Leetcode 107: Binary Tree Level Order Traversal II
grid47 Exploring patterns and algorithms
Oct 27, 2024
6 min read
Solution to LeetCode 107: Binary Tree Level Order Traversal II Problem
Given the root of a binary tree, return the bottom-up level order traversal of its nodes’ values. This means that for each level, starting from the leaf level and moving towards the root, you should collect the node values from left to right.
Problem
Approach
Steps
Complexity
Input: The input consists of a binary tree represented by its root node.
Example: root = [5,3,8,1,4,7,9]
Constraints:
• The number of nodes in the tree is in the range [0, 2000].
• -1000 <= Node.val <= 1000
Output: Return a list of lists representing the node values at each level from bottom to top.
Example: [[1, 4], [3, 8], [5]]
Constraints:
• The output should represent the nodes' values level by level from leaf to root.
Goal: The goal is to perform a bottom-up level order traversal of the binary tree, ensuring each level is collected in the correct order, from leaf to root.
Steps:
• Use a queue to perform a breadth-first traversal of the tree.
• For each level, collect the values into a list and store it.
• Since we need the levels from bottom to top, push each level's result onto a stack.
• Finally, pop the elements from the stack to return the bottom-up level order.
Goal: The solution should handle up to 2000 nodes in the tree efficiently.
Steps:
• The solution must handle the maximum number of nodes, 2000, efficiently.
Assumptions:
• The binary tree is non-empty, or it is an empty tree.
• Input: Input: root = [3,9,20,null,null,15,7]
• Explanation: In this case, the binary tree can be visualized as:
3
/ \
9 20
/ \
15 7
The bottom-up level order traversal is: [[15,7], [9,20], [3]].
• Input: Input: root = [1]
• Explanation: In this case, the binary tree consists of a single node 1. The bottom-up level order traversal is simply: [[1]].
• Input: Input: root = []
• Explanation: If the tree is empty, the bottom-up level order traversal should return an empty list: [].
Approach: The approach for solving this problem involves using a breadth-first search (BFS) to explore the tree level by level. Since we need the result in bottom-up order, we can utilize a stack to reverse the order after performing the traversal.
Observations:
• A level order traversal typically uses a queue, but we need the result in reverse order (bottom-up).
• We can store the level order results in a stack and then pop the stack to get the desired bottom-up order.
Steps:
• Initialize an empty queue and push the root of the tree into it.
• While the queue is not empty, process each level of the tree by iterating over the nodes at that level.
• For each node, push its children into the queue and store the node's value for that level.
• Push the list of values for each level into a stack.
• After processing all levels, pop the elements from the stack and return them as the result.
Empty Inputs:
• If the root is null (empty tree), return an empty list.
Large Inputs:
• The algorithm should be efficient enough to handle trees with up to 2000 nodes.
Special Values:
• Handle trees where all nodes are on one side (skewed trees).
Constraints:
• Ensure the solution works for both balanced and unbalanced trees.
