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Length of the longest substring with equal 1s and 0s

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  • Difficulty Level : Medium
  • Last Updated : 20 Jul, 2022

Given a binary string. We need to find the length of the longest balanced substring. A substring is balanced if it contains an equal number of 0 and 1.

Examples:  

Input : input = 110101010
Output : Length of longest balanced
         sub string = 8

Input : input = 0000
Output : Length of longest balanced
         sub string = 0

A simple solution is to use two nested loops to generate every substring. And a third loop to count number of 0s and 1s in current substring. Time complexity of this would be O(n3)

Below is the implementation of the above approach:  

C++




// C++ program to find the length of
// the longest balanced substring
#include<bits/stdc++.h>
using namespace std;
 
// Function to check if a string contains
// equal number of one and zeros or not
bool isValid(string p)
{
    int n = p.length();
    int c1 = 0, c0 = 0;
     
    for(int i =0; i < n; i++)
    {
        if(p[i] == '0')
            c0++;
        if(p[i] == '1')
            c1++;
    }
     
    return (c0 == c1) ? true : false;
}
 
// Function to find the length of
// the longest balanced substring
int longestSub(string s)
{
    int max_len = 0;
    int n = s.length();
     
    for(int i = 0; i < n; i++)
    {
        for(int j = i; j < n; j++)
        {
            if(isValid(s.substr(i, j - i + 1)) && max_len < j - i + 1)
                max_len = j - i + 1;
        }
         
    }
    return max_len;
     
}
 
// Driver code
int main()
{
    string s = "101001000";
     
    // Function call
    cout << longestSub(s);
     
    return 0;
}

Java




// Java program to find the length of 
// the longest balanced substring
import java.io.*;
import java.util.*;
class GFG
{
 
  // Function to check if a string contains
  // equal number of one and zeros or not
  public static boolean isValid(String p)
  {
    int n = p.length();
    int c1 = 0, c0 = 0;
    for (int i = 0; i < n; i++)
    {
      if(p.charAt(i) == '0')
      {
        c0++;
      }
      if(p.charAt(i) == '1')
      {
        c1++;
      }
    }
    if(c0 == c1)
    {
      return true;
    }
    else
    {
      return false;
    }
  }
  // Function to find the length of 
  // the longest balanced substring
  public static int longestSub(String s)
  {
    int max_len = 0;
    int n = s.length();
    for(int i = 0; i < n; i++)
    {
      for(int j = i; j < n; j++)
      {
        if(isValid(s.substring(i, j + 1)) && max_len < j - i + 1)
        {
          max_len = j - i + 1;
        }
      }
    }
    return max_len;
  }
 
  // Driver code
  public static void main (String[] args)
  {
    String s = "101001000";
 
    // Function call
    System.out.println(longestSub(s));
  }
}
 
//  This code is contributed by avanitrachhadiya2155

Python3




# Python3 program to find the length of
# the longest balanced substring
 
# Function to check if a contains
# equal number of one and zeros or not
def isValid(p):
 
    n = len(p)
    c1 = 0
    c0 = 0
 
    for i in range(n):
        if (p[i] == '0'):
            c0 += 1
        if (p[i] == '1'):
            c1 += 1
 
    if (c0 == c1):
        return True
    else:
        return False
 
# Function to find the length of
# the longest balanced substring
def longestSub(s):
     
    max_len = 0
    n = len(s)
 
    for i in range(n):
        for j in range(i, n):
            if (isValid(s[i : j - i + 1]) and
                    max_len < j - i + 1):
                max_len = j - i + 1
 
    return max_len
 
# Driver code
if __name__ == '__main__':
     
    s = "101001000"
 
    # Function call
    print(longestSub(s))
 
# This code is contributed by mohit kumar 29

C#




// C# program to find the length of 
// the longest balanced substring
using System;
 
class GFG{
     
// Function to check if a string contains
// equal number of one and zeros or not
static bool isValid(string p)
{
    int n = p.Length;
    int c1 = 0, c0 = 0;
     
    for(int i = 0; i < n; i++)
    {
        if (p[i] == '0')
        {
            c0++;
        }
        if (p[i] == '1')
        {
            c1++;
        }
    }
    if (c0 == c1)
    {
        return true;
    }
    else
    {
        return false;
    }
}
 
// Function to find the length of 
// the longest balanced substring
public static int longestSub(string s)
{
    int max_len = 0;
    int n = s.Length;
     
    for(int i = 0; i < n; i++)
    {
        for(int j = i; j < n; j++)
        {
            if (isValid(s.Substring(i, j - i + 1)) &&
                             max_len < j - i + 1)
            {
                max_len = j - i + 1;
            }
        }
    }
    return max_len;
}
 
