DSA

Phase 2 — Lab 3: Guardrail Arena

Big-O ceiling, Big-Ω floor, and the Θ tunnel (tight bound).

1) Choose the scenario

Scenario

Upper bound candidate (Big-O)

Lower bound candidate (Big-Ω)

Input size (n)

Reveal duration (curve draw time)

7.0s

Stress sensitivity (sparks intensity)

1.2×

Coach: In industry, “fast” is not a vibe. It is a guarantee. The ceiling is your insurance policy.

Goal: pick a ceiling and floor that do not get violated, and try to make them tight.

2) Live guarantee dashboard

Work f(n)

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Ceiling g(n)

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Floor h(n)

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Big-O check

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Big-Ω check

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Tightness

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Θ lock

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Press “Run Proof”. The white curve is the measured work. The cyan ceiling is Big-O. The green floor is Big-Ω.

If the curve hits the ceiling, sparks fly. If the floor is set too high, the floor gets violated (red sparks).

3) Quick legend (meaning of animations)

Cyan ceiling (laser/glass) = “at most” guarantee (Big-O).
Green floor (beam) = “at least” guarantee (Big-Ω).
Yellow loose ceiling = technically true but not useful.
Golden tunnel = ceiling and floor are the same order → Θ tight bound.

The arena contains no explanatory text. Explanations live here only.