The table below shows the limits that can be reached in a few seconds by algorithms of different complexities, n being the input size. I've added some algorithms and data structure examples for each complexity class.
|_. maximum n |_. complexity |_. algorithms |_. data structures|

| 1,000,000,000 | log n, sqrt n | binary search, ternary search, fast exponentiation, euclid algorithm |   |

| 1,000,000,000 and higher | log n, sqrt n | binary search, ternary search, fast exponentiation, euclid algorithm |   |

| 10,000,000 | n, n log log n, n log* n | set intersection, Eratosthenes sieve, radix sort, KMP, topological sort, Euler tour, strongly connected components, 2sat | disjoint sets, tries, hash_map, 'rolling hash':blog/rolling-hash deque|
| 1,000,000 | n log n | sorting, divide and conquer, sweep line, Kruskal, Dijkstra | segment trees, range trees, heaps, treaps, binary indexed trees, suffix arrays |
| 100,000 | n log^2^ n| divide and conquer | 2d range trees |