Is Water Bottles easy or hard?

Water Bottles is classified as an Easy problem with a high acceptance rate around 70%+. The simulation solution is straightforward, and the challenge mainly lies in recognizing the mathematical shortcut that converts the process into a constant-time calculation.

Water Bottles Python/Java solution

In Python or Java, the common implementation uses a loop that continues while empty bottles are greater than or equal to numExchange. Each iteration computes new bottles from integer division, updates the total drinks, and tracks remaining empties. The logic uses only a few variables and runs in O(n) time with constant space.

How to solve Water Bottles in O(1)?

Use the observation that exchanging numExchange empty bottles for one full bottle returns one empty after drinking. The net cost per additional drink becomes numExchange − 1 empties. The maximum bottles you can drink equals numBottles + (numBottles − 1) / (numExchange − 1), which computes the result in constant time.

What is the best approach for Water Bottles?

Two common approaches exist: iterative simulation and a mathematical formula. The simulation method repeatedly exchanges empty bottles for full ones and runs in O(n) time with O(1) space. The mathematical approach derives that each extra drink costs (numExchange − 1) empty bottles, producing an O(1) time solution.

Is Water Bottles asked at Google/Amazon/Meta?

Water Bottles is a typical easy-level interview problem focused on simulation and simple mathematical reasoning. Similar exchange or resource-conversion problems appear in interviews at large tech companies including Amazon and Google as warm-up or screening questions.

What data structure is used in Water Bottles?

No specialized data structure is required. The solution relies on integer arithmetic and counters to track full bottles, empty bottles, and exchanges. It primarily tests simulation logic and mathematical reasoning rather than data structure design.

What is the time complexity of Water Bottles?

The simulation approach runs in O(n) time where n is the number of bottles consumed through exchanges, with constant O(1) space. The optimized mathematical solution reduces the complexity to O(1) time and O(1) space by computing the result directly using arithmetic.

Description Hints 1 Solution Video 10:44

1518. Water Bottles

Easy72.6% acceptance9 companies

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:

Input: numBottles = 9, numExchange = 3
Output: 13
Explanation: You can exchange 3 empty bottles to get 1 full water bottle.
Number of water bottles you can drink: 9 + 3 + 1 = 13.

Example 2:

Input: numBottles = 15, numExchange = 4
Output: 19
Explanation: You can exchange 4 empty bottles to get 1 full water bottle. 
Number of water bottles you can drink: 15 + 3 + 1 = 19.

Constraints: