My Calendar I
Signals to notice
Brute force first
For each booking, check all existing bookings for overlap — total. That direct path helps you understand the question, but it tends to treat every possibility as brand new instead of learning from earlier steps.
The key insight
Maintain a sorted list of intervals. For each new booking, binary search for the insertion point and check neighbors for overlap. over all operations. Or use a balanced BST (TreeMap). Instead of recomputing the world every time, you preserve just enough context to let the next decision become obvious.
What must stay true
Two intervals [s1,e1) and [s2,e2) overlap if and only if s1 < e2 AND s2 < e1. Checking only the neighboring intervals in sorted order is sufficient. As long as that statement keeps holding, you can trust the steps built on top of it.
Easy way to go wrong
Checking all existing intervals — with a sorted structure, you only need to check the neighbors at the insertion point. The fix is usually to return to the meaning of each move, not just the steps themselves.