Update persistent_segment_tree.py

data_structures/persistent_segment_tree.py

@@ -7,18 +7,23 @@ 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, 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
@@ -29,19 +34,26 @@ class PersistentSegmentTree:
         return node
 
     def update(self, version: int, index: int, value: int) -> int:
-        """
-        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)
-        9
-        """
         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)
 
@@ -60,34 +72,33 @@ class PersistentSegmentTree:
         return new_node
 
     def query(self, version: int, left: int, right: int) -> int:
-        """
-        Query the sum in the given range for the specified version.
-
-        >>> pst = PersistentSegmentTree([1, 2, 3])
-        >>> pst.query(0, 0, 2)
-        6
-        >>> 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)
 
     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 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
-        )
+        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.")