Leetcode #2509: Cycle Length Queries in a Tree
In this guide, we solve Leetcode #2509 Cycle Length Queries in a Tree in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an integer n. There is a complete binary tree with 2n - 1 nodes.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Tree, Array, Binary Tree
Intuition
The input is a tree, so recursive decomposition is a natural fit.
We can compute the answer by combining results from left and right subtrees.
Approach
Use DFS and pass the required state through recursive calls.
Combine child results to compute the answer for each node.
Steps:
- Pick traversal order.
- Recurse with state.
- Combine results from children.
Example
Input: n = 3, queries = [[5,3],[4,7],[2,3]]
Output: [4,5,3]
Explanation: The diagrams above show the tree of 23 - 1 nodes. Nodes colored in red describe the nodes in the cycle after adding the edge.
- After adding the edge between nodes 3 and 5, the graph contains a cycle of nodes [5,2,1,3]. Thus answer to the first query is 4. We delete the added edge and process the next query.
- After adding the edge between nodes 4 and 7, the graph contains a cycle of nodes [4,2,1,3,7]. Thus answer to the second query is 5. We delete the added edge and process the next query.
- After adding the edge between nodes 2 and 3, the graph contains a cycle of nodes [2,1,3]. Thus answer to the third query is 3. We delete the added edge.
Python Solution
class Solution:
def cycleLengthQueries(self, n: int, queries: List[List[int]]) -> List[int]:
ans = []
for a, b in queries:
t = 1
while a != b:
if a > b:
a >>= 1
else:
b >>= 1
t += 1
ans.append(t)
return ans
Complexity
The time complexity is , where is the length of the queries array. The space complexity is O(h).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.