1, 5) + >>> pst.query(version_1, 0, 1) + 6 + >>> pst.query(version_1, 0, 2) 9 """ return self._query(self.roots[version], 0, self.n - 1, left, right) @@ -76,6 +80,12 @@ class PersistentSegmentTree: 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 - ) + return (self._query(node.left, start, mid, left, right) + + self._query(node.right, mid + 1, end, left, right)) + + +if __name__ == "__main__": + import doctest + print("Running doctests...") + result = doctest.testmod() + print(f"Ran {result.attempted} tests, {result.failed} failed.")