Atlassian·Machine Learning Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

May 2026

Summary

Atlassian ML Engineer interview that went deep on graph theory, specifically a nasty DAG variant of LCA that I was not expecting to come up in this context. The problem was genuinely hard and I fumbled parts of it, but it was an interesting conversation.

Questions Asked (1)

Given a Directed Acyclic Graph where nodes can have multiple parents, define what 'Lowest Common Ancestor' means in this setting and describe an algorithm to compute it.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This wrecked me a little.

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AI HintsAI Generated

Suggested Approach

Start by clarifying that in a DAG with multiple parents, the Lowest Common Ancestor (LCA) of two nodes is the deepest node that is an ancestor of both, where depth is measured by longest path from a source. Then describe an algorithm that computes all ancestors of each node (e.g., via topological order and bitsets) and finds the common ancestor with maximum depth.

Pro tip: Mention that bitsets are efficient for dense graphs, but for sparse graphs, a hash set intersection or iterative marking may be more memory-friendly; also note that the LCA may not be unique if multiple nodes share the same maximum depth, so clarify tie-breaking or return all.

1. Define LCA in DAG with multiple parents

Explain that LCA is the common ancestor with the greatest depth (longest path from any source), and note that there can be multiple LCAs if they share the same depth.

2. Compute ancestors for each node

Process nodes in topological order, maintaining a set (or bitset) of ancestors for each node by unioning the ancestor sets of all its parents plus the parents themselves.

3. Find common ancestors and select deepest

Intersect the ancestor sets of the two target nodes, then among the common ancestors, select the one(s) with the maximum depth (precomputed via longest path from sources).

4. Analyze complexity and trade-offs

Discuss time and space complexity: O(V+E) for topological sort, O(V^2/word_size) for bitset unions, and O(V) for intersection; mention alternatives like iterative marking for sparse graphs.

Key Points to Mention

Definition of LCA in DAG: deepest common ancestor, possibly multiple.
Depth metric: longest path from any source (or shortest path, but longest is standard for DAG LCA).
Topological sorting to process nodes in dependency order.
Ancestor set representation: bitsets for efficiency or hash sets for sparsity.
Complexity: O(V+E) for topological sort, O(V^2/word_size) for bitset operations, O(V) for intersection.
Handling multiple LCAs: return all or define a tie-breaking rule (e.g., smallest node ID).

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