Python3 Program to Find Lexicographically smallest rotated sequence | Set 2

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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.

Python 3

# Python 3 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. 
import copy 
  
  
def printSmallestSequence(s): 
    m = copy.copy(s) 
    for i in range(len(s) - 1): 
  
        if m > s[i:] + s[:i]: 
            m = s[i:] + s[:i] 
  
    return m 
  
#Driver Code 
if __name__ == '__main__': 
  
    st = 'DCACBCAA'
    print(printSmallestSequence(st)) 
  
  
# This code is contributed by Koushik Reddy B 

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!

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