Maximum difference of zeros and ones in binary string | Set 2 (O(n) time)
Last Updated :
01 Aug, 2022
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Given a binary string of 0s and 1s. The task is to find the maximum difference between the number of 0s and number of 1s in any sub-string of the given binary string. That is maximize ( number of 0s - number of 1s ) for any sub-string in the given binary string.
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 Programming 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.
// 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>
Output
6
Time Complexity: O(n)
Space complexity: O(n), since string gets copied when we pass it to a function.
