Solution: K Empty Slots

Understand how to solve the K Empty Slots problem by transforming bulb activation days into an array and applying a min heap to identify the earliest day two bulbs turn on with exactly k bulbs turned off between them. This approach avoids simulating day-by-day states and achieves a linear time complexity with efficient space use.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given $n$ bulbs arranged in a row, numbered from $1$ to $n$ . Initially, all bulbs are turned off.

Each day, exactly one bulb is switched on. You are given an array, bulbs of length $n$ where bulbs[i] $= x$ means that on day $i + 1$ (1‑indexed), the bulb at position $x$ (also 1‑indexed) is turned on.

So, given an integer k, determine the earliest day (the smallest day number) on which there are two bulbs that are on such that exactly k bulbs are off between them.

If no such day exists, return $- 1$ ...