C++ 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. 

C++

// C++ program to find lexicographically
// smallest sequence with rotations.
#include <iostream>
using namespace std;

// Function to compare lexicographically
// two sequence with different starting
// indexes. It returns true if sequence
// beginning with y is lexicographically
// greater.
bool compareSeq(char S[], int x, int y, int n)
{
    for (int 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
int smallestSequence(char S[], int n)
{
    int index = 0;
    for (int 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
void printSmallestSequence(char S[], int n)
{
    int starting_index = smallestSequence(S, n);
    for (int i = 0; i < n; i++)
        cout << S[(starting_index + i) % n];
}

// driver code
int main()
{
    char S[] = "DCACBCAA";
    int n = 8;
    printSmallestSequence(S, n);
    return 0;
}

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!