Maximum Genetic Difference Query

Maximum Genetic Difference Query

What is this problem about?

The Maximum Genetic Difference Query coding problem presents a rooted tree of nodes, where each node has a numeric value (its index). Given a set of offline queries, each specifying a node and a value, you must find the node on the path from the root to the queried node whose XOR with the given value is maximized. This is essentially a "maximum XOR on a path" problem with multiple queries processed efficiently.

Why is this asked in interviews?

Media.net and similar companies use this problem to test advanced data structure knowledge, specifically the combination of tree traversal with a binary trie for XOR maximization. It bridges two distinct algorithmic domains — tree DFS and trie-based bit manipulation — making it ideal for evaluating candidates who can compose data structures. The offline processing aspect further tests knowledge of query batching techniques.

Algorithmic pattern used

The solution uses DFS with an online/offline trie. You perform a DFS traversal of the tree, maintaining a trie of all node values currently on the root-to-current path. When you enter a node, you insert its value into the trie. When you exit, you remove it. For each query at a node, you query the trie for the maximum XOR with the target value. This gives O((n + q) log(max_value)) overall, where q is the number of queries.

Example explanation

Tree: 0 → 1 → 2, root is 0. Query: at node 2, maximize XOR with value 5.

Path from root to node 2: [0, 1, 2]

• XOR(0, 5) = 5
• XOR(1, 5) = 4
• XOR(2, 5) = 7

Answer = 7 (from node 2 itself).

The trie at node 2 contains {0, 1, 2}. Querying for max XOR with 5 (binary: 101) — the trie greedily picks bit 2 (value with bit set at position 2) = 7.

Common mistakes candidates make

• Using online queries naively: Processing each query by walking up the tree is O(n) per query, giving O(nq) total — too slow.
• Not removing nodes on exit: Forgetting to remove a node's value from the trie when backtracking in DFS corrupts the path-only invariant.
• Binary trie depth: Using a trie depth less than the bit length of node values causes incorrect maximum XOR calculations.

Interview preparation tip

For the Array Hash Table Trie Depth-First Search Bit Manipulation interview pattern, practice the "insert on enter, delete on exit" DFS trie technique on simpler problems first. Understand how a binary trie supports maximum XOR queries by greedily choosing the opposite bit at each level.