Diferencia máxima de ceros y unos en string binaria | Conjunto 2 (tiempo O(n))

Dada una string binaria de 0s y 1s. La tarea es encontrar la diferencia máxima entre el número de 0 y el número de 1 en cualquier substring de la string binaria dada. Eso es maximizar (número de 0 – número de 1) para cualquier substring en la string binaria dada. 

Ejemplos: 

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

Hemos discutido el enfoque de programación dinámica en la siguiente publicación: 

Diferencia máxima de ceros y unos en string binaria | conjunto 1 . 
En la publicación vimos un método eficiente que funciona en tiempo O(n) y en espacio adicional O(1). Idea detrás de eso si convertimos todos los ceros en 1 y todos los unos en -1. Ahora nuestro problema se reduce a encontrar la suma máxima de sub_array usando el algoritmo de Kadane . 

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

A continuación se muestra la implementación de la idea anterior.  

// 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 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 maximum 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));
    }
}

# 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.

// C# Program to find the length of
// substring with maximum difference of
// zeroes and ones in binary string.
using System;
 
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[i] == '0' ? 1 : -1);
 
        if (current_sum < 0)
        {
            current_sum = 0;
        }
 
        // update maximum 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;
}
 
// Driver Code
public static void Main(string[] args)
{
    string str = "11000010001";
    int n = str.Length;
 
    Console.WriteLine(findLength(str, n));
}
}
 
// This code is contributed by Shrikant13

<?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
?>

<script>
 
// JavaScript program to find the length of
// substring with maximum difference of
// zeroes and ones in binary string.
 
// Find the length of substring with
// maximum difference of zeros and
// ones in binary string
function findLength(str, n)
{
   
    let current_sum = 0;
    let max_sum = 0;
   
    // traverse a binary string
    // from left to right
    for (let 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 = 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;
}
 
// Driver Code
 
    let str = "11000010001";
    let n = str.length;
   
    document.write(findLength(str, n));
       
      // This code is contributed by chinmoy1997pal.
</script>

Producción: 

6 

Complejidad de tiempo: O(n) 
Complejidad de espacio: O(n), ya que la string se copia cuando la pasamos a una función.