1518.water-bottles.cpp

//  Tag: Math, Simulation
//  Time: O(LogN)
//  Space: O(1)
//  Ref: -
//  Note: -
//  Video: https://youtu.be/ahWvHRgMGPk

//  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:
//  
//  1 <= numBottles <= 100
//  2 <= numExchange <= 100
//  
//  

class Solution {
public:
    int numWaterBottles(int numBottles, int numExchange) {
        int res = 0;
        int empty = 0;
        while (numBottles > 0 || empty >= numExchange) {
            res += numBottles;
            empty += numBottles;
            numBottles = empty / numExchange;
            empty = empty % numExchange;
        }

        return res;
    }
};

class Solution {
public:
    int numWaterBottles(int numBottles, int numExchange) {
        return (numBottles - 1) / (numExchange - 1) + numBottles;
    }
};