💡 Problem Formulation: In certain binary tree operations, it may be required to prune nodes that have only one child, leaving nodes with either two children or no children (leaf nodes). This modification can simplify specific tree algorithms or simply restructure the tree for data processing needs. For instance, if the input is a binary tree where nodes ‘B’ and ‘D’ have only one child, the expected output is a tree with ‘B’ and ‘D’ removed.
Method 1: Recursion
This method employs a recursive function that travels through the binary tree and selectively bypasses nodes with only one child. The function remove_single_child_nodes(root) returns the updated subtree which does not include nodes with only one child except for leaf nodes.
Here’s an example:
class TreeNode:
def __init__(self, val=0, left=None, right=None):
self.val = val
self.left = left
self.right = right
def remove_single_child_nodes(node):
if node:
if not node.left:
return remove_single_child_nodes(node.right)
if not node.right:
return remove_single_child_nodes(node.left)
node.left = remove_single_child_nodes(node.left)
node.right = remove_single_child_nodes(node.right)
return node
Output: The binary tree without nodes that had only one child, effectively pruned recursively.
This code snippet defines a function that steps through the tree. At each node, if it has only one child, the function returns the subtree of the present child node, hence removing the parent node. If a node has two children or is a leaf node, it remains unaffected. Recursive calls ensure this logic applies to the entire tree.
Method 2: Iterative Depth-First Search (DFS)
Unlike recursion, the iterative DFS approach uses a stack to manually track nodes to visit in the binary tree. The function, iterative_remove_single_child_nodes(root), iteratively visits each node, checking for single children and modifying the tree accordingly.
Here’s an example:
def iterative_remove_single_child_nodes(root):
stack = [(root, None, None)] # Node, Parent, Is Left Child
while stack:
node, parent, is_left = stack.pop()
if node:
if not node.left or not node.right: # Single child case
child = node.left if node.left else node.right
if parent:
if is_left:
parent.left = child
else:
parent.right = child
else: # Push children into stack for the further traverse
stack.append((node.right, node, False))
stack.append((node.left, node, True))
return root if root and root.left and root.right else None
Output: A modified binary tree with single-child nodes removed using an iterative approach.
This code utilizes a stack to perform a depth-first traversal, modifying the tree structure along the way. If a single-child node is encountered, it is removed by connecting the parent directly to the grandchild node. The iterative approach can be more efficient in terms of memory consumption for deep trees compared to recursion.
Method 3: Modified Post-Order Traversal
Post-order traversal ensures that we deal with the children before dealing with the parent node. A modification of this traversal can be used to manage single-child removal in an elegant manner. The function, modified_post_order_remove(root), applies this principle.
Here’s an example:
def modified_post_order_remove(node):
if node:
node.left = modified_post_order_remove(node.left)
node.right = modified_post_order_remove(node.right)
if node.left and not node.right:
return node.left
if node.right and not node.left:
return node.right
return node
Output: The binary tree with all nodes having only one child removed, achieved through a modified post-order traversal.
This method post-order traverses the binary tree and removes the single-child nodes from the bottom-up. By handling children first, it ensures the parent nodes are restructured correctly, connecting to the correct descendants after the removals.
Method 4: Breadth-First Search (BFS) Modification
In a BFS modification approach, we use a queue to level-order traverse the tree. By tracking parent-child relationships, we can rewire nodes with single children effectively. The implementation could be encapsulated in a modified_bfs_remove(root) function.
Here’s an example:
from collections import deque
def modified_bfs_remove(root):
if not root: return None
queue = deque([(root, None, None)]) # Node, Parent, Is Left Child
while queue:
node, parent, is_left = queue.popleft()
has_single_child = (node.left and not node.right) or (not node.left and node.right)
if has_single_child:
child = node.left if node.left else node.right
if parent: # Connect parent directly to the grandchild
if is_left:
parent.left = child
else:
parent.right = child
else:
if node.left:
queue.append((node.left, node, True))
if node.right:
queue.append((node.right, node, False))
return root if root and root.left and root.right else None
Output: The binary tree modified by BFS, removing all single-child nodes.
Using the BFS approach, each node is processed level by level. Single-child nodes are directly eliminated by linking their parents with their children. It’s a non-recursive solution that can be easier to understand for large trees.
Bonus One-Liner Method 5: Functional Approach
For those who prefer a more concise representation, Python’s functional programming capabilities can offer a one-liner solution using lambda functions and short-circuit evaluation.
Here’s an example:
remove_single_child_nodes = lambda n: n and (n.left and remove_single_child_nodes(n.left)) or (n.right and remove_single_child_nodes(n.right)) or n
Output: A pruned binary tree.
This one-liner uses logical operations to traverse and modify the tree in a functional style. It’s elegant and concise but may compromise readability for those unfamiliar with such patterns.
Summary/Discussion
- Method 1: Recursion. Simple to implement and understand. May cause stack overflow in deep trees.
- Method 2: Iterative DFS. Memory efficient and safe for deep trees. More complex due to explicit stack management.
- Method 3: Modified Post-Order Traversal. Intuitive bottom-up approach. Limited by the same constraints as typical recursion.
- Method 4: BFS Modification. Iterative and easy to follow. Can be less memory efficient due to the queue in broad trees.
- Method 5: Functional Approach. Elegant and succinct. Potentially difficult to debug or understand for beginners.