Disney·Machine Learning Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026

Summary

Disney ML Engineer interview with a computational geometry/simulation problem that honestly felt more like a physics puzzle than anything I'd call machine learning. One question, pretty deep, left me second-guessing my approach the whole way through.

Questions Asked (1)

You have N points arranged in a cycle in 2D space. Each point continuously chases the next point in the cycle at constant speed. Determine whether all points ever converge to the same location simultaneously, and if so, output the meeting time and coordinates.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I stared at this for a good 30 seconds before saying anything.

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AI HintsAI Generated

Suggested Approach

Model the motion using differential equations and exploit the cyclic symmetry to reduce the problem to a single relative coordinate. Determine convergence by analyzing whether the distance between adjacent points decreases to zero, and if so, compute the meeting time and location using the initial geometry.

Pro tip: For a regular polygon, all points meet at the center after time t = r / (v (1 - cos(2π/N))) where r is the circumradius; mention this as a sanity check and note that for irregular polygons, convergence depends on the initial configuration.

1. Understand the motion

Each point moves at constant speed directly toward the next point in the cycle. This creates a system of coupled differential equations.

2. Exploit symmetry

For a regular polygon, the configuration remains a scaled and rotated version of itself, so the points always form a regular polygon. This reduces the problem to tracking the distance from the center or the side length.

3. Set up relative motion

Consider the distance between two adjacent points. The rate of change of this distance depends on the angle between the velocity vectors, which can be expressed in terms of the current geometry.

4. Solve for convergence

Integrate the differential equation for the distance. If the distance reaches zero in finite time, compute that time. Otherwise, conclude they never meet.

5. Compute meeting point

By symmetry, for a regular polygon the meeting point is the center. For irregular polygons, solve the full system or argue based on the center of mass.

Key Points to Mention

Differential equations governing the motion
Symmetry and reduction to a single variable
Relative velocity and angle between velocity vectors
Time to convergence formula for regular polygons
Center of mass remains stationary
Edge cases: N=2, irregular polygons, and infinite time

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