K. Keep Calm and Sell Balloons

Codeforces

IDCF10234K

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 even, $ 2 \leq n \leq 50 $. The wall is an $ n \times n $ grid. Position $ (i, j) $ must contain: - Stone block if $ i + j \equiv 0 \pmod{2} $, - Sand block if $ i + j \equiv 1 \pmod{2} $. **Constraints** - Only two operations allowed: 1. Place a single block of correct type on a *free* position. 2. Fill all empty positions in a $ 2 \times 2 $ square with a single block type, provided at least one position in the square is *free* and the entire square lies within bounds ($ 1 \leq x, y \leq n-1 $). - No block may be placed in a position where its type contradicts the chequered pattern. - Total operations $ k \leq \frac{3n^2}{4} $. **Objective** Construct a sequence of operations (each of type 1 or 2) that fills the grid according to the chequered pattern, using at most $ \frac{3n^2}{4} $ operations.

API Response (JSON)

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