Time complexity of quicksort: O(n log n) average, O(n²) worst case

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

Binary search reduces search space by half with each iteration, achieving O(log n) complexity

Why attention is O(n²) in sequence length: every token attends to every other token

Attention mechanism's complexity arises from pairwise token interactions, leading to quadratic time complexity

Time complexity of Dijkstra's algorithm: O((V+E) log V) with a priority queue

Dijkstra's algorithm: O((V+E) log V) using a Fibonacci heap

Why second-order methods (Newton's) converge faster but are expensive: O(n³) per step

Newton's method has quadratic convergence but requires cubic computational cost per iteration

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

LSM trees optimize write-heavy workloads through in-memory buffering

Why memory coalescing matters — adjacent threads reading adjacent memory addresses

Memory coalescing reduces cache misses, improving multithreaded application performance