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

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

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

Quicksort's average-case time complexity: O(n log n), worst-case: O(n²)

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

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

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

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 a message queue decouples: producer and consumer can operate at different speeds

Message queues decouple producers and consumers, allowing asynchronous processing