BEADS  Glass Beads
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 = a_{1}a_{2} ... a_{m} specifying sizes of the particular beads, where the last character a_{m} is considered to precede character a_{1} in circular fashion.
The disjoint point i is said to be worse than the disjoint point j if and only if the string a_{i}a_{i+1} ... a_{n}a_{1} ... a_{i1} is lexicografically smaller than the string a_{j}a_{j+1} ... a_{n}a_{1} ... a_{j1}. String a_{1}a_{2} ... a_{n} is lexicografically smaller than the string b_{1}b_{2} ... b_{n} if and only if there exists an integer i, i <= n, so that a_{j}=b_{j}, for each j, 1 <= j < i and a_{i} < b_{i}.
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 lowercase character of the english alphabet (az), 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
karan_yadav:
20180724 09:39:09
O(n)  Duval Algorithm, Google it! 

deepk_keshri:
20170828 13:32:46
solved in O(N),just find min of all possible string made by considering from a( i .. n ..i1). 

ayush_mawandia:
20170616 12:39:41
easy one...AC in O(N).


nilabja16180:
20170403 11:17:52
O(n^2 log n ) works.. 

Peshal Agarwal:
20161218 16:11:47
getting TLE even though using break in both loops 

its_mrsuit21:
20161128 03:56:02
Help pls! I have tried every test cases i can think of : aaaa, aabb, bbaacc. And still get WA :( 

kishalve pethia:
20151210 20:33:43
can someone share O(n) algo Last edit: 20151211 15:20:45 

poojan :
20150818 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: 20150827 18:01:45 

vikram bhat:
20150707 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: 20150707 09:07:40 

cracked:
20150429 20:57:31
Bruteforce in Java. AC. 
Added by:  adrian 
Date:  20040606 
Time limit:  0.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  ACM Central European Programming Contest, Prague 1998 