Statistics

Problem Statement for "RingLex"

Problem Statement

Hero has an infinite periodic string t. You are given the String s that is the period of Hero's string. For example, if s = "abc", Hero's actual string is t = "abcabcabcabc..." Let n be the length of string s. Hero is now going to use the infinite string t to generate a new n-character string by doing the following steps:
  1. He will choose an offset: a non-negative integer x.
  2. He will choose the length of a step: a prime number p that is less than n.
  3. The new string will consists of the first n characters we can read in the string t if we start at the index x and after each character we move p positions to the right.
Formally, Hero's new string will consist of the following characters, in order: t[x], t[x + p], t[x + 2*p], ..., t[x + (n-1)*p]. Find and return the lexicographically smallest string Hero can produce.

Definition

Class:
RingLex
Method:
getmin
Parameters:
String
Returns:
String
Method signature:
String getmin(String s)
(be sure your method is public)

Notes

  • Given two distinct strings of the same length, the lexicographically smaller one is the one that has a smaller character at the first position where they differ.
  • A positive integer p is a prime if it has exactly two distinct divisors: 1 and p. Note that the number 1 is not a prime.

Constraints

  • s will contain between 3 and 50 characters, inclusive.
  • Each character in s will be between 'a' and 'z', inclusive.

Examples

  1. "cba"

    Returns: "abc"

    Hero should choose the offset x=2 and the step p=2. The resulting string is t[2]+t[4]+t[6] = 'a'+'b'+'c' = "abc".

  2. "acb"

    Returns: "abc"

    Here, Hero should choose x=0 and p=2.

  3. "abacaba"

    Returns: "aaaabcb"

  4. "aaabb"

    Returns: "aabab"

  5. "azzzabbb"

    Returns: "abazabaz"

    Note that Hero cannot choose x=0 and p=4, because 4 is not a prime number.

  6. "abbaac"

    Returns: "aaaaaa"

  7. "fsdifyhsoe"

    Returns: "dehifsfsoy"

  8. "ikeff"

    Returns: "efkfi"

  9. "nimkkasvwsrenzkycxfxtlsgypsfadpooefxzbcoejuvpva"

    Returns: "aaefascrkvoeflyskpcostkwmvbopxzviuzpyfnsnjxdgxe"

  10. "ygpoeylfpbnpljvrvipyamyehwqnqrqpmxujjloovaowuxwhms"

    Returns: "aasqfjrueppnophqyujomyrplvxhompvymnljvwygqboiwwexl"

  11. "bxcoksfzkvatxdknlyjyhfixjswn"

    Returns: "adlyisbofvxnjfjncsktkyhxwxkz"

  12. "ufnuxxzrzbmnmgqooketlyhnkoaugzqrcddiuteiojwayyzpvs"

    Returns: "aamuyngymzzgqpqrvocsodukdfeintuultxyexhiznorkjzowb"

  13. "psajlfvgubfaaovlzylntrkdcpwsrtesjwhdizcobzcnfwlqij"

    Returns: "aanhpzgioerajfdwyujbskolwislbpzjdvflzrnfscwclvqctt"

  14. "dwvxhrcbldvgyl"

    Returns: "bcrhxvwdlygvdl"

  15. "busbmborxtl"

    Returns: "bblmtbxsruo"

  16. "smpxohgmgnkeufdxotogbgxpeyanfetcukepzshkljugggekjd"

    Returns: "aczjemgeogaczjemgeogaczjemgeogaczjemgeogaczjemgeog"

  17. "jenpevqgxiepjsrdzjazujllchhbfqmkimwzobiwy"

    Returns: "abdwjkifqhpljzizzsieqgheleuwjormpmxbvcnjy"

  18. "duunfsksrsrtekmqdcyzjeeuhmsrqcozijipfioneeddps"

    Returns: "cdceehsfzuzmdssoefjdsqteukpyuokdmrijniqprrnesi"

  19. "navymmtatbdzqsoemuvnpppsuacbazuxmhec"

    Returns: "aaxeamadsmnpaaxeamadsmnpaaxeamadsmnp"

  20. "legrpunkdmbppweq"

    Returns: "bedqnwppgmlkeupr"

  21. "joparmowzdqyoxytjbbhawdydcprjbxphoohpkwqyuhrqzhnbn"

    Returns: "aakrwwmdqoyywduzchdprqrqyjzobhxxnypbthnjojboobhphp"

