Alice and Bob are playing a turn-based game on a field, with two lanes of flowers between them. There are x flowers in the first lane between Alice and Bob, and y flowers in the second lane between them. The game proceeds as follows: Alice takes th

flowerGame.js

/**
 * @param {number} n
 * @param {number} m
 * @return {number}
 */
var flowerGame = function(n, m) {
    // Count how many odd numbers are in [1, n]
    const oddX = Math.floor(n / 2) + (n % 2);   // e.g., 1, 3, 5...
    const evenX = Math.floor(n / 2);            // e.g., 2, 4, 6...

    // count how many odd numbers are in [1, m]
    const oddY = Math.floor(m / 2) + (m % 2);
    const evenY = Math.floor(m / 2);

    // Valid pairs are:
    // - odd x with even y
    // - even x with odd y
    const validPairs = (oddX * evenY) + (evenX * oddY);

    return validPairs;
};