Water Bottles 2 — Algorithm Visualization & Coding Challenge

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Understanding Water Bottles 2

Detailed explanation and reference materials

Problem Overview

Water Bottles II

Medium

Hint

You are given two integers numBottles and numExchange.

numBottles represents the number of full water bottles that you initially have.
In one operation, you can perform one of the following operations:

Drink any number of full water bottles turning them into empty bottles.
Exchange numExchange empty bottles with one full water bottle. Then, increase numExchange by one.

⚠️ Note: You cannot exchange multiple batches of empty bottles for the same value of numExchange.
For example, if numBottles == 3 and numExchange == 1, you cannot exchange 3 empty water bottles for 3 full bottles.

Return the maximum number of water bottles you can drink.

Example 1

Input:

numBottles = 13, numExchange = 6

Output:

Step-by-step table (Full / Empty / numExchange / cumulative drunk):

Step	Action	Full (after)	Empty (after)	numExchange (used → new / or current)	Drunk (cumulative)
0	Start	13	0	6	0
1	Drink 13	0	13	6	13
2	Exchange (use 6)	1	7	6 → 7	13
3	Exchange (use 7)	2	0	7 → 8	13
4	Drink 2	0	2	8	15

Final answer: 15

Example 2

Input:

numBottles = 10, numExchange = 3

Output:

Step-by-step table (Full / Empty / numExchange / cumulative drunk):

Step	Action	Full (after)	Empty (after)	numExchange (used → new / or current)	Drunk (cumulative)
0	Start	10	0	3	0
1	Drink 10	0	10	3	10
2	Exchange (use 3)	1	7	3 → 4	10
3	Exchange (use 4)	2	3	4 → 5	10
4	Drink 2	0	5	5	12
5	Exchange (use 5)	1	0	5 → 6	12
6	Drink 1	0	1	6	13

Final answer: 13

Constraints

1 <= numBottles <= 100
1 <= numExchange <= 100

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/water-bottles-ii/description/

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