Persistent Segment Tree

data_structures/persistent_segment_tree.py

@@ -0,0 +1,83 @@
+from __future__ import annotations
+
+class Node:
+    def __init__(self, value: int = 0) -> None:
+        self.value: int = value
+        self.left: Node | None = None
+        self.right: Node | None = None
+
+class PersistentSegmentTree:
+    def __init__(self, arr: list[int]) -> None:
+        self.n: int = 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.
+        """
+        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 value at the given index and returns the new version.
+        """
+        new_root = self._update(self.roots[version], 0, self.n - 1, index, value)
+        self.roots.append(new_root)
+        return len(self.roots) - 1
+
+    def _update(self, node: Node | None, start: int, end: int, index: int, value: int) -> Node:
+        """
+        Updates the node for the specified index and value and returns the new node.
+        """
+        if node is None:  # Handle the None case
+            node = Node()  # Create a new node if None
+
+        if start == end:
+            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  # Ensure right node is the same as the original
+        else:
+            new_node.left = node.left  # Ensure left node is the same as the original
+            new_node.right = self._update(node.right, mid + 1, end, index, value)
+
+        new_node.value = new_node.left.value + (new_node.right.value if new_node.right else 0)
+
+        return new_node
+
+    def query(self, version: int, left: int, right: int) -> int:
+        """
+        Queries the sum in the given range for the specified version.
+        """
+        return self._query(self.roots[version], 0, self.n - 1, left, right)
+
+    def _query(self, node: Node | None, start: int, end: int, left: int, right: int) -> int:
+        """
+        Queries the sum of values in the range [left, right] for the given node.
+        """
+        if node is None or 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))
+
+# Running the doctests
+if __name__ == "__main__":
+    import doctest
+    print("Running doctests...")
+    result = doctest.testmod()
+    print(f"Ran {result.attempted} tests, {result.failed} failed.")