I struggle to grasp dietpepsi's concise O(1) space complexity algorithm. I've utilized the following visualization to analyze each step systematically to comprehend it fully.

Key Points:

1. Use BFS to traverse the tree.
2. In BFS traversal, consider each level as a linked list problem. Utilize a "tail" and a "dummy" node to handle the child layer.

"""
# Definition for a Node.
class Node:
    def __init__(self, val: int = 0, left: 'Node' = None, right: 'Node' = None, next: 'Node' = None):
        self.val = val
        self.left = left
        self.right = right
        self.next = next
"""
class Solution:
    def connect(self, node: 'Node') -> 'Node':
        """
        if there is parent node
        BFS
        """
        root = node
        tail = dummy = Node(0)
        while node:
            tail.next = node.left
            if tail.next:
                tail = tail.next
            tail.next = node.right
            if tail.next:
                tail = tail.next
            node = node.next
            if not node:
                tail = dummy
                node = dummy.next
        return(root)