Periodic Binary String: A Binary string is called periodic if it can be written as a repetition of a binary string of smaller or same length. For example, 101010 is a periodic binary string with period 10 as we can get the string by repeatedly appending 10 to itself. In general, the string S with period P means, Si is equal to Si + P.
Problem: Given a binary string S, the task is to find the periodic string with minimum possible period with the following additional conditions
1) The given string S should be a subsequence of the result
2) Length of the result should not be more than twice the length of input string.
Examples:
Input:S = “01”
Output:0101
Explanation:The output string has period as 2 and has given string as subsequence.Input :S = “111”
Output :111
Explanation:The output string has period as 1.Input:S = “110”
Output: 101010
Explanation:The output string has period as 2 and has given string as subsequence. Please note that 110110 is not answer because the period length is more.
Approach:
The main idea depends on two possibilities:
- If the string consists all 1s or all 0s, the answer is the given string S itself having period as 1.
- If the string consists of dissimilar elements, find the string with period 2 and having length as twice the length of given string S
Below is the implementation of the above approach:
// C++ implementation to find the // periodic string with minimum period #include <bits/stdc++.h> using namespace std;
// Function to find the periodic string // with minimum period void findPeriodicString(string S)
{ int l = 2 * S.length();
int count = 0;
for ( int i = 0; i < S.length(); i++) {
if (S[i] == '1' )
count++;
}
// Print the string S if it
// consists of similar elements
if (count == S.length() || count == 0)
cout << S << "\n" ;
// Find the required periodic
// string with period 2
else {
char arr[l];
for ( int i = 0; i < l; i += 2) {
arr[i] = '1' ;
arr[i + 1] = '0' ;
}
for ( int i = 0; i < l; i++)
cout << arr[i];
cout << "\n" ;
}
} // Driver Code int main()
{ string S = "1111001" ;
findPeriodicString(S);
return 0;
} |
// Java implementation to find the // periodic string with minimum period class GFG{
// Function to find the periodic string // with minimum period static void findPeriodicString(String S)
{ int l = 2 * S.length();
int count = 0 ;
for ( int i = 0 ; i < S.length(); i++)
{
if (S.charAt(i) == '1' )
count++;
}
// Print the string S if it
// consists of similar elements
if (count == S.length() || count == 0 )
System.out.println(S);
// Find the required periodic
// string with period 2
else
{
char arr[] = new char [l];
for ( int i = 0 ; i < l; i += 2 )
{
arr[i] = '1' ;
arr[i + 1 ] = '0' ;
}
for ( int i = 0 ; i < l; i++)
System.out.print(arr[i]);
System.out.println();
}
} // Driver Code public static void main (String[] args)
{ String S = "1111001" ;
findPeriodicString(S);
} } // This code is contributed by chitranayal |
# Python3 implementation to find the # periodic with minimum period # Function to find the periodic string # with minimum period def findPeriodicString(S):
l = 2 * len (S)
count = 0
for i in range ( len (S)):
if (S[i] = = '1' ):
count + = 1
# Print the S if it
# consists of similar elements
if (count = = len (S) or count = = 0 ):
print (S)
# Find the required periodic
# with period 2
else :
arr = [ '0' ] * l
for i in range ( 0 , l, 2 ):
arr[i] = '1'
arr[i + 1 ] = '0'
for i in range (l):
print (arr[i],end = "")
# Driver Code if __name__ = = '__main__' :
S = "1111001"
findPeriodicString(S)
# This code is contributed by mohit kumar 29 |
// C# implementation to find the // periodic string with minimum period using System;
class GFG{
// Function to find the periodic string // with minimum period static void findPeriodicString( string S)
{ int l = 2 * S.Length;
int count = 0;
for ( int i = 0; i < S.Length; i++)
{
if (S[i] == '1' )
count++;
}
// Print the string S if it
// consists of similar elements
if (count == S.Length || count == 0)
Console.WriteLine(S);
// Find the required periodic
// string with period 2
else
{
char [] arr = new char [l];
for ( int i = 0; i < l; i += 2)
{
arr[i] = '1' ;
arr[i + 1] = '0' ;
}
for ( int i = 0; i < l; i++)
Console.Write(arr[i]);
Console.WriteLine();
}
} // Driver code public static void Main ()
{ string S = "1111001" ;
findPeriodicString(S);
} } // This code is contributed by sanjoy_62 |
<script> // Javascript implementation to find the // periodic string with minimum period // Function to find the periodic string // with minimum period function findPeriodicString(S)
{ let l = 2 * S.length;
let count = 0;
for (let i = 0; i < S.length; i++)
{
if (S[i] == '1' )
count++;
}
// Print the string S if it
// consists of similar elements
if (count == S.length || count == 0)
document.write(S + "<br>" );
// Find the required periodic
// string with period 2
else
{
let arr = new Array(l);
for (let i = 0; i < l; i += 2)
{
arr[i] = '1' ;
arr[i + 1] = '0' ;
}
for (let i = 0; i < l; i++)
document.write(arr[i]);
document.write( "<br>" );
}
} // Driver Code let S = "1111001" ;
findPeriodicString(S); // This code is contributed by avanitrachhadiya2155 </script> |
10101010101010
Time Complexity: O(N)
Auxiliary Space: O(2*N)