modify doctest

data_structures/binary_tree/lowest_common_ancestor.py

@@ -23,24 +23,24 @@ def swap(a: int, b: int) -> tuple[int, int]:
 
 
 def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
-    """
+    r"""
     Create a sparse table that saves each node's 2^i-th parent.
-    
-    The given ``parent`` table should have the direct parent of each node in row 0.
-    This function fills in:
-    
+
+    The given ``parent`` table should have the direct parent of each node
+    in row 0. This function fills in:
+
         parent[j][i] = parent[j - 1][parent[j - 1][i]]
-    
+
     for each j where 2^j is less than max_node.
-    
+
     For example, consider a small tree where:
       - Node 1 is the root (its parent is 0),
       - Nodes 2 and 3 have parent 1.
-    
+
     We set up the parent table for only two levels (row 0 and row 1)
     for max_node = 3. (Note that in practice the table has many rows.)
-    
-    >>> parent0 = [0, 0, 1, 1]  # 0 is unused; node1's parent=0, nodes 2 and 3's parent=1.
+
+    >>> parent0 = [0, 0, 1, 1]
     >>> parent1 = [0, 0, 0, 0]
     >>> parent = [parent0, parent1]
     >>> sparse = create_sparse(3, parent)
@@ -59,18 +59,17 @@ def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
 def lowest_common_ancestor(
     u: int, v: int, level: list[int], parent: list[list[int]]
 ) -> int:
-    """
+    r"""
     Return the lowest common ancestor (LCA) of nodes u and v in a tree.
-    
-    The lists ``level`` and ``parent`` must be precomputed. ``level[i]`` is the depth
-    of node i, and ``parent`` is a sparse table where parent[0][i] is the direct parent
-    of node i.
-    
+
+    The lists ``level`` and ``parent`` must be precomputed.
+
     >>> # Consider a simple tree:
     >>> #       1
     >>> #      / \\
     >>> #     2   3
-    >>> # With levels: level[1]=0, level[2]=1, level[3]=1 and parent[0]=[0, 0, 1, 1]
+    >>> # With levels: level[1]=0, level[2]=1, level[3]=1 and
+    >>> # parent[0]=[0, 0, 1, 1]
     >>> level = [-1, 0, 1, 1]  # index 0 is dummy
     >>> parent = [[0, 0, 1, 1]] + [[0, 0, 0, 0] for _ in range(19)]
     >>> lowest_common_ancestor(2, 3, level, parent)
@@ -104,12 +103,12 @@ def breadth_first_search(
     graph: dict[int, list[int]],
     root: int = 1,
 ) -> tuple[list[int], list[list[int]]]:
-    """
+    r"""
     Run a breadth-first search (BFS) from the root node of the tree.
-    
+
     This sets each node's direct parent (stored in parent[0]) and calculates the
     depth (level) of each node from the root.
-    
+
     >>> # Consider a simple tree:
     >>> #    1
     >>> #   / \\
@@ -117,7 +116,7 @@ def breadth_first_search(
     >>> graph = {1: [2, 3], 2: [], 3: []}
     >>> level = [-1] * 4   # index 0 is unused; nodes 1 to 3.
     >>> parent = [[0] * 4 for _ in range(20)]
-    >>> new_level, new_parent = breadth_first_search(level, parent, 3, graph, root=1)
+    >>> new_level, new_parent=breadth_first_search(level,parent,3,graph,root=1)
     >>> new_level[1:4]
     [0, 1, 1]
     >>> new_parent[0][1:4]
@@ -137,12 +136,12 @@ def breadth_first_search(
 
 
 def main() -> None:
-    """
+    r"""
     Run a BFS to set node depths and parents in a sample tree, then create the
     sparse table and compute several lowest common ancestors.
-    
+
     The sample tree used is:
-    
+
                 1
              /  |  \ 
             2   3   4
@@ -150,7 +149,7 @@ def main() -> None:
           5   6   7   8
          / \\   |    / \\
         9  10  11  12  13
-    
+
     The expected lowest common ancestors are:
       - LCA(1, 3)  --> 1
       - LCA(5, 6)  --> 1
@@ -158,9 +157,9 @@ def main() -> None:
       - LCA(6, 7)  --> 3
       - LCA(4, 12) --> 4
       - LCA(8, 8)  --> 8
-    
+
     To test main() without it printing to the console, we capture the output.
-    
+
     >>> import sys
     >>> from io import StringIO
     >>> backup = sys.stdout