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MongoDB·Machine Learning Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Did a technical round for an MLE role at MongoDB and got completely stuck on a dynamic programming problem. The interviewer was patient and walked me through it with hints, but when you don't have the core idea, hints only go so far.

Questions Asked (1)

Q1

Given two integer arrays of equal length, assign elements from one array to the other (as a permutation) to minimize the total XOR sum across all pairs.

Algorithms & Data Structures
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AI HintsAI Generated

Suggested Approach

Clarify the problem and constraints, then propose an efficient algorithm based on bitwise trie matching to minimize total XOR. Explain the greedy bit-by-bit approach and analyze its time and space complexity.

Pro tip: Mention that this is equivalent to finding a minimum weight perfect matching in a complete bipartite graph with XOR costs, and that the trie-based greedy is optimal due to the properties of XOR and binary representation.

1. Understand the problem

Restate the problem: given two arrays of equal length, find a permutation of one array that minimizes the sum of XORs of corresponding pairs. Clarify that elements are integers and arrays are of equal length.

2. Identify the algorithmic approach

Recognize that this is a minimum weight perfect matching problem in a bipartite graph with edge weights equal to XOR. Propose using a binary trie to efficiently pair numbers to minimize XOR sum.

3. Explain the trie-based greedy algorithm

Describe building a trie from one array, then for each element in the other array, traverse the trie to find the element that minimizes XOR. Alternatively, use a recursive divide-and-conquer on bits: at each bit, pair numbers with the same bit if possible, otherwise pair across bits.

4. Analyze complexity and correctness

State that the trie approach runs in O(n * log(max_value)) time and O(n * log(max_value)) space. Argue correctness by showing that minimizing XOR at higher bits takes precedence, and the greedy choice is optimal.

5. Discuss edge cases and extensions

Consider cases with duplicate numbers, negative integers (if allowed), and large values. Mention that the algorithm can be adapted for streaming or large datasets if needed.

Key Points to Mention

  • XOR properties: XOR is commutative and associative, and minimizing XOR sum is equivalent to minimizing the sum of bitwise differences.
  • Binary trie (prefix tree) for efficient XOR minimization.
  • Greedy bit-by-bit matching: process bits from most significant to least significant, pairing numbers with the same bit when possible.
  • Divide-and-conquer approach: recursively split numbers based on bits and pair across groups only when necessary.
  • Time complexity: O(n log C) where C is the maximum value, and space complexity O(n log C).
  • Connection to minimum weight perfect matching in bipartite graphs and why the greedy approach is optimal for XOR costs.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.