Maximum difference of zeros and ones in binary string | Set 2 (O(n) time)

Given a binary string of 0s and 1s. The task is to find the length of substring which is having a maximum difference of number of 0s and number of 1s (number of 0s – number of 1s). In case of all 1s print -1.

Examples:

Input : S = "11000010001"
Output : 6
From index 2 to index 9, there are 7
0s and 1 1s, so number of 0s - number
of 1s is 6.

Input : S = "1111"
Output : -1



We have discussed Dynamic Programing approach in below post :
Maximum difference of zeros and ones in binary string | Set 1.

In the post we seen an efficient method that work in O(n) time and in O(1) extra space. Idea behind that if we convert all zeros into 1 and all ones into -1.now our problem reduces to find out the maximum sum sub_array Using Kadane’s Algorithm.

Input : S = "11000010001"
     After converting '0' into 1 and
     '1' into -1 our S Look Like
      S  = -1 -1 1 1 1 1 -1 1 1 1 -1
 Now we have to find out Maximum Sum sub_array 
 that is  : 6 is that case 
    
Output : 6

Below is the implementation of above idea.

C++

// CPP Program to find the length of
// substring with maximum difference of
// zeros and ones in binary string.
#include <iostream>
using namespace std;
  
// Returns the length of substring with
// maximum difference of zeroes and ones 
// in binary string
int findLength(string str, int n)
{
    int current_sum = 0;
    int max_sum = 0;
  
    // traverse a binary string from left 
    // to right
    for (int i = 0; i < n; i++) {
  
        // add current value to the current_sum
        // according to the Character
        // if it's '0' add 1 else -1
        current_sum += (str[i] == '0' ? 1 : -1);
  
        if (current_sum < 0)
            current_sum = 0;
  
        // update maximum sum
        max_sum = max(current_sum, max_sum);
    }
  
    // return -1 if string does not contain
    // any zero that means all ones 
    // otherwise max_sum
    return max_sum == 0 ? -1 : max_sum;
}
  
// Driven Program
int main()
{
    string s = "11000010001";
    int n = 11;
    cout << findLength(s, n) << endl;
    return 0;
}

Java

// Java Program to find the length of
// substring with maximum difference of
// zeroes and ones in binary string.
import java.util.*;
import java.lang.*;
import java.io.*;
  
class GFG {
  
    // Find the length of substring with maximum
    // difference of zeros and ones in binary
    // string
    public static int findLength(String str, int n)
    {
  
        int current_sum = 0;
        int max_sum = 0;
  
        // traverse a binary string from left to right
        for (int i = 0; i < n; i++) {
  
            // add current value to the current_sum
            // according to the Character
            // if it's '0' add 1 else -1
            current_sum += (str.charAt(i) == '0' ? 1 : -1);
  
            if (current_sum < 0)
                current_sum = 0;
  
            // update maxium sum
            max_sum = Math.max(current_sum, max_sum);
        }
        // return -1 if string does not contain any zero
        // that means string contains all ones otherwise max_sum
        return max_sum == 0 ? -1 : max_sum;
    }
  
    public static void main(String[] args)
    {
        String str = "11000010001";
        int n = str.length();
  
        System.out.println(findLength(str, n));
    }
}

Python3

# Python Program to find the length of
# substring with maximum difference of
# zeros and ones in binary string.
  
# Returns the length of substring with
# maximum difference of zeroes and ones 
# in binary string
def findLength(string, n):
    current_sum = 0
    max_sum = 0
  
    # traverse a binary string from left 
    # to right
    for i in range(n):
  
        # add current value to the current_sum
        # according to the Character
        # if it's '0' add 1 else -1
        current_sum += (1 if string[i] == '0' else -1)
  
        if current_sum < 0:
            current_sum = 0
  
        # update maximum sum
        max_sum = max(current_sum, max_sum)
  
    # return -1 if string does not contain
    # any zero that means all ones 
    # otherwise max_sum
    return max_sum if max_sum else 0
  
# Driven Program
s = "11000010001"
n = 11
print(findLength(s, n))
  
# This code is contributed by Ansu Kumari.

PHP

<?php
// PHP Program to find the length of
// substring with maximum difference of
// zeros and ones in binary string.
  
// Returns the length of substring with
// maximum difference of zeroes and ones 
// in binary string
function findLength($str, $n)
{
    $current_sum = 0;
    $max_sum = 0;
  
    // traverse a binary string
    // from left to right
    for ($i = 0; $i < $n; $i++) 
    {
  
        // add current value to the current_sum
        // according to the Character
        // if it's '0' add 1 else -1
        $current_sum += ($str[$i] == '0' ? 1 : -1);
  
        if ($current_sum < 0)
            $current_sum = 0;
  
        // update maximum sum
        $max_sum = max($current_sum, $max_sum);
    }
  
    // return -1 if string does not contain
    // any zero that means all ones 
    // otherwise max_sum
    return $max_sum == 0 ? -1 : $max_sum;
}
  
    // Driver Code
    $s = "11000010001";
    $n = 11;
    echo findLength($s, $n),"\n";
      
// This code is contributed by aj_36
?>


Output:

6 

Time Complexity : O(n)
Space complexity : O(1)



My Personal Notes arrow_drop_up


Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : jit_t