Minimum number of palindromic subsequences to be removed to empty a binary string

Last Updated : 20 Feb, 2023

Given a binary string, count minimum number of subsequences to be removed to make it an empty string.

Examples :

Input: str[] = "10001"
Output: 1
Since the whole string is palindrome, 
we need only one removal.

Input: str[] = "10001001"
Output: 2
We can remove the middle 1 as first 
removal, after first removal string
becomes 1000001 which is a palindrome.

Expected time complexity : O(n)

We strongly recommend that you click here and practice it, before moving on to the solution.

The problem is simple and can be solved easily using below two facts.

If given string is palindrome, we need only one removal.
Else we need two removals. Note that every binary string has all 1's as a subsequence and all 0's as another subsequence. We can remove any of the two subsequences to get a unary string. A unary string is always palindrome.

Implementation:

C++

// C++ program to count minimum palindromic subsequences
// to be removed to make an string empty.
#include <bits/stdc++.h>
using namespace std;

// A function to check if a string str is palindrome
bool isPalindrome(const char *str)
{
    // Start from leftmost and rightmost corners of str
    int l = 0;
    int h = strlen(str) - 1;

    // Keep comparing characters while they are same
    while (h > l)
        if (str[l++] != str[h--])
            return false;

    return true;
}

// Returns count of minimum palindromic subsequences to
// be removed to make string empty
int minRemovals(const char *str)
{
   // If string is empty
   if (str[0] == '\0')
      return 0;

   // If string is palindrome
   if (isPalindrome(str))
      return 1;

   // If string is not palindrome
   return 2;
}

// Driver code to test above
int main()
{
   cout << minRemovals("010010") << endl;
   cout << minRemovals("0100101") << endl;
   return 0;
}

Java

// Java program to count minimum palindromic
// subsequences to be removed to make 
// an string empty.
import java.io.*;

class GFG {
    
// A function to check if a string
// str is palindrome
static boolean isPalindrome(String str)
{
    // Start from leftmost and rightmost
    // corners of str
    int l = 0;
    int h = str.length() - 1;

    // Keep comparing characters 
    // while they are same
    while (h > l)
        if (str.charAt(l++) != str.charAt(h--))
            return false;

    return true;
}

// Returns count of minimum palindromic 
// subsequences to be removed to
// make string empty
static int minRemovals(String str)
{
    // If string is empty
    if (str.charAt(0) == '')
        return 0;

    // If string is palindrome
    if (isPalindrome(str))
        return 1;

    // If string is not palindrome
    return 2;
}

// Driver code to test above
public static void main (String[] args) 
{
    System.out.println (minRemovals("010010"));
    System.out.println (minRemovals("0100101"));
        
}
}

// This code is contributed by vt_m.

Python3

# Python program to count minimum
# palindromic subsequences to 
# be removed to make an string
# empty.

# A function to check if a 
# string str is palindrome
def isPalindrome(str):
    
    # Start from leftmost and 
    # rightmost corners of str
    l = 0
    h = len(str) - 1
    
    # Keep comparing characters 
    # while they are same
    while (h > l):
        if (str[l] != str[h]):
            return 0
        l = l + 1
        h = h - 1
        
    return 1
    
# Returns count of minimum 
# palindromic subsequences to
# be removed to make string
# empty
def minRemovals(str):
    
    #If string is empty
    if (str[0] == ''):
        return 0
    
    #If string is palindrome
    if (isPalindrome(str)):
        return 1
    
    # If string is not palindrome
    return 2
    
# Driver code 
print(minRemovals("010010"))
print(minRemovals("0100101"))

# This code is contributed by Sam007.

// C# program to count minimum palindromic
// subsequences to be removed to make 
// an string empty.
using System;

class GFG
{
    
    // A function to check if a 
    // string str is palindrome
    static bool isPalindrome(String str)
    {
        // Start from leftmost and 
        // rightmost corners of str
        int l = 0;
        int h = str.Length - 1;
    
        // Keep comparing characters 
        // while they are same
        while (h > l)
            if (str[l++] != str[h--])
                return false;
    
        return true;
    }
    
    // Returns count of minimum palindromic 
    // subsequences to be removed to
    // make string empty
    static int minRemovals(String str)
    {
        // If string is empty
        if (str[0] == '')
            return 0;
    
        // If string is palindrome
        if (isPalindrome(str))
            return 1;
    
        // If string is not palindrome
        return 2;
    }
    
    // Driver code to 
    public static void Main () 
    {
        Console.WriteLine(minRemovals("010010"));
        Console.WriteLine(minRemovals("0100101"));
            
    }
    
}

// This code is contributed by Sam007

PHP

<?php
// PHP program to count minimum 
// palindromic subsequences to 
// be removed to make an string empty.

// A function to check if a 
// string str is palindrome
function isPalindrome($str)
{
    // Start from leftmost and
    // rightmost corners of str
    $l = 0;
    $h = strlen($str) - 1;

    // Keep comparing characters
    // while they are same
    while ($h > $l)
        if ($str[$l++] != $str[$h--])
            return false;

    return true;
}

// Returns count of minimum 
// palindromic subsequences 
// to be removed to make
// string empty
function minRemovals($str)
{
// If string is empty
if ($str[0] == '')
    return 0;

// If string is palindrome
if (isPalindrome($str))
    return 1;

// If string is not palindrome
return 2;
}

// Driver Code
echo minRemovals("010010"), "\n";
echo minRemovals("0100101") , "\n";

// This code is contributed by ajit
?>

JavaScript

<script>

    // Javascript program to count 
    // minimum palindromic
    // subsequences to be removed to make 
    // an string empty.
    
    // A function to check if a 
    // string str is palindrome
    function isPalindrome(str)
    {
        // Start from leftmost and 
        // rightmost corners of str
        let l = 0;
        let h = str.length - 1;
      
        // Keep comparing characters 
        // while they are same
        while (h > l)
            if (str[l++] != str[h--])
                return false;
      
        return true;
    }
      
    // Returns count of minimum palindromic 
    // subsequences to be removed to
    // make string empty
    function minRemovals(str)
    {
        // If string is empty
        if (str[0] == '')
            return 0;
      
        // If string is palindrome
        if (isPalindrome(str))
            return 1;
      
        // If string is not palindrome
        return 2;
    }
    
 // Driver Code
 
    document.write(minRemovals("010010") + "</br>");
      document.write(minRemovals("0100101"));
    
</script>

Output

1
2

Time Complexity: O(n)

Auxiliary Space : O(1)

Exercises:

Extend the above solution to count minimum number of subsequences to be removed to make it an empty string.
What is the maximum count for ternary strings

This problem and solution are contributed by Hardik Gulati.