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;
} |
Java
// Java program to find lexicographically // smallest sequence with rotations. import java.util.*;
import java.lang.*;
import java.io.*;
/* Name of the class */ class LexoSmallest {
// Function to compare lexicographically
// two sequence with different starting
// indexes. It returns true if sequence
// beginning with y is lexicographically
// greater.
static boolean 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
static 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
static void printSmallestSequence(String str, int n)
{
char [] S = str.toCharArray();
int starting_index = smallestSequence(S, n);
for ( int i = 0 ; i < n; i++)
System.out.print(S[(starting_index + i) % n]);
}
// driver code
public static void main(String[] args)
{
String S = "DCACBCAA" ;
int n = 8 ;
printSmallestSequence(S, n);
}
} // This code is contributed by Mr Somesh Awasthi |
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 |
C#
// C# program to find lexicographically // smallest sequence with rotations. using System;
class LexoSmallest {
// Function to compare lexicographically
// two sequence with different starting
// indexes. It returns true if sequence
// beginning with y is lexicographically
// greater.
static bool compareSeq( string 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
static int smallestSequence( string 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
static void printSmallestSequence( string str, int n)
{
// char[] S=str.toCharArray();
int starting_index = smallestSequence(str, n);
for ( int i = 0; i < n; i++)
Console.Write(str[(starting_index + i) % n]);
}
// driver code
public static void Main()
{
string S = "DCACBCAA" ;
int n = 8;
printSmallestSequence(S, n);
}
} // This code is contributed by vt_m. |
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. ?> |
Javascript
<script> // Javascript 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 (let 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)
{
let index = 0;
for (let 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(str,n)
{
let S = str.split( "" );
let starting_index = smallestSequence(S, n);
for (let i = 0; i < n; i++)
document.write(S[(starting_index + i) % n]);
}
// driver code
let S = "DCACBCAA" ;
let n = 8;
printSmallestSequence(S, n);
// This code is contributed by avanitrachhadiya2155
</script> |
Output
AADCACBC
Time Complexity : O(n^2)
Auxiliary Space : O(1)