{ "data": { "question": { "questionId": "3279", "questionFrontendId": "3021", "boundTopicId": null, "title": "Alice and Bob Playing Flower Game", "titleSlug": "alice-and-bob-playing-flower-game", "content": "

Alice and Bob are playing a turn-based game on a circular field surrounded by flowers. The circle represents the field, and there are x flowers in the clockwise direction between Alice and Bob, and y flowers in the anti-clockwise direction between them.

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The game proceeds as follows:

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    \n\t
  1. Alice takes the first turn.
  2. \n\t
  3. In each turn, a player must choose either the clockwise or anti-clockwise direction and pick one flower from that side.
  4. \n\t
  5. At the end of the turn, if there are no flowers left at all, the current player captures their opponent and wins the game.
  6. \n
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Given two integers, n and m, the task is to compute the number of possible pairs (x, y) that satisfy the conditions:

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Return the number of possible pairs (x, y) that satisfy the conditions mentioned in the statement.

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Example 1:

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\nInput: n = 3, m = 2\nOutput: 3\nExplanation: The following pairs satisfy conditions described in the statement: (1,2), (3,2), (2,1).\n
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Example 2:

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\nInput: n = 1, m = 1\nOutput: 0\nExplanation: No pairs satisfy the conditions described in the statement.\n
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Constraints:

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Compiled with clang 17 using the latest C++ 20 standard.

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Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

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Most standard library headers are already included automatically for your convenience.

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OpenJDK 21. Using compile arguments: --enable-preview --release 21

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Most standard library headers are already included automatically for your convenience.

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Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

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Python 2.7.12.

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Compiled with gcc 11 using the gnu11 standard.

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C# 12 with .NET 8 runtime

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Node.js 20.10.0.

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Your code is run with --harmony flag, enabling new ES6 features.

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lodash.js library is included by default.

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Ruby 3.2

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Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

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Swift 5.9.

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Go 1.21

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Python 3.11.

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Scala 2.13.7.

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Kotlin 1.9.0.

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Rust 1.74.1

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PHP 8.2.

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TypeScript 5.1.6, Node.js 20.10.0.

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Racket CS v8.11

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