Etar, I write it one more time: you just OVERestimate your actual power.

You use "square root method", but count the whole range. It is not correct.
Your example with 5 rooms x 200 people each and only one David zmong them: if you ask the whole room you perform ONLY one operation, but not 200 operations. Yes, it is better not to ask every person in every room, but ask once per room. This is efficient way. But it does not mean that you actually ask everybody. This will be overestimation.

Most famous Square root methods:
- Baby-step Gian-step
- Pollard's Rho algorithm
- Pollard's kangaroo algorithm

Have a look this link as well: https://www.embeddedrelated.com/showarticle/1093.php