Running Times for CS140 / CS302 Algorithms

• Inserting to the beginning of a vector: O(n).
• Appending to the end of a vector: O(1).
• Erasing from the beginning of a vector: O(n).
• Erasing from the end of a vector: O(1).

• Inserting to the beginning of a deque: O(1).
• Appending to the end of a deque: O(1).
• Erasing from the beginning of a deque: O(1).
• Erasing from the end of a deque: O(1).

• Inserting anywhere in a list: O(1).
• Erasing anywhere from a list: O(1).

• Inserting anything in a set or map: O(log n).
• Inserting anywhere in a set or map: O(log n).
• Erasing anywhere from a set or map: O(log n).
• Traversing a set or map: O(n).
• Creating a set or map: O(n log(n)).

• Enumerating permutations: O(n!).
• Enumerating pairs: O(n²).
• Enumerating bit strings: O(2ⁿ).

• Find in a disjoint set O(α(n)).
• Union in a disjoint set O(1).

• Push in a heap: O(log(n))
• Pop in a heap: O(log(n))
• Creating a heap O(n).

• Bubble sort, selection sort, worst-case insertion sort, worst-case quicksort: O(n²))
• Heap sort, merge sort, average-case quicksort: O(n log(n))
• Bucket sort, "nearly"-sorted insertion sort: O(n)

• Edges in a dense graph with n nodes: O(n²)

• DFS, BFS, Topological sort in general: O(|V|+|E|)
• DFS, BFS, Topological sort on a connected graph: O(|E|)
• Dijkstra's shortest paths, Prim's minimum spanning tree: O(|E| log |V|)
• Kruskal's minimum spanning tree: O(|E|log |E|).
• Of course, log|E| is O(log|V|), so you don't have to be too anal about it.

• The Ford-Fulkerson algorithm in general when the max flow is f: O(f|E|)
• The Edmonds-Karp algorithm for network flow: O(|V||E|²).

• Dynamic programming: You have to analyze each program individually. In general, if you've done step 2, then the running time is roughly the size of the cache.