To all the men, I need your support. I swear I’m innocent in this. Last night, my ex drunk-called me out of nowhere. Past midnight. My phone started vibrating on the table, and when I saw her name, I froze for a second. I hadn’t heard from her in months. I thought she had moved on. I thought I had erased every trace. But I picked up. She didn’t even say hello. The first thing I heard was her breathing heavy, then a sharp voice: “You never returned the gift I gave you.” For a moment, I didn’t even know what she was talking about. A gift? Two years ago? She was holding on to that? I laughed nervously, which only made it worse. She started listing everything I had forgotten: the gift, the dates, the things I promised. She remembered it all in perfect order, detail by detail. And as she went on, I had this weird thought: this is exactly how Big Tech remembers us. You try creating a username — type “abhishek123” — and instantly the system knows if it’s taken. Not after searching, not after thinking. Instantly. Just like her. Here’s how they do it: Hashmap – Redis in memory A hashmap is like her memory of me. You ask, “is ‘abhishek123’ taken?” and it replies instantly. The lookup is O(1), meaning constant time no matter if there are 10 users or 10 billion. That’s why Redis hashmaps are used for username availability checks — pure speed, no waiting. B+ Tree(Indexing) – Hashmaps are fast, but they only give you a yes or no. Databases need more than that. They need order. That’s where B+ Trees come in. Every major database — MySQL, Postgres, MongoDB — uses B+ Trees for indexing. And the beauty is, they don’t just work for numbers like user IDs. They also handle strings like usernames. In that case, the values are stored in lexicographic order — just like words in a dictionary. That makes them a perfect fit for our username example. So if you type “abhi,” the database knows exactly where that prefix starts in the sorted structure. From there it can scan forward through the leaves, which are linked together, and retrieve all the matches in sequence. Time complexity? Searching for a starting point costs O(log N). Scanning through K results costs O(K). Together, it’s O(log N + K). This is why B+ Trees are the backbone of range-based queries. Whether it’s “all usernames starting with ab,” or “all users with IDs between 1000 and 2000,” the tree can deliver results efficiently because everything inside it is kept sorted automatically. Trie – prefix matching and autocomplete But sometimes you don’t even finish the name. You type “abhi” and expect suggestions: “abhishek,” “abhilash,” “abhinav.” That’s where a Trie comes in. Every character is a step down a path. The cost of lookup or insertion is O(L), where L is the length of the word. Even if there are millions of names stored, checking a 5-letter prefix takes just 5 steps. That’s why Tries power autocomplete and prefix search. So the next time you see “username already taken,” remember what’s happening behind the screen. Hashmaps handle the instant yes-or-no. B+ Trees keep everything sorted for range queries. Tries make autocomplete possible. My ex never forgot that gift. Big Tech never forgets your username. The only difference is that Big Tech actually designed its memory to be that way.