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g1901_2000.s1938_maximum_genetic_difference_query.readme.md Maven / Gradle / Ivy

1938\. Maximum Genetic Difference Query

Hard

There is a rooted tree consisting of `n` nodes numbered `0` to `n - 1`. Each node's number denotes its **unique genetic value** (i.e. the genetic value of node `x` is `x`). The **genetic difference** between two genetic values is defined as the **bitwise-XOR** of their values. You are given the integer array `parents`, where `parents[i]` is the parent for node `i`. If node `x` is the **root** of the tree, then `parents[x] == -1`.

You are also given the array `queries` where queries[i] = [nodei, vali]. For each query `i`, find the **maximum genetic difference** between vali and pi, where pi is the genetic value of any node that is on the path between nodei and the root (including nodei and the root). More formally, you want to maximize vali XOR pi.

Return _an array_ `ans` _where_ `ans[i]` _is the answer to the_ ith _query_.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/06/29/c1.png)

**Input:** parents = [-1,0,1,1], queries = [[0,2],[3,2],[2,5]]

**Output:** [2,3,7]

**Explanation:** The queries are processed as follows: 

- [0,2]: The node with the maximum genetic difference is 0, with a difference of 2 XOR 0 = 2. 

- [3,2]: The node with the maximum genetic difference is 1, with a difference of 2 XOR 1 = 3. 

- [2,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7.

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/06/29/c2.png)

**Input:** parents = [3,7,-1,2,0,7,0,2], queries = [[4,6],[1,15],[0,5]]

**Output:** [6,14,7]

**Explanation:** The queries are processed as follows: 

- [4,6]: The node with the maximum genetic difference is 0, with a difference of 6 XOR 0 = 6. 

- [1,15]: The node with the maximum genetic difference is 1, with a difference of 15 XOR 1 = 14. 

- [0,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7.

**Constraints:**

*   2 <= parents.length <= 105
*   `0 <= parents[i] <= parents.length - 1` for every node `i` that is **not** the root.
*   `parents[root] == -1`
*   1 <= queries.length <= 3 * 104
*   0 <= nodei <= parents.length - 1
*   0 <= vali <= 2 * 105