3021. Alice and Bob Playing Flower Game #2110
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Topics: Alice and Bob are playing a turn-based game on a field, with two lanes of flowers between them. There are
Given two integers,
Return the number of possible pairs Example 1:
Example 2:
Constraints:
Hint:
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We need to determine the number of valid pairs Approach
Let's implement this solution in PHP: 3021. Alice and Bob Playing Flower Game <?php
/**
* @param Integer $n
* @param Integer $m
* @return Integer
*/
function flowerGame($n, $m) {
$even_n = (int)($n / 2);
$odd_n = $n - $even_n;
$even_m = (int)($m / 2);
$odd_m = $m - $even_m;
return $even_n * $odd_m + $odd_n * $even_m;
}
// Test cases
// Example 1
echo flowerGame(3, 2) . "\n"; // Output: 3
// Example 2
echo flowerGame(1, 1) . "\n"; // Output: 0
?> Explanation:
This approach efficiently computes the solution by leveraging basic arithmetic operations and counting, ensuring optimal performance even for large values of |
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We need to determine the number of valid pairs
(x, y)
wherex
represents the number of flowers in the first lane andy
represents the number of flowers in the second lane. The conditions are that Alice wins the game, andx
andy
must be within the ranges[1, n]
and[1, m]
respectively.Approach
x + y
must be odd. This means that ifx
is e…