FINDSR - Find String Roots

no tags 

In mathematics, the N-th root of a number M, is a number K such that KN = M , i.e. KKK . . . K = M where K is multiplied N times.
We can translate this into strings. In string notation, the yuxtaposition is concatenation instead of multiplication. So, the N-th root of a string S is another string T such that TN = S, where T N = T T T . . . T is the string T concatenated N times. For instance, if S = “abcabcabcabc”, for N = 2 the string T = “abcabc” is the N-th root of S, while for N = 4 its N-th root is T = “abc”. Note that for N = 1 any string S is the N-th root
of S itself.
Given a string S you have to find the maximum N such that the N-th root of S exists. In the above example the answer would be 4, because there is no N-th root of S = “abcabcabcabc” for N > 4.


The input contains several test cases, each one described in a single line. The line contains
a non-empty string S of at most 105 characters, entirely formed of digits and lowercase
letters. The last line of the input contains a single asterisk (“*”) and should not be
processed as a test case.


For each test case output a single line with the greatest integer N such that there exists
a string T that concatenated N times is equal to S.



Output: 4

hide comments
nadstratosfer: 2017-09-13 05:38:52

Pleased to find out that O(n) passes comfortably in Python. Comments were helpful - learn a new bit about KMP instead of wasting time on breaking open doors.

vijay kumar paliwal: 2017-07-25 14:11:11

Same as PERIOD !! Indeed PERIOD is generalization of this..

up79: 2017-06-25 11:27:34

afetr 3 WA . finally AC .

sifat_15: 2017-01-10 08:41:24


Last edit: 2017-01-16 19:20:06
teja349: 2016-12-28 18:57:18

is the complexity N logN??

kira28: 2016-12-27 11:50:22

Almost the same as xD xD ; easy KMP
AC in one go!!!!

sas1905: 2016-12-22 20:54:16

3 Sigsegv for taking a small array..:(..Simple adhoc.

siddharth_0196: 2016-10-29 11:05:12

Simple adhoc!

sieunhanbom04: 2016-08-19 10:45:27

Learn something new about KMP. thank you, author

Liquid_Science: 2016-01-23 17:14:43

after 2 wa ,learnt something ,worth it.

Added by:Pablo Ariel Heiber
Time limit:0.613s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 VB.NET
Resource:FCEyN UBA ICPC Selection 2009