Javascript Program to FInd Lexicographically smallest rotated sequence | Set 2

Write code to find lexicographic minimum in a circular array, e.g. for the array BCABDADAB, the lexicographic minimum is ABBCABDAD
Input Constraint: 1 < n < 1000 
Examples:

Input:  GEEKSQUIZ
Output: EEKSQUIZG

Input:  GFG
Output: FGG

Input :  CAPABCQ
Output : ABCQCAP

We have discussed a O(n²Logn) solution in Lexicographically minimum string rotation | Set 1. Here we need to find the starting index of minimum rotation and then print the rotation.

1) Initially assume 0 to be current min 
   starting index.
2) Loop through i = 1 to n-1.
   a) For each i compare sequence starting 
      at i with current min starting index
   b) If sequence starting at i is lexicographically 
      smaller, update current min starting 
      index.

Here is pseudo-code for algorithm 

function findIndexForSmallestSequence(S, n):
    result = 0
    for i = 1:n-1
        if (sequence beginning at i < 
               sequence beginning at result)
            result = i
        end if
    end for
    return result

Here is implementation of above algorithm. 

Javascript

<script>
// Javascript program to find lexicographically
// smallest sequence with rotations.

    // Function to compare lexicographically
    // two sequence with different starting
    // indexes. It returns true if sequence
    // beginning with y is lexicographically
    // greater.
    function compareSeq(S,x,y,n)
    {
        for (let i = 0; i < n; i++)
        {
            if (S[x] < S[y])
                return false;
            else if (S[x] > S[y])
                return true;
            x = (x + 1) % n;
            y = (y + 1) % n;
        }
        return true;
    }

    // Function to find starting index
    // of lexicographically smallest sequence
    function smallestSequence(S,n)
    {
        let index = 0;
        for (let i = 1; i < n; i++)

            // if new sequence is smaller
            if (compareSeq(S, index, i, n))

                // change index of current min
                index = i;

        return index;
    }

    // Function to print lexicographically
    // smallest sequence
    function printSmallestSequence(str,n)
    {
        let S = str.split("");
        let starting_index = smallestSequence(S, n);
        for (let i = 0; i < n; i++)
            document.write(S[(starting_index + i) % n]);
    }

    // driver code
    let S = "DCACBCAA";
    let  n = 8;
    printSmallestSequence(S, n);

    // This code is contributed by avanitrachhadiya2155

</script>

Output:

AADCACBC

Time Complexity : O(n^2) 
Auxiliary Space : O(1)
Please refer complete article on Lexicographically smallest rotated sequence | Set 2 for more details!