C. Pig Latin

Codeforces

IDCF10221C

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

https://en.wikipedia.org/wiki/Pig_Latin Pig Latin is a secret language which is similar to English. To convert an English word to Pig Latin, take the first letter of that word, move it to the end, and then add "ay". Peccy and Danbo are two Amazon mascots. They like sending each other messages over Amazon Chime, but they've realised that their messages are unencrypted! Help Peccy and Danbo encrypt their messages by converting them into Pig Latin. Make sure to check the examples. The first line will contain an integer T, where T is the number of sentences given. Each sentence will be on a new line and will not contain punctuation. However, they will be capitalised at the beginning (but not anywhere else). Make sure you check the examples given. A list of sentences in Pig Latin. Each sentence should be on a new line and should not contain punctuation, but it should start with a capital letter. #cf_span(class=[tex-font-style-underline], body=[Constraints]): 1 ≤ T ≤ 20 Each sentence will not contain punctuation and will be all lowercase English characters, except for the very first letter of the very first word, which will be an uppercase English character. ## Input The first line will contain an integer T, where T is the number of sentences given. Each sentence will be on a new line and will not contain punctuation. However, they will be capitalised at the beginning (but not anywhere else). Make sure you check the examples given. ## Output A list of sentences in Pig Latin. Each sentence should be on a new line and should not contain punctuation, but it should start with a capital letter. [samples] ## Note #cf_span(class=[tex-font-style-underline], body=[Constraints]):1 ≤ T ≤ 20Each sentence will not contain punctuation and will be all lowercase English characters, except for the very first letter of the very first word, which will be an uppercase English character.

**Definitions** Let $ V \in \mathbb{R}^+ $ be the input voltage. Let $ R, L, C \in \mathbb{R}^+ $ be the resistance, inductance, and capacitance, respectively, satisfying $ L < 4R^2C $. The voltage across the resistor is given by: $$ V_r(t) = V \left(1 - e^{-\alpha t} \left( \cos(\omega_d t) + \frac{\alpha}{\omega_d} \sin(\omega_d t) \right) \right) $$ where $$ \alpha = \frac{R}{2L}, \quad \omega_d = \frac{1}{L} \sqrt{L C^{-1} - \frac{R^2}{4}} $$ **Constraints** 1. $ 1 \le V \le 20 $ 2. $ 0.1 \le R, L, C \le 20 $ 3. $ L < 4 R^2 C $ **Objective** Find $ t_{\min}, t_{\max} \in \mathbb{R}^+ $ and the corresponding values $ V_{\min}, V_{\max} $ such that: - $ V_{\min} = \min_{t > 0} V_r(t) $ - $ V_{\max} = \max_{t > 0} V_r(t) $ before $ V_r(t) $ stabilizes (i.e., before $ t $ where $ |V_r(t) - V| < \epsilon $ for small $ \epsilon $, but the extrema occur before asymptotic convergence). Output: First line: $ V_{\min} $ and $ t_{\min} $ Second line: $ V_{\max} $ and $ t_{\max} $

API Response (JSON)

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    "name": "C. Pig Latin",
    "description": {
      "content": "https://en.wikipedia.org/wiki/Pig_Latin Pig Latin is a secret language which is similar to English. To convert an English word to Pig Latin, take the first letter of that word, move it to the end, an",
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    },
    "platform": "Codeforces",
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      "memory_limit": 262144
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