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1518. Water Bottles

SourceWeekly Contest 198 Q1DifficultyEasyRating1245

Description

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

Solutions

Solution 1

Thinking

Empty bottles exchange for a full one every \(numExchange\) empties; we want the total number drunk. The values are small enough to simulate each exchange rather than seek a closed form.

Drink the initial \(numBottles\) first. Whenever the empty count is at least the rate, spend \(numExchange\) empties for one full bottle; after drinking it, the empty count falls by \(numExchange-1\) and the answer grows by one. Stop when a further exchange is impossible.

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class Solution:
    def numWaterBottles(self, numBottles: int, numExchange: int) -> int:
        ans = numBottles
        while numBottles >= numExchange:
            numBottles -= numExchange - 1
            ans += 1
        return ans

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class Solution {
    public int numWaterBottles(int numBottles, int numExchange) {
        int ans = numBottles;
        for (; numBottles >= numExchange; ++ans) {
            numBottles -= (numExchange - 1);
        }
        return ans;
    }
}

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class Solution {
public:
    int numWaterBottles(int numBottles, int numExchange) {
        int ans = numBottles;
        for (; numBottles >= numExchange; ++ans) {
            numBottles -= (numExchange - 1);
        }
        return ans;
    }
};

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func numWaterBottles(numBottles int, numExchange int) int {
    ans := numBottles
    for ; numBottles >= numExchange; ans++ {
        numBottles -= (numExchange - 1)
    }
    return ans
}

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function numWaterBottles(numBottles: number, numExchange: number): number {
    let ans = numBottles;
    for (; numBottles >= numExchange; ++ans) {
        numBottles -= numExchange - 1;
    }
    return ans;
}

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/**
 * @param {number} numBottles
 * @param {number} numExchange
 * @return {number}
 */
var numWaterBottles = function (numBottles, numExchange) {
    let ans = numBottles;
    for (; numBottles >= numExchange; ++ans) {
        numBottles -= numExchange - 1;
    }
    return ans;
};

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class Solution {
    /**
     * @param Integer $numBottles
     * @param Integer $numExchange
     * @return Integer
     */
    function numWaterBottles($numBottles, $numExchange) {
        $ans = $numBottles;
        while ($numBottles >= $numExchange) {
            $numBottles = $numBottles - $numExchange + 1;
            $ans++;
        }
        return $ans;
    }
}

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