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

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

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

Greedy vs beam search decoding: greedy picks best token, beam maintains k candidates

Greedy decoding selects one token, while beam search retains multiple candidates

Why the curse of dimensionality makes nearest neighbor search unreliable

High-dimensional spaces increase distance ambiguity, reducing nearest neighbor search reliability

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