my submission: https://codeforces.me/contest/126/submission/190247628 //
as far as I can see, My solution is O(n²) when there is no solution and it got AC. and the string length is ~~ 1e6
my submission: https://codeforces.me/contest/126/submission/190247628 //
as far as I can see, My solution is O(n²) when there is no solution and it got AC. and the string length is ~~ 1e6
| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | Benq | 3676 |
| 2 | Kevin114514 | 3659 |
| 3 | jiangly | 3640 |
| 4 | turmax | 3450 |
| 5 | tourist | 3382 |
| 6 | strapple | 3360 |
| 7 | Um_nik | 3354 |
| 8 | squareOf105 | 3348 |
| 9 | maroonrk | 3312 |
| 10 | idontwannadothis…e | 3191 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | Qingyu | 155 |
| 2 | nik_exists | 151 |
| 3 | maspy | 149 |
| 4 | AmShZ | 145 |
| 5 | Um_nik | 143 |
| 6 | Errichto | 139 |
| 7 | BledDest | 136 |
| 8 | adamant | 134 |
| 9 | maroonrk | 132 |
| 10 | cry | 130 |
This problem is very old (Beta round) so test cases are likely to be weak.
It's actually not $$$n^2$$$. The hashes are done in $$$O(1)$$$ so comparing each suffix with the prefix is $$$n \cdot O(1)$$$. Suppose $$$A$$$ is the shortest substring of $$$S$$$ such that $$$A$$$ is both a suffix and a prefix. Then $$$S = ATA$$$. Suppose $$$AB$$$ is the second shortest substring such that $$$AB$$$ is both a suffix and a prefix. Then $$$S = ABT^\prime AB$$$. This implies that $$$A$$$ was also an infix of $$$S$$$. So when we actually ran the algorithm, we should've stopped at just $$$A$$$.
What all this implies is that there can be at most one candidate prefix/suffix. If there is more than one, we know that the first candidate also appears somewhere inside of $$$S$$$ and we'd just print it. This makes the algorithm $$$O(n)$$$.
(Edit: simplified argument slightly)
But in the code I m not stopping at the shortest, the opposite, I m searching for the longest ones , starting from the prefix at string.length()-2
My bad for not noticing but the idea is the same. Here we could call the longest suffix/prefix $$$AB$$$ and the second longest $$$A$$$ and the rest of the argument is identical.