My Calendar I - Algorithm

The simple approach: store all booked intervals. For each new booking, check against all existing ones. If no overlap, add it. Time: $O(n)$ per booking where $n$ is number of existing bookings. For $n$ total bookings, $O(n^2)$ overall. Space: $O(n)$ to store all bookings.

A better approach uses a balanced tree to store intervals sorted by start time. Binary search finds potential overlaps in $O(\log n)$. For now, the simple approach works for most constraints.