merge sort: O(n log n) always

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

Best, worst and average case

Quicksort's average time complexity is O(n log n)

Binary search

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

Dijkstra's algorithm

Dijkstra's algorithm time complexity: O((V+E) log V)

Hash table

Hash table lookup: O(1) average time complexity

Graph (abstract data type)

Time complexity of BFS and DFS: O(V + E)