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Php 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 


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 

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. 


// PHP 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, $n)
    for($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)
    $index = 0;
    for ( $i = 1; $i < $n; $i++)
        // if new sequence is smaller
        if (compareSeq($S, $index, $i, $n))
            // change index of current min
            $index = $i;
    return $index;
// Function to print lexicographically
// smallest sequence
function printSmallestSequence($S, $n)
    $starting_index = smallestSequence($S, $n);
    for ($i = 0; $i < $n; $i++)
        echo $S[($starting_index + $i) % $n];
    // Driver Code
    $S= "DCACBCAA";
    $n = 8;
    printSmallestSequence($S, $n);
// This code is contributed by Ajit.



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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Last Updated : 10 Jan, 2022
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