E. Meetings

Codeforces

IDCF10125E

Time1000ms

Memory64MB

Difficulty—

English · Original

Formal · Original

Two cities A and B are connected by a straight road that is exactly l meters long. At the initial moment of time a cyclist starts moving from city A to city B at a speed v1 meters/second, and a pedestrian starts moving from city B to city A at a speed v2 meters/second. When one of them reaches a city, the road ends, so the person has to turn around and start moving in the opposite direction by the same road, keeping the original speed. As a result, the cyclist and the pedestrian are traveling between cities A and B indefinitely. Your task is to calculate the number of times they will meet during the first t seconds. If they meet in exactly t seconds after the initial moment of time, this meeting should also be counted. The only line of input contains four integer numbers: l, v1, v2 and t. All numbers are between 1 and 109, inclusively. Print a single integer — the number of times the cyclist and the pedestrian will meet during the first t seconds. ## Input The only line of input contains four integer numbers: l, v1, v2 and t. All numbers are between 1 and 109, inclusively. ## Output Print a single integer — the number of times the cyclist and the pedestrian will meet during the first t seconds. [samples]

**Definitions** Let $ T_1 = \{a_1, a_2, a_3\} $ and $ T_2 = \{b_1, b_2, b_3\} $ be two distinct triangles, where each vertex is an integer in $ \{1, 2, \dots, 6\} $. An **edge** is an unordered pair of distinct vertices. Define the set of edges of a triangle $ T = \{x, y, z\} $ as: $$ E(T) = \{ \{x,y\}, \{y,z\}, \{z,x\} \} $$ Let $ E = E(T_1) \cup E(T_2) $ be the multiset of all edges from both triangles. A **boundary edge** is an edge that appears in exactly one triangle. **Constraints** - $ T_1 \neq T_2 $ (differ by at least one vertex). - All vertices are integers in $ \{1, 2, \dots, 6\} $. **Objective** Compute the number of edges in $ E $ that have multiplicity 1: $$ \left| \{ e \in E \mid \text{multiplicity of } e \text{ in } E \text{ is } 1 \} \right| $$

API Response (JSON)

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    "name": "E. Meetings",
    "description": {
      "content": "Two cities A and B are connected by a straight road that is exactly l meters long. At the initial moment of time a cyclist starts moving from city A to city B at a speed v1 meters/second, and a pedest",
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    },
    "platform": "Codeforces",
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      "statement_type": "Markdown",
      "content": "Two cities A and B are connected by a straight road that is exactly l meters long. At the initial moment of time a cyclist starts moving from city A to city B at a speed v1 meters/second, and a pedest...",
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      "content": "**Definitions**  \nLet $ T_1 = \\{a_1, a_2, a_3\\} $ and $ T_2 = \\{b_1, b_2, b_3\\} $ be two distinct triangles, where each vertex is an integer in $ \\{1, 2, \\dots, 6\\} $.  \n\nAn **edge** is an unordered p...",
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