Periodic Binary String With Minimum Period and a Given Binary String as Subsequence.
Last Updated :
04 Jan, 2023
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++
// 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
// 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
# 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#
// 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
JavaScript
<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>
Time Complexity: O(N)
Auxiliary Space: O(2*N)