A. Smiley Faces (A)

Codeforces

IDCF10140A

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Mr. Light got some pieces of paper, each contains one of the three symbols: '.', ':', and ')'. He wants to use these pieces to form as many smiley faces as possible. To form one smiley face he needs one piece with a bracket ')' on it and either two pieces with dots '.', or one piece with a colon ':'. Mr. Light has A, B, and C of each symbol of '.', ':', ad ')', respectively. What is the maximum number of smiley faces he can form? The input contains three space-separated integers A B C (0 ≤ A, B, C ≤ 100), the number of pieces with each symbol of '.', ':', and ')', respectively. Print the maximum number of smiley faces Mr. Light can form, on a single line. ## Input The input contains three space-separated integers A B C (0 ≤ A, B, C ≤ 100), the number of pieces with each symbol of '.', ':', and ')', respectively. ## Output Print the maximum number of smiley faces Mr. Light can form, on a single line. [samples]

**Definitions** Let $ A, B, C \in \mathbb{Z}_{\geq 0} $ denote the counts of symbols '.', ':', and ')', respectively. **Constraints** $ 0 \leq A, B, C \leq 100 $ **Objective** Maximize the number of smiley faces $ S $, where each smiley requires: - One ')' (i.e., consumes 1 from $ C $), and - Either: - Two '.' (i.e., consumes 2 from $ A $), or - One ':' (i.e., consumes 1 from $ B $). Let $ x $ be the number of smileys formed using two '.' and one ')', and $ y $ be the number of smileys formed using one ':' and one ')'. Then: $$ S = x + y $$ subject to: $$ 2x \leq A, \quad y \leq B, \quad x + y \leq C, \quad x, y \in \mathbb{Z}_{\geq 0} $$ Maximize $ S = x + y $ under these constraints.

API Response (JSON)

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