1518. Water Bottles #281
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Topics: There are numBottles water bottles that are initially full of water. You can exchange numExchange empty water bottles from the market with one full water bottle. The operation of drinking a full water bottle turns it into an empty bottle. Given the two integers numBottles and numExchange, return the maximum number of water bottles you can drink. Example 1:
Example 2:
Constraints:
Hint:
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The problem is to maximize the number of water bottles that can be consumed, given a starting number of full water bottles ( Key Points
ApproachTo solve this, we can simulate the process:
The key challenge is to keep track of the full and empty bottles and handle the exchange process effectively. Plan
Let's implement this solution in PHP: 1518. Water Bottles <?php
/**
* @param Integer $numBottles
* @param Integer $numExchange
* @return Integer
*/
function numWaterBottles($numBottles, $numExchange) {
$totalDrunk = 0;
$emptyBottles = 0;
while ($numBottles > 0) {
// Drink all the current full bottles
$totalDrunk += $numBottles;
// Collect the empty bottles
$emptyBottles += $numBottles;
// Exchange the empty bottles for new full ones
$numBottles = floor($emptyBottles / $numExchange);
$emptyBottles = $emptyBottles % $numExchange;
}
return $totalDrunk;
}
// Example usage:
$numBottles = 9;
$numExchange = 3;
echo numWaterBottles($numBottles, $numExchange) . "\n"; // Output: 13
$numBottles = 15;
$numExchange = 4;
echo numWaterBottles($numBottles, $numExchange) . "\n"; // Output: 19
?> Explanation:
Example WalkthroughExample 1:
Example 2:
Time Complexity
Output for ExampleExample 1:
Example 2:
The problem can be solved efficiently by simulating the exchange process and keeping track of full and empty bottles. This approach ensures we maximize the total number of bottles drunk while following the exchange rules. The solution is both time-efficient and space-efficient, making it well-suited for the given constraints. |
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The problem is to maximize the number of water bottles that can be consumed, given a starting number of full water bottles (
numBottles
) and an exchange rate (numExchange
). Each time you drink a full bottle, it becomes an empty bottle. Once you have enough empty bottles (equal tonumExchange
), you can trade them for full bottles. The goal is to compute how many total water bottles you can drink, including those obtained through exchanges.Key Points
numExchange
) for one full bottle.