6. Kitchen Plates

Codeforces

IDCF102156

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You are given 5 different sizes of kitchen plates. Each plate is marked with a letter *A, B, C, D, or E*. You are given $5$ statements comparing two different plates, you need to rearrange the plates from smallest size to biggest size. For example: the sizes of these plates The input consist of $5$ lines. In each line there will be $3$ characters, the first and last character will be either *A, B, C, D, or E* and the middle character will be either *>* or *<* describing the comparison between two plates sizes. No two plates will be equal. The output consist of 5 characters, the sorted order of balls from smallest to biggest plate. Otherwise, if the statements are contradicting print *impossible*. If there are multiple answers, print any of them ## Input The input consist of $5$ lines. In each line there will be $3$ characters, the first and last character will be either *A, B, C, D, or E* and the middle character will be either *>* or *<* describing the comparison between two plates sizes. No two plates will be equal. ## Output The output consist of 5 characters, the sorted order of balls from smallest to biggest plate. Otherwise, if the statements are contradicting print *impossible*. If there are multiple answers, print any of them [samples]

**Definitions** Let $ P = \{A, B, C, D, E\} $ be the set of plate labels. Let $ S \subseteq P \times \{<, >\} \times P $ be a set of 5 strict binary comparison statements, where each statement is of the form $ (X, \text{op}, Y) $ with $ X \ne Y $ and $ \text{op} \in \{<, >\} $, meaning $ X < Y $ or $ X > Y $. **Constraints** 1. Each statement in $ S $ compares two distinct plates. 2. No two plates are equal (all sizes are distinct). 3. $ |S| = 5 $. **Objective** Find a total order $ \pi = (p_1, p_2, p_3, p_4, p_5) $ of $ P $ such that for every statement $ (X, \text{op}, Y) \in S $: - If $ \text{op} = < $, then $ \pi^{-1}(X) < \pi^{-1}(Y) $, - If $ \text{op} = > $, then $ \pi^{-1}(X) > \pi^{-1}(Y) $. If no such total order exists, output *impossible*. If multiple exist, output any one.

API Response (JSON)

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      "content": "You are given 5 different sizes of kitchen plates. Each plate is marked with a letter *A, B, C, D, or E*. You are given $5$ statements comparing two different plates, you need to rearrange the plates ...",
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