Largest sub-string of a binary string divisible by 2

Last Updated : 28 Oct, 2022

Given binary string str of length N, the task is to find the longest sub-string divisible by 2. If no such sub-string exists then print -1.

Examples:

Input: str = "11100011"
Output: 111000
Largest sub-string divisible by 2 is "111000".
Input: str = "1111"
Output: -1
There is no sub-string of the given string
which is divisible by 2.

Naive approach: A naive approach will be to generate all such sub-strings and check if they are divisible by 2. The time complexity of this approach will be O(N³).

Better approach: A straightforward approach will be to remove characters from the end of the string while the last character is 1. The moment a 0 is encountered, the current string will be divisible by 2 as it ends at a 0.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the largest
// substring divisible by 2
string largestSubStr(string s)
{
    // While the last character of
    // the string is '1', pop it
    while (s.size() and s[s.size() - 1] == '1')
        s.pop_back();

    // If the original string had no '0'
    if (s.size() == 0)
        return "-1";
    else
        return s;
}

// Driver code
int main()
{
    string s = "11001";

    cout << largestSubStr(s);

    return 0;
}

Java

// Java implementation of the approach 
class GFG
{
    
    // Function to return the largest 
    // substring divisible by 2 
    static String largestSubStr(String s) 
    { 
        // While the last character of 
        // the string is '1', pop it 
        while (s.length() != 0 && 
               s.charAt(s.length() - 1) == '1') 
            s = s.substring(0, s.length() - 1); 
    
        // If the original string had no '0' 
        if (s.length() == 0) 
            return "-1"; 
        else
            return s; 
    } 
    
    // Driver code 
    public static void main (String[] args)
    { 
        String s = "11001"; 
    
        System.out.println(largestSubStr(s)); 
    } 
}

// This code is contributed by AnkitRai01

Python3

# Python3 implementation of the approach 

# Function to return the largest 
# substring divisible by 2 
def largestSubStr(s) : 

    # While the last character of 
    # the string is '1', pop it 
    while (len(s) and s[len(s) - 1] == '1') :
        s = s[:len(s) - 1]; 

    # If the original string had no '0' 
    if (len(s) == 0) :
        return "-1"; 
    else :
        return s; 

# Driver code 
if __name__ == "__main__" :

    s = "11001"; 

    print(largestSubStr(s)); 

# This code is contributed by AnkitRai01

// C# implementation of the approach 
using System;

class GFG 
{ 
    
    // Function to return the largest 
    // substring divisible by 2 
    static string largestSubStr(string s) 
    { 
        // While the last character of 
        // the string is '1', pop it 
        while (s.Length != 0 && 
               s[s.Length - 1] == '1') 
            s = s.Substring(0, s.Length - 1); 
    
        // If the original string had no '0' 
        if (s.Length == 0) 
            return "-1"; 
        else
            return s; 
    } 
    
    // Driver code 
    public static void Main () 
    { 
        string s = "11001"; 
    
        Console.WriteLine(largestSubStr(s)); 
    } 
} 

// This code is contributed by AnkitRai01

JavaScript

<script>

// Javascript implementation of the approach

// Function to return the largest
// substring divisible by 2
function largestSubStr(s)
{
    // While the last character of
    // the string is '1', pop it
    while (s.length && s[s.length - 1] == '1')
        s = s.substring(0,s.length-1);;

    // If the original string had no '0'
    if (s.length == 0)
        return "-1";
    else
        return s;
}

// Driver code
var s = "11001";
document.write( largestSubStr(s));

</script>

Output:

Time Complexity: O(n), where n is the length of the string s
Auxiliary Space: O(1)

Number of sub-strings in a given binary string divisible by 2

DivyanshuShekhar1

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