How do you solve Find Duplicate Subtrees on LeetCode?

Find Duplicate Subtrees (LeetCode #652) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using serialization helps in uniquely identifying subtrees.

What is the brute force solution for Find Duplicate Subtrees?

The brute force approach for Find Duplicate Subtrees is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every subtree in the binary tree and comparing it with every other subtree to find duplicates. This is straightforward but inefficient, especially for larger trees. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find Duplicate Subtrees?

Find Duplicate Subtrees uses the following concepts: Hash Table, Tree, Depth-First Search, Binary Tree. The recommended patterns to study are: Hash Map, Tree Traversal.

What are the interview tips for Find Duplicate Subtrees?

Explain your thought process clearly while coding. Discuss edge cases, like trees with only one node. Practice serialization techniques beforehand.

What are common mistakes when solving Find Duplicate Subtrees?

Not considering null nodes in serialization. Failing to track duplicates correctly in the hash map.

#652

Find Duplicate Subtrees

Medium

Hash TableTreeDepth-First SearchBinary TreeHash MapTree Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses serialization of subtrees and a hash map to track occurrences. This allows us to efficiently identify duplicates without unnecessary comparisons.

⚙️

Algorithm

3 steps

1Step 1: Use a helper function to serialize each subtree into a string representation.
2Step 2: Use a hash map to count occurrences of each serialized subtree.
3Step 3: If a serialized subtree appears more than once, add its root to the result list.

solution.py24 lines

1# Full working Python code
2class TreeNode:
3    def __init__(self, val=0, left=None, right=None):
4        self.val = val
5        self.left = left
6        self.right = right
7
8class Solution:
9    def findDuplicateSubtrees(self, root):
10        from collections import defaultdict
11        count = defaultdict(int)
12        result = []
13
14        def serialize(node):
15            if not node:
16                return '#'
17            serial = f'{node.val},{serialize(node.left)},{serialize(node.right)}'
18            count[serial] += 1
19            if count[serial] == 2:
20                result.append(node)
21            return serial
22
23        serialize(root)
24        return result

ℹ

Complexity note: The time complexity is O(n) because we traverse each node once to serialize the tree, and the space complexity is O(n) due to the storage of serialized strings in the hash map.

1Using serialization helps in uniquely identifying subtrees.
2Hash maps are effective for counting occurrences efficiently.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.