  22. "vqnqqlrzjpxiogvliexdzuzosrkrusvojbrzmwzpowkjilefra"

    Returns: "aejowrourzdigxzqqrlkpmbvrsuxloprqvfiwzzjskozevijln"

  23. "digpn"

    Returns: "dgnip"

  24. "uhgxpqnjwjmwaxxmnsnhhlqqrzudltfzotcjtnzxuglsdsmzcn"

    Returns: "aghnljtmdqgzmxnzuqcxllutwnnsrxowuhcdnjxsqhfjzsmzpt"

  25. "kvfajfrmxothowkbjzwuc"

    Returns: "acjoxjkzwofvwktrfubhm"

  26. "jfrimpmyhchzriwkbarxbgfcbceyhjugi"

    Returns: "abcejirphzwabcejirphzwabcejirphzw"

  27. "tbvtrehbbcpxifbxvfbcgkcfqckcotzgku"

    Returns: "bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb"

  28. "jrmbsztsshfroefwsjrxjhguzyupzwweiqurpixiqflduuveoo"

    Returns: "bfjzexumhsuwiurswgwpdjsfhzrlotejpufozoxuqqesrryiiv"

  29. "cudhnefnjhaimuczfskuiduburiswtbrecuykabfcvkdzeztoi"

    Returns: "aacftdrodzscukheewuutidffmyjrnscbzukzbiunbhiiuekvc"

  30. "kuhjzefczzzbfkqdpqzikfob"

    Returns: "bfkkjzqkcqfzbzuzdoefihzp"

  31. "dhthxdjgkjelrlpaxamceroswitdptpcclifkeljytihrcqayb"

    Returns: "aacrsidtclfejthcabhhdgjllaacrsidtclfejthcabhhdgjll"

  32. "fxnxvgzedyyhngyc"

    Returns: "cngdhyxveygfxzyn"

  33. "udmphmeckotr"

    Returns: "cemhpmdurtok"

  34. "spofghfozqvlqfxwwkmfxdyygmdcaszsgovsodkjghcwmbmxrm"

    Returns: "abqsmfzxxsrwgmwoskvpmsofofxdgdkhyjfygoghzmcqdwvcml"

  35. "yfyqgajqkcklznayxqkqoyzwmy"

    Returns: "aazngyzqolyqkfkcyqkyxqmyjw"

  36. "zazcpkhktkydziv"

    Returns: "ackkkdizzphtyzv"

  37. "ypurfmbisgekyrgzvxdhpoamvafyrarxsvkhtqdihersigbhzj"

    Returns: "aahvreifpzgritvryvodzygbryhiedhsafmpxgksmujbshqkxr"

  38. "jxmmyspnaraewkegjccvhhrjvbjtsqdjootgpknfpfycgfieow"

    Returns: "aawejchrvjsdotpnpygiojmypaawejchrvjsdotpnpygiojmyp"

  39. "wwwpzsqme"

    Returns: "eqzwwmspw"

  40. "gepspxnvjiupalyynmkmnuvklhsecdwracgfmzkgipdfodkjmj"

    Returns: "adjugjukmjahkeyeisnddxkrovnckivfmplzglsgpycppmwfnm"

  41. "iqpuoqhimvfvuzwyvijgfullkjduhsjaf"

    Returns: "aipohmfuwvjflkdhjfquqivvzyiguljus"

  42. "lkmfqrmyjfjnhhssqctydteamdcjbprhtnegyiwxgcjwlg"

    Returns: "abnwwmyhcejtijkmnqtchyclrjsddrgggqfsympexlfjht"

  43. "meaearwtvj"

    Returns: "aawvmaawvm"

  44. "baoiojlwhypnvruihoswkifygtydhacwyhsgewzmtgonz"

    Returns: "aasgwggrcowehtouwikwyyniyoizpdzhhjfmnhboslytv"

  45. "jhga"

    Returns: "aghj"

  46. "asdfg"

    Returns: "adgsf"

  47. "dhkajshdkjash"

    Returns: "aajsshhddhkkj"

  48. "acccaccc"

    Returns: "acacacac"

  49. "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz"

    Returns: "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz"

  50. "bcabcbbbcbbcbcbcbcbbcbaaabcbacbaaca"

    Returns: "aaaabccbccaccabbbbbcbbabbcccbbcbbab"

  51. "zzzzzzzzzz"

    Returns: "zzzzzzzzzz"

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