Count Palindromic Substrings in a Binary String

Last Updated : 11 Nov, 2023

Given a binary string S i.e. which consists only of 0's and 1's. Calculate the number of substrings of S which are palindromes. String S contains at most two 1's.

Examples:

Input: S = "011"
Output: 4
Explanation: "0", "1", "1" and "11" are the palindromic substrings.

Input: S = "0"
Output: 1
Explanation: "0" is the only palindromic substring.

Approach: This can be solved with the following idea:

Using some mathematical observation can find out number of possible palindrome substring of size 2. Rest of all size, we can find out by reducing indexes from left and right side. For more clarification, see steps.

Below are the steps to solve the problem:

Iterate in for loop from 0 to N - 1.
Checking whether adjacent characters are equal or not and adding in the count.
Again iterate in the loop, and look for the following conditions:
- Start reducing the index from left and if s[i - 1]== '0', we can decrement l by 1.
- After that, iterate from right and if s[i + 1] == '0', we can increment r by 1.
Update ans += min(abs(l - i), abs(r - i)).
- And if S[ i - 1] == '1', we can increment total count of palindrome by 1.

Below is the implementation of the code:

C++

// C++ code for the above approach:
#include <bits/stdc++.h>
#include <iostream>
using namespace std;

// Function to count number of plaindrome
long long countPalindrome(string S)
{

    // Size of string
    int N = S.size();
    long long ans = 0, x = 0;

    for (int i = 0; i < N; i++) {
        x++;

        // If adjacent character are same
        if (i + 1 < N && S[i] == S[i + 1])
            continue;

        // Count total number of possibility
        ans += (x * (x + 1)) / 2;
        x = 0;
    }

    int last = -1;
    for (int i = 0; i < N; i++) {
        if (S[i] == '1') {
            int l = i;
            int r = i;

            // Start iterating from right side
            while (l - 1 >= 0 && S[l - 1] == '0')
                l--;

            // Start iterating from left side
            while (r + 1 < N && S[r + 1] == '0')
                r++;
            ans += min(abs(l - i), abs(r - i));
            if (last == -1) {
                last = i;
            }
            else {

                // Add the min value
                ans += min(last, N - i - 1);
                if (S[i - 1] != '1') {
                    ans++;
                }
            }
        }
    }

    // Return the total count of
    // palindromic substrings
    return ans;
}

// Driver code
int main()
{

    string s = "01110";

    // Function call
    cout << countPalindrome(s);

    return 0;
}

Java

// Code contributed by Flutterfly
import java.util.*;

class Main {
    public static long countPalindrome(String S) {
      // Size of string
        int N = S.length();
        long ans = 0, x = 0;
        for (int i = 0; i < N; i++) {
            x++;
          // If adjacent character are same
            if (i + 1 < N && S.charAt(i) == S.charAt(i + 1))
                continue;
          // Count total number of possibility
            ans += (x * (x + 1)) / 2;
            x = 0;
        }
        int last = -1;
        for (int i = 0; i < N; i++) {
            if (S.charAt(i) == '1') {
                int l = i;
                int r = i;
              // Start iterating from right side
                while (l - 1 >= 0 && S.charAt(l - 1) == '0')
                    l--;
              // Start iterating from left side
                while (r + 1 < N && S.charAt(r + 1) == '0')
                    r++;
                ans += Math.min(Math.abs(l - i), Math.abs(r - i));
                if (last == -1) {
                    last = i;
                } else {
                  // Add the min value
                    ans += Math.min(last, N - i - 1);
                    if (S.charAt(i - 1) != '1') {
                        ans++;
                    }
                }
            }
        }
      // Return the total count of
      // palindromic substrings
        return ans;
    }
// Driver code
    public static void main(String[] args) {
        String s = "01110";
      //Function call
        System.out.println(countPalindrome(s));
    }
}

Python

# code contributed by Flutterfly

# Function to count number of palindrome
def countPalindrome(S):
  #Size of string
    N = len(S)
    ans = 0
    x = 0
    for i in range(N):
        x += 1
        #If adjacent character are same
        if i + 1 < N and S[i] == S[i + 1]:
            continue
        #Count total number of possibility
        ans += (x * (x + 1)) // 2
        x = 0
    last = -1
    for i in range(N):
        if S[i] == '1':
            l = i
            r = i
            #Start iterating from right side
            while l - 1 >= 0 and S[l - 1] == '0':
                l -= 1
            #Start iterating from left side
            while r + 1 < N and S[r + 1] == '0':
                r += 1
            ans += min(abs(l - i), abs(r - i))
            if last == -1:
                last = i
            else:
            #Add the min value
                ans += min(last, N - i - 1)
                if S[i - 1] != '1':
                    ans += 1
    #Return the total count of palindromic substrings
    return ans
#Driver code
s = "01110"
#Function call
print(countPalindrome(s))

// Code contributed by Flutterfly
using System;

public class Program
{
  // Function to count number of plaindrome
    public static long CountPalindrome(string S)
    {
          // Size of string
        int N = S.Length;
        long ans = 0, x = 0;
        
        for (int i = 0; i < N; i++)
        {
            x++;
            // If adjacent character are same
            if (i + 1 < N && S[i] == S[i + 1])
                continue;
            // Count total number of possibility
            ans += (x * (x + 1)) / 2;
            x = 0;
        }
        
        int last = -1;
        
        for (int i = 0; i < N; i++)
        {
            if (S[i] == '1')
            {
                int l = i;
                int r = i;

                // Start iterating from right side
                while (l - 1 >= 0 && S[l - 1] == '0')
                    l--;
                // Start iterating from left side
                while (r + 1 < N && S[r + 1] == '0')
                    r++;
                    
                ans += Math.Min(Math.Abs(l - i), Math.Abs(r - i));
                
                if (last == -1)
                {
                    last = i;
                }
                else
                {
                    // Add the min value
                    ans += Math.Min(last, N - i - 1);
                    
                    if (S[i - 1] != '1')
                    {
                        ans++;
                    }
                }
            }
        }
        // Return the total count of
        // palindromic substrings
        return ans;
    }
//Driver code
    public static void Main()
    {
        string s = "01110";
      
    // Function call
        Console.WriteLine(CountPalindrome(s));
    }
}

JavaScript

// JavaScript code for the above approach:

// Function to count number of plaindrome
function countPalindrome(S) {
    
    // Size of string
    const N = S.length;
    let ans = 0;
    let x = 0;

    for (let i = 0; i < N; i++) {
        x++;

        // If adjacent character are same
        if (i + 1 < N && S[i] === S[i + 1])
            continue;
        
        // Count total number of possibility
        ans += (x * (x + 1)) / 2;
        x = 0;
    }

    let last = -1;
    for (let i = 0; i < N; i++) {
        if (S[i] === '1') {
            let l = i;
            let r = i;

            // Start iterating from right side
            while (l - 1 >= 0 && S[l - 1] === '0')
                l--;

            // Start iterating from left side
            while (r + 1 < N && S[r + 1] === '0')
                r++;

            ans += Math.min(Math.abs(l - i), Math.abs(r - i));

            if (last === -1) {
                last = i;
            } else {
                
                // Add the min value
                ans += Math.min(last, N - i - 1);
                if (S[i - 1] !== '1') {
                    ans++;
                }
            }
        }
    }
    // Return the total count of
    // palindromic substrings
    return ans;
}

// Driver code
const S = "01110";

// Function call
console.log(countPalindrome(S));

Output

Time Complexity: O(N)
Auxiliary Space: O(1)

Count Palindromic Substrings in a Binary String

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