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.
PHP
<?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. ?> |
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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