Best Position for a Service Centre
A hard-tier problem at 35% community acceptance, tagged with Array, Math, Geometry. Reported in interviews at Citadel and 0 others.
Citadel asks this problem, and it's hard for a reason: the naive greedy approach will fail on you in the assessment. You're given a set of points and need to find the optimal position for a service center that minimizes total travel distance. The trick isn't obvious at first, which is exactly why candidates get stuck during live coding. StealthCoder is your backstop if the geometry and optimization don't click under pressure. With a 35% acceptance rate, most people either brute-force incorrectly or miss the critical insight about how to handle the search space.
Companies that ask "Best Position for a Service Centre"
Best Position for a Service Centre is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE.
Get StealthCoderThe core problem combines geometry with optimization in a way that punishes linear thinking. You can't just average coordinates or use binary search naively on continuous space. The real solution involves recognizing that you're minimizing a convex function (sum of distances), which means you can use ternary search or a numerical method to converge on the answer. Many candidates start with Array and Math intuition, but the Geometry insight is what separates the solve from the timeout. Randomized hinting in the topic list suggests some approaches explore stochastic methods too. If you hit this on a live assessment and feel lost on the search strategy, StealthCoder surfaces a working solution in seconds, invisible to the proctor.
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Best Position for a Service Centre recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Best Position for a Service Centre interview FAQ
Is ternary search really the intended approach here?+
Ternary search works because the total distance function is unimodal in both x and y dimensions. You can ternary search x, then ternary search y to narrow down the optimal position. It's not the only approach, but it's clean and avoids floating-point pitfalls if you're careful with precision.
Why does the greedy center-of-mass approach fail?+
The arithmetic mean of all points minimizes squared error, not absolute distance. For L1 distance (Manhattan) or Euclidean, the optimal point is the geometric median, which has no closed form and requires iterative refinement. That's the gotcha.
How do I handle floating-point precision without it timing out?+
Ternary search with a fixed number of iterations (around 100-200) converges to sufficient precision. Set an epsilon threshold and stop when the search interval shrinks below it. Avoid re-sorting or recomputing distances per iteration; cache them if possible.
Will Citadel ask follow-up variations on this?+
Citadel's track record suggests they dig into variants: weighted distances, multiple service centers, or constraints. Understanding the core geometric optimization here is the foundation for defending against curveballs in live discussion.
What's the relationship between Array, Math, Geometry, and Randomized tags?+
Array stores the points. Math covers distance formulas and optimization. Geometry is the insight about convexity and medians. Randomized hints that some solutions use sampling or stochastic descent to approximate the median, especially useful for very large point sets.
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