What is the optimal time complexity of solving Subtree of Another Tree?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Subtree of Another Tree?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Subtree of Another Tree?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Subtree of Another Tree?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Subtree of Another Tree

Learn how to solve the 'Subtree of Another Tree' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Given the roots of two binary trees root and subRoot, return true if there is a subtree of root with the same structure and node values of subRoot and false otherwise.

A subtree of a binary tree tree is a tree that consists of a node in tree and all of this node's descendants. The tree tree could also be considered as a subtree of itself.

The trees are represented as level-order lists. Implement a function isSubtree(root: list, subRoot: list) -> bool.

Constraints

•The number of nodes in the root tree is in the range [1, 2000]
•The number of nodes in the subRoot tree is in the range [1, 1000]
•-10000 <= root.val <= 10000
•-10000 <= subRoot.val <= 10000

Examples

Example 1

Input

[3,4,5,1,2], [4,1,2]

Output

True

Explanation

The subtree rooted at node 4 in the main tree matches subRoot exactly.

Example 2

Input

[3,4,5,1,2,None,None,None,None,0], [4,1,2]

Output

False

Explanation

The subtree rooted at 4 in the main tree has an extra node 0 under 2, so it doesn't match subRoot.

Need a Hint?

Perform a recursive tree traversal (DFS) or level-order traversal (BFS) using a queue/stack.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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