Solution: K Empty Slots

Discover how to determine the earliest day two turned-on bulbs have exactly k off bulbs between them. Learn to transform bulb positions into activation days and use a min heap to efficiently track the earliest activation day among the bulbs in between. This lesson helps you implement an O(n) time complexity solution while understanding key data structures.

We'll cover the following...

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 $- 1$ ...