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#3021 - Alice and Bob Playing Flower Game
Problem Description
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.
The game proceeds as follows:
- Alice takes the first turn.
- In each turn, a player must choose either the clockwise or anti-clockwise direction and pick one flower from that side.
- At the end of the turn, if there are no flowers left at all, the current player captures their opponent and wins the game.
Given two integers, n and m, the task is to compute the number of possible pairs (x, y) that satisfy the conditions:
- Alice must win the game according to the described rules.
- The number of flowers x in the clockwise direction must be in the range [1,n].
- The number of flowers y in the anti-clockwise direction must be in the range [1,m].
Return the number of possible pairs (x, y) that satisfy the conditions mentioned in the statement.
Solution
/**
* @param {number} n
* @param {number} m
* @return {number}
*/
var flowerGame = function(n, m) {
const evenN = Math.floor(n / 2);
const evenM = Math.floor(m / 2);
return evenN * (m - evenM) + (n - evenN) * evenM;
};