Problem Description
You are given a perfect binary tree where all leaves are on the same level, and every parent has two children. Your task is to populate each next pointer to point to its next right node. If there is no next right node, the next pointer should be set to NULL. Initially, all next pointers are set to NULL.
Key Insights
- The tree is a perfect binary tree, meaning all levels are fully filled.
- Each node has a pointer (
next) that should point to its immediate right neighbor. - We can utilize the properties of the perfect binary tree to connect nodes without using additional space.
Space and Time Complexity
Time Complexity: O(N) - where N is the number of nodes in the tree, as we need to visit each node once. Space Complexity: O(1) - we are using constant extra space as we are modifying the tree in place.
Solution
We can solve this problem using a level-order traversal approach. Since the tree is perfect, we can connect nodes at the same level using their next pointers directly. We can start from the root and iterate through each level, connecting the left child of a node to the right child of the same node, and the right child to the left child of the next node in line. This can be done iteratively or recursively without any additional space.