B-trees optimize: disk-based sorted data with O(log n) reads per query

LSM trees optimize: write-heavy workloads by buffering writes in memory

LSM trees optimize write-heavy workloads by buffering writes in memory

O(n log n) is the lower bound for comparison-based sorting

O(n log n) is the lower bound because each of n elements must be compared at least log n times to ensure all permutations are considered

merge sort: O(n log n) always

Merge sort consistently performs at O(n log n) time complexity for any input size

Binary search

Time complexity of binary search: O(log n) — halves search space each step

consistent hashing does: minimizes remapping when nodes join/leave

Consistent hashing distributes data across nodes, minimizing remapping when nodes join/leave

BFS vs DFS: BFS finds shortest path in unweighted graphs, DFS uses less memory

BFS finds shortest path in unweighted graphs; DFS uses less memory