LeetCode Entry

1518. Water Bottles

01.10.2025 easy 2025 kotlin rust

Total drinks with exchange empty for full

1518. Water Bottles easy blog post substack youtube

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Problem TLDR

Total drinks with exchange empty for full #easy #simulation

Intuition

Simulate the process. Don’t forget to keep lefover empty bottles.

Approach

  • the single math formula can be derived from: s = b + b/x + (b/x+b%x)/x + ((b/x+b%x)/x+(b/x+b%x)%x)/x...
  • or s = b*(1 + 1/x + 1/x^2 + 1/x^3 + ...), geometric series converges to 1/(1-r) where r=1/x
  • so s = b*(1/(1-1/x)) = b/(1-1/x) = b*x/(x-1) (ask chatgpt why it is (b*x-1) instead)

Complexity

  • Time complexity: \(O(1)\)

  • Space complexity: \(O(1)\)

Code


// 0ms
    fun numWaterBottles(b: Int, x: Int, e: Int = 0): Int =
    b + if (b < 1) 0 else numWaterBottles((b+e)/x, x, (b+e)%x)



// 0ms
    pub fn num_water_bottles(b: i32, x: i32) -> i32 {
        (b*x-1)/(x-1)
    }