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.
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 stringint 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 Programint 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 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)); }} |
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 stringdef 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 Programs = "11000010001"n = 11print(findLength(s, n))# This code is contributed by Ansu Kumari. |
C#
// 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 Codepublic 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// 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 stringfunction 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?> |
Javascript
<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.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
