PHP Program to Find Lexicographically smallest rotated sequence | Set 2
Last Updated :
22 Jul, 2024
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Write code to find the 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 the pseudo-code for the 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
// 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, $n);
// This code is contributed by Ajit.
?>
<?php// PHP program to find lexicographically// smallest sequence with rotations.// Function to compare lexicographically// two sequence with different starting// indexes. It returns true if sequence// beginning with y is lexicographically// greater.function compareSeq($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) % $n; } return true;}// Function to find starting index// of lexicographically smallest// sequencefunction smallestSequence($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 $index;}// Function to print lexicographically// smallest sequencefunction printSmallestSequence($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.?>Output
AADCACBC
Complexity Analysis:
- Time Complexity : O(n^2)
- Auxiliary Space : O(1)
Please refer complete article on Lexicographically smallest rotated sequence | Set 2 for more details!
