BEADS - Glass Beads

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Once upon a time there was a famous actress. As you may expect, she played mostly Antique Comedies most of all. All the people loved her. But she was not interested in the crowds. Her big hobby were beads of any kind. Many bead makers were working for her and they manufactured new necklaces and bracelets every day. One day she called her main Inspector of Bead Makers (IBM) and told him she wanted a very long and special necklace.

The necklace should be made of glass beads of different sizes connected to each other but without any thread running through the beads, so that means the beads can be disconnected at any point. The actress chose the succession of beads she wants to have and the IBM promised to make the necklace. But then he realized a problem. The joint between two neighbouring beads is not very robust so it is possible that the necklace will get torn by its own weight. The situation becomes even worse when the necklace is disjoined. Moreover, the point of disconnection is very important. If there are small beads at the beginning, the possibility of tearing is much higher than if there were large beads. IBM wants to test the robustness of a necklace so he needs a program that will be able to determine the worst possible point of disjoining the beads.

The description of the necklace is a string A = a1a2 ... am specifying sizes of the particular beads, where the last character am is considered to precede character a1 in circular fashion.

The disjoint point i is said to be worse than the disjoint point j if and only if the string aiai+1 ... ana1 ... ai-1 is lexicografically smaller than the string ajaj+1 ... ana1 ... aj-1. String a1a2 ... an is lexicografically smaller than the string b1b2 ... bn if and only if there exists an integer i, i <= n, so that aj=bj, for each j, 1 <= j < i and ai < bi.

Input

The input consists of N cases. The first line of the input contains only positive integer N. Then follow the cases. Each case consists of exactly one line containing necklace description. Maximal length of each description is 10000 characters. Each bead is represented by a lower-case character of the english alphabet (a--z), where a < b ... z.

Output

For each case, print exactly one line containing only one integer -- number of the bead which is the first at the worst possible disjoining, i.e. such i, that the string A[i] is lexicographically smallest among all the n possible disjoinings of a necklace. If there are more than one solution, print the one with the lowest i.

Example

Sample input:

4
helloworld
amandamanda
dontcallmebfu
aaabaaa

Sample output:

10
11
6
5

hide comments
its_mrsuit21: 2016-11-28 03:56:02

Help pls! I have tried every test cases i can think of : aaaa, aabb, bbaacc. And still get WA :(

kishalve pethia: 2015-12-10 20:33:43

can someone share O(n) algo

Last edit: 2015-12-11 15:20:45
poojan : 2015-08-18 09:27:46

got it finally ac! But my run time is .10 anyone tell me approach more faster than my?i use suffix array O(n* log n*log n).

Last edit: 2015-08-27 18:01:45
vikram bhat: 2015-07-07 08:54:16

Nice question , I did something different to solve it . Normal way would be suffix array or duval algorithm, but I used rolling hash with binary search and recheck match with logn intervals. The solution was indeterministic but I guess there it very hard to produce failure case for it. The time complexity being O(n(logn)^2)

Last edit: 2015-07-07 09:07:40
cracked: 2015-04-29 20:57:31

Bruteforce in Java. AC.

Vamsi Krishna Avula: 2015-01-20 10:08:08

bruteforce in Python AC :v

Ashwini: 2014-06-25 20:50:51

yipee. AC both by O(n) algo(took help from google) and by suffix array(my first suffix array program..)

Saurabh Jain: 2014-06-17 17:02:48

What are the constraints on N???

Paul Draper: 2012-12-14 05:12:50

MINMOVES


Added by:adrian
Date:2004-06-06
Time limit:0.5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6 VB.net
Resource:ACM Central European Programming Contest, Prague 1998