Union-Find: The Matrix of Disjoint Sets

The Quest Begins (The "Why") I still remember the first time I stared at a LeetCode problem that asked me to count how many separate groups of friends existed in a social network. My initial instinct was to throw a nested loop at it, compare every pair, and mark visited nodes. The code worked on the tiny examples, but as soon as the input size crept past a few thousand, my solution started to feel like I was trying to bail out a sinking ship with a teaspoon. I was frustrated, not because I lacked effort, but because I was solving the wrong problem—I was treating connectivity as a series of pai