Minimum Lexicographic Rotation Using Suffix Array

Question

    Consider a string of length n (1 <= n <= 100000). 
    Determine its minimum lexicographic rotation. 
    For example, the rotations of the string “alabala         


        

Answer 1

If you are using O(n log n) algorithm (sort by first letter, then by first two letters, then by first four, ...), you can make a little bit modified suffix array.

Don't sort suffixes of string but it's cyclic rotations. It should be really small modification in the algorithm. A then you will get desired result directly.

If you still want to use your method, then just take first index which is between 0 and N.

Answer 2

It seems that you should take first suffix in SA, which index is between 0 and length(S) - 1.

Some explanation: all rotations of S are in the beginning of S' suffixes from positions between 0 and length(S) - 1. Suffix array keeps suffixes in lexicographical order, so you just need to pick the first one which begins from rotation of S.

Answer 3

Thanks all .Both the answer by vkorchagin and usamec is correct for most Test Cases ,but they won't work for the Following Test Case(S="baabaa")

S=baabaa; S'=baabaabaabaa;

Suffix| Suffix  |  Suffixes
Index | Length  |

11      1       a
10      2       aa
7       5       aabaa
4       8       aabaabaa
1       11      aabaabaabaa
8       4       abaa
5       7       abaabaa
2       10      abaabaabaa
9       3       baa
6       6       baabaa
3       9       baabaabaa
0       12      baabaabaabaa

Taking the First Suffix whose Index is between 0 to S.length()-1 does not work for the above test case.If I does so ,then the result is 4 ,but the correct answer is 1.

So I modified the answer ,a bit .

This is what i did or added/modified an extra condition to the above answers ::

(1)I took the First Suffix whose Index is between 0 to S.length()-1 .

Lets say its index is :=ExpectedIdx.

In the above Example ExpectedIdx=4.

(2).Now the ExpectedIdx may or may not be the answer. The reason is the Next suffix in Suffix Array may produce the same answer.

Example ::

Taking the suffix whose starting Index is 4 (ExpectedIdx),aabaabaa.,we get aabaab as Minimum Lexograhic rotated String.

Taking the Next suffix , aabaabaabaa.

We also get aabaab as Minimum Lexograhic rotated String.

But the former one requires the shift of 4 while the latter one requires the shift of 1 .So correct answer is 1 ,not 4.

So i used the concept of Longest Common Prefix (LCP) to check the similarities and Finally got accepted.http://livearchive.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=756

Edit:: This is the Pseudocode -

int ExpectedIdx,ExpectedSuffixNumber,ExpectedSuffixLength;
for(int i=0;i<strlen(str);++i)//str = Length of S'
{
    suffixsize=strlen(str)-SA[i];
    if(suffixsize>(Len/2))//Len/2:=Size of S
    {
        ExpectedIdx=SA[i];
        ExpectedSuffixNumber=i;
        ExpectedSuffixLength=suffixsize;
        break;
    }
}
//Now this ExpectediDx may or may not be the correct answer.

int finalans=ExpectedIdx;//Lets assume initially that ExpectedIdx is a correct/final answer.
for(int i=(ExpectedSuffixNumber+1);i<Len;++i)//Check the Next Suffix 
{
    if(LCP[i]>Len/2)//LCP[i]=Lingest common prefix of adjacent prefixes in a suffix Array.
    {
        if(SA[i]>finalans)
        {
            finalans=SA[i];
        }
    }
    else
        break;
}