#1123

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auto_awesomeBinary-tree traversal and state tracking

LeetCode Problem Workspace

Lowest Common Ancestor of Deepest Leaves

Find the lowest common ancestor of the deepest leaves in a binary tree using efficient traversal and state tracking techniques.

hash table tree depth first search breadth first search binary tree

Problem Statement

Given the root of a binary tree, return the lowest common ancestor of its deepest leaves. In a binary tree, the deepest leaves are those with the greatest depth. The lowest common ancestor is the shared ancestor of two or more nodes that is located furthest from the root.

For example, in a tree with root = [3,5,1,6,2,0,8,null,null,7,4], the LCA of the deepest leaves, nodes 7 and 4, is node 2. Similarly, for simpler cases like root = [1], the only node is the LCA by default.

Examples

Example 1

Input: root = [3,5,1,6,2,0,8,null,null,7,4]

Output: [2,7,4]

We return the node with value 2, colored in yellow in the diagram. The nodes coloured in blue are the deepest leaf-nodes of the tree. Note that nodes 6, 0, and 8 are also leaf nodes, but the depth of them is 2, but the depth of nodes 7 and 4 is 3.

Example 2

Input: root = [1]

Output: [1]

The root is the deepest node in the tree, and it's the lca of itself.

Example 3

Input: root = [0,1,3,null,2]

Output: [2]

The deepest leaf node in the tree is 2, the lca of one node is itself.

Constraints

The number of nodes in the tree will be in the range [1, 1000].
0 <= Node.val <= 1000
The values of the nodes in the tree are unique.

Solution Approach

Postorder Traversal with State Tracking

Start by performing a postorder traversal of the tree. This helps process nodes from the bottom to the top. As you traverse, track the deepest leaf's depth and check for the lowest common ancestor of all nodes at the deepest level.

Depth Comparison During Traversal

As the traversal progresses, compare the depths of encountered leaf nodes. For each leaf node, determine if its depth is the deepest encountered so far. If multiple nodes share the deepest level, determine the LCA from those nodes.

Efficient DFS Approach

Depth-First Search (DFS) allows an optimal exploration of the tree with minimal space complexity. Using recursion, return both the depth and the LCA during traversal to ensure efficiency in reaching the solution.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity is O(n) because each node is visited once during the traversal. The space complexity is O(n) due to the recursion stack and auxiliary data structures used to track the depths and ancestors of nodes.

What Interviewers Usually Probe

The candidate demonstrates understanding of binary tree traversal techniques.
The candidate uses an optimal approach, focusing on DFS and state tracking.
The candidate explains how to compare depths and find the LCA efficiently.

Common Pitfalls or Variants

Common pitfalls

Failing to correctly identify the deepest leaves before determining the LCA.
Misunderstanding that the LCA must be common to the deepest nodes only.
Overcomplicating the solution with unnecessary space or traversal steps.

Follow-up variants

Handling different tree structures, such as skewed trees or trees with only one node.
Optimizing for larger input sizes with stricter time/space constraints.
Adapting the solution to find the LCA for multiple nodes at varying depths.

FAQ

What is the pattern for solving the Lowest Common Ancestor of Deepest Leaves problem?

The pattern involves using a postorder DFS traversal with state tracking for depth and ancestor identification. This ensures efficient tracking of the deepest leaves and their common ancestor.

How do I identify the deepest leaves in a binary tree?

By performing a traversal and comparing node depths, the deepest leaves are identified as those with the greatest depth in the tree.

What is the time complexity of the solution?

The time complexity is O(n), where n is the number of nodes in the tree, as each node is visited once.

Can this solution handle very large trees?

Yes, the solution is efficient enough to handle large trees within the problem's constraints, with a time complexity of O(n) and space complexity of O(n).

What are common mistakes when solving this problem?

Common mistakes include failing to correctly track the depth of leaf nodes and not properly identifying the LCA of multiple deepest leaves.

terminal

Solution

Solution 1: DFS

We design a function `dfs(root)` that returns a tuple `(l, d)`, where `l` is the deepest common ancestor of node `root`, and `d` is the depth of node `root`. The execution logic of the function `dfs(root)` is as follows:

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def lcaDeepestLeaves(self, root: Optional[TreeNode]) -> Optional[TreeNode]:
        def dfs(root):
            if root is None:
                return None, 0
            l, d1 = dfs(root.left)
            r, d2 = dfs(root.right)
            if d1 > d2:
                return l, d1 + 1
            if d1 < d2:
                return r, d2 + 1
            return root, d1 + 1

        return dfs(root)[0]

Continue Practicing

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