Solution Explanation

This problem involves rerooting a binary tree, where a given leaf node becomes the new root. The process involves iterating from the leaf node up to the original root, modifying parent-child relationships at each step.

Algorithm:

The solution uses an iterative approach. It starts at the given leaf node and iteratively moves towards the original root. In each iteration, it performs the following steps:

1. Handle the right child: If the current node (cur) has a left child, this child becomes the right child of cur. This step ensures the right subtree is preserved.

2. Change parent-child links: The current node's parent (p) becomes the left child of cur. The parent-child link between p and cur is broken.

3. Null out parent's child: We check if p was the parent of cur as a left or right child and set the appropriate child pointer to null in p. This avoids dangling references and ensures the tree structure remains consistent.

4. Move up the tree: The pointers cur and p are updated to continue the process up to the original root.

5. Set the new root's parent to null: Finally, the parent of the new root (leaf) is set to null.

Time Complexity: O(H), where H is the height of the tree. In the worst case (a skewed tree), the algorithm iterates through all nodes from the leaf to the root.

Space Complexity: O(1). The algorithm uses only a constant amount of extra space to store variables.

Code Explanation (Python):

class Solution:
    def flipBinaryTree(self, root: "Node", leaf: "Node") -> "Node":
        cur = leaf
        p = cur.parent
        while cur != root:
            gp = p.parent #Grandparent needed to move up correctly
            if cur.left:
                cur.right = cur.left
            cur.left = p
            p.parent = cur
            if p.left == cur:
                p.left = None
            elif p.right == cur:
                p.right = None
            cur = p
            p = gp
        leaf.parent = None
        return leaf

The Python code directly implements the algorithm described above. The while loop continues until the current node (cur) reaches the original root. Inside the loop, the steps to handle the right child, change parent-child links, null out parent's child, and move up the tree are performed. The use of gp (grandparent) is crucial for correctly traversing up the tree.

The other languages (Java, C++, JavaScript, C#) follow a very similar structure, adapting syntax to their respective languages but maintaining the same algorithmic approach. The core logic remains consistent across all implementations.