H. Hour for a Run

Codeforces

IDCF10234H

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

The complete problemset is available on http://maratona.ime.usp.br/primfase19/provas/competicao/maratona_en.pdf [samples]

**Definitions** Let $ n \in \mathbb{Z} $ be the number of lanterns. Let $ X = (x_1, x_2, \dots, x_n) $ be a strictly increasing sequence of lantern coordinates, where $ 0 \le x_1 < x_2 < \dots < x_n \le 10^{18} $. **Constraints** $ 3 \le n \le 3000 $ **Objective** Find the maximum size $ k $ of a subsequence $ (x_{i_1}, x_{i_2}, \dots, x_{i_k}) $ with $ i_1 < i_2 < \dots < i_k $ such that: $$ x_{i_2} - x_{i_1} = x_{i_3} - x_{i_2} = \dots = x_{i_k} - x_{i_{k-1}} $$ (i.e., the selected lanterns form an arithmetic progression). If $ k < 3 $, any selection is valid — but we seek the *maximum* such $ k $.

API Response (JSON)

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