Populating Next Right Pointers In Each Node Ii

To solve this coding challenge, we need to populate the
next
pointers of a binary tree such that each node's
next
pointer points to its next right node. If there is no next right node, the
next
pointer should be set to
NULL
. Let's break this problem down step-by-step and generate the pseudocode for the solution.

Explanation

  1. Understanding the Tree Structure :
    • Each node of the tree has a
      val
      ,
      left
      (left child),
      right
      (right child), and
      next
      (next right node) pointer.
    • Our task is to link the
      next
      pointer of each node to the node that lies to its immediate right at the same level in the binary tree. If no such node exists, the
      next
      pointer should be set to
      NULL
      .
  2. Initial Setup :
    • If the tree is empty, return
      None
      .
    • If it’s not empty, we will use a breadth-first search (BFS) traversal technique to process nodes level by level. BFS works well for this task because it processes all nodes at the same level before moving on to the next level.
  3. Using a Queue for BFS :
    • We will use a queue to keep track of nodes at each level.
    • Initialize the queue with the root node.
  4. Processing Each Level :
    • For each level in the tree, process each node in the queue.
    • Link each node's
      next
      pointer to the node that follows it in the queue (if any).
    • Add the children of each node to the queue to process the next level.
  5. Edge Cases :
    • An empty tree should return
      []
      (empty list).
    • Nodes without children should have their
      next
      set to
      NULL
      .
    Now, let's provide pseudocode to elaborate on these steps:

    Pseudocode with Comments

                                                
    # Begin by defining the structure of a Node and a placeholder for the tree root
    
    class Node:
    def __init__(self, value=0, left=None, right=None, next=None):
    self.val = value
    self.left = left
    self.right = right
    self.next = next
    
    # The solution function to connect the `next` pointers
    
    def connect(root):
    # If the tree root is `None`, return `None`
    if root is None:
    return None
    
    # Initialize a queue for BFS with the root node
    queue = [root]
    
    # Loop until the queue is empty
    while queue:
    
    # Get the number of nodes at the current level
    level_size = len(queue)
    
    # Process all nodes at the current level
    for i in range(level_size):
    
    # Pop the first node from the queue
    current_node = queue.pop(0)
    
    # If this is not the last node in the level, set its `next` to the node in queue front
    if i < level_size - 1:
    current_node.next = queue[0]
    else:
    # If this is the last node, ensure its `next` is `NULL`
    current_node.next = None
    
    # Add the left child to the queue if it exists
    if current_node.left is not None:
    queue.append(current_node.left)
    
    # Add the right child to the queue if it exists
    if current_node.right is not None:
    queue.append(current_node.right)
    
    # Return the root after fully populating `next` pointers
    return root
    
                                            

    Step-by-Step Explanation of the Pseudocode

  6. Node and Tree Definition :
    • The
      Node
      class is defined with
      val
      ,
      left
      ,
      right
      , and
      next
      attributes.
    • The
      connect
      function is defined to operate on the tree's root.
  7. Initial Root Check :
    • If the root is
      None
      , it returns
      None
      immediately as there are no nodes to process.
  8. Queue Initialization :
    • A queue is initialized with the root node to start BFS.
  9. Processing Loop :
    • While the queue contains nodes, continue processing.
  10. Level Processing :
    • Determine the size of the current level by the queue's length.
    • Iterate through each node in the current level.
  11. Next Pointer Assignment :
    • For each node, set its
      next
      to the next node in the queue if it is not the last node in the level.
    • If it is the last node, set its
      next
      to
      NULL
      .
  12. Child Nodes Enqueue :
    • Append the left and right children (if they exist) to the queue for the next level of processing.
  13. Return the Root :
    • After all levels are processed and
      next
      pointers are set, return the root node of the modified tree.
This pseudocode outlines a clear and systematic approach to solving the problem efficiently using BFS, ensuring constant extra space usage aside from the implicit stack space.