I knew the Haversine formula existed but definitely could not have recited it cold.
Start by clarifying the function signature and validation rules, then implement the Haversine formula step by step, converting degrees to radians and using the Earth's mean radius. Test with known distances and edge cases like antipodal points and invalid inputs.
Pro tip: Mention that you'll use the haversine formula's numerically stable form (using atan2) to avoid precision issues for small distances, and discuss the trade-off between using a spherical Earth model versus a more accurate ellipsoidal model like Vincenty's.
Confirm the expected input format (e.g., two lat/lon pairs), output (distance in km), and error handling (return ERROR for out-of-range coordinates). Ask about precision requirements and whether to use a spherical or ellipsoidal Earth model.
Check that latitudes are between -90 and 90 and longitudes between -180 and 180. If any coordinate is out of range, return ERROR immediately.
Convert all latitude and longitude values from degrees to radians, as trigonometric functions in most languages expect radians.
Compute the differences in latitude and longitude, then calculate a = sin²(Δφ/2) + cos φ1 * cos φ2 * sin²(Δλ/2). Use c = 2 * atan2(√a, √(1−a)) for numerical stability, and distance = R * c, where R is Earth's radius (mean radius 6371 km).
Test with known distances (e.g., between two cities) and edge cases (same point, antipodal points). Discuss the trade-off between simplicity (Haversine) and accuracy (Vincenty), and mention potential floating-point precision issues.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.