Persistent Segment Tree

data_structures/persistent_segment_tree.py

@@ -0,0 +1,138 @@
+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.
+
+        >>> 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
+        """
+        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.
+
+        >>> 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
+        """
+        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, start: int, end: int, index: int, value: int) -> Node:
+        """
+        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
+        """
+        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.
+
+        >>> 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
+        8
+        """
+        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:
+        """
+        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
+        """
+        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.")