2509. Cycle Length Queries in a Tree
Description
You are given an integer n
. There is a complete binary tree with 2n - 1
nodes. The root of that tree is the node with the value 1
, and every node with a value val
in the range [1, 2n - 1 - 1]
has two children where:
- The left node has the value
2 * val
, and - The right node has the value
2 * val + 1
.
You are also given a 2D integer array queries
of length m
, where queries[i] = [ai, bi]
. For each query, solve the following problem:
- Add an edge between the nodes with values
ai
andbi
. - Find the length of the cycle in the graph.
- Remove the added edge between nodes with values
ai
andbi
.
Note that:
- A cycle is a path that starts and ends at the same node, and each edge in the path is visited only once.
- The length of a cycle is the number of edges visited in the cycle.
- There could be multiple edges between two nodes in the tree after adding the edge of the query.
Return an array answer
of length m
where answer[i]
is the answer to the ith
query.
Example 1:
![](https://spcdn.pages.dev/leetcode/problems/2509.Cycle%20Length%20Queries%20in%20a%20Tree/images/bexample1.png)
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.
Example 2:
![](https://spcdn.pages.dev/leetcode/problems/2509.Cycle%20Length%20Queries%20in%20a%20Tree/images/aexample2.png)
Input: n = 2, queries = [[1,2]] Output: [2] Explanation: The diagram above shows the tree of 22 - 1 nodes. Nodes colored in red describe the nodes in the cycle after adding the edge. - After adding the edge between nodes 1 and 2, the graph contains a cycle of nodes [2,1]. Thus answer for the first query is 2. We delete the added edge.
Constraints:
2 <= n <= 30
m == queries.length
1 <= m <= 105
queries[i].length == 2
1 <= ai, bi <= 2n - 1
ai != bi
Solutions
Solution 1
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