Persistent Segment Tree

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))