// Driver code
static public void Main()
{
    string s = "101001000";
     
    // Function call
    Console.WriteLine(longestSub(s));
}
}
 
// This code is contributed by rag2127

Javascript




<script>
 
// Javascript program to find the length of
// the longest balanced substring
 
// Function to check if a string contains
// equal number of one and zeros or not
function isValid(p)
{
    var n = p.length;
    var c1 = 0, c0 = 0;
     
    for(var i =0; i < n; i++)
    {
        if(p[i] == '0')
            c0++;
        if(p[i] == '1')
            c1++;
    }
     
    return (c0 == c1) ? true : false;
}
 
// Function to find the length of
// the longest balanced substring
function longestSub(s)
{
    var max_len = 0;
    var n = s.length;
     
    for(var i = 0; i < n; i++)
    {
        for(var j = i; j < n; j++)
        {
            if(isValid(s.substr(i, j - i + 1)) && max_len < j - i + 1)
                max_len = j - i + 1;
        }
         
    }
    return max_len;
     
}
 
// Driver code
var s = "101001000";
 
// Function call
document.write( longestSub(s));
 
</script>

Output

6

An efficient solution is to use hashing. 

  1. Traverse string and keep track of counts of 1s and 0s as count_1 and count_0 respectively. 
  2. See if current difference between two counts has appeared before (We use hashing to store all differences and first index where a difference appears). If yes, then substring from previous appearance and current index has same number of 0s and 1s.

Below is the implementation of above approach.

C++




// C++ for finding length of longest balanced
// substring
#include<bits/stdc++.h>
using namespace std;
 
// Returns length of the longest substring
// with equal number of zeros and ones.
int stringLen(string str)
{
    // Create a map to store differences
    // between counts of 1s and 0s.
    map<int, int> m;
     
    // Initially difference is 0.
    m[0] = -1;  
     
    int count_0 = 0, count_1 = 0;
    int res = 0;
    for (int i=0; i<str.size(); i++)
    {
        // Keeping track of counts of
        // 0s and 1s.
        if (str[i] == '0')
            count_0++;
        else
            count_1++;
             
        // If difference between current counts
        // already exists, then substring between
        // previous and current index has same
        // no. of 0s and 1s. Update result if this
        // substring is more than current result.
        if (m.find(count_1 - count_0) != m.end())
            res = max(res, i - m[count_1 - count_0]);
             
        // If current difference is seen first time.       
        else
            m[count_1 - count_0] = i;
    }
 
    return res;
}
 
// driver function
int main()
{
    string str = "101001000";
    cout << "Length of longest balanced"
            " sub string = ";
    cout << stringLen(str);
    return 0;
}

Java




// Java Code for finding the length of
// the longest balanced substring
 
import java.io.*;
import java.util.*;
 
public class MAX_LEN_0_1 {
    public static void main(String args[])throws IOException
    {
        String str = "101001000";
             
    // Create a map to store differences
    //between counts of 1s and 0s.
    HashMap<Integer,Integer> map = new HashMap<Integer,Integer>();
     
    // Initially difference is 0;
            map. put(0, -1);
            int res =0;
            int count_0 = 0, count_1 = 0;
            for(int i=0; i<str.length();i++)
            {
                // Keep track of count of 0s and 1s
                if(str.charAt(i)=='0')
                    count_0++;
                else
                    count_1++;
 
        // If difference between current counts
        // already exists, then substring between
        // previous and current index has same
        // no. of 0s and 1s. Update result if this
        // substring is more than current result.
 
                if(map.containsKey(count_1-count_0))
                    res = Math.max(res, (i - map.get(count_1-count_0)));
     
        // If the current difference is seen first time.
                else
                    map.put(count_1-count_0,i);
                 
            }
             
            System.out.println("Length of longest balanced sub string = "+res);
    }
}

Python3




# Python3 code for finding length of
# longest balanced substring
 
# Returns length of the longest substring
# with equal number of zeros and ones.
def stringLen( str ):
 
    # Create a python dictionary to store
    # differences between counts of 1s and 0s.
    m = dict()
     
    # Initially difference is 0.
    m[0] = -1
     
    count_0 = 0
    count_1 = 0
    res = 0
    for i in range(len(str)):
         
        # Keeping track of counts of
        # 0s and 1s.
        if str[i] == '0':
            count_0 += 1
        else:
            count_1 += 1
             
        # If difference between current
        # counts already exists, then
        # substring between previous and
        # current index has same no. of
        # 0s and 1s. Update result if
        # this substring is more than
        # current result.
        if m.get(count_1 - count_0)!=None:
            res = max(res, i - m[count_1 - count_0])
         
        # If current difference is
        # seen first time.
        else:
            m[count_1 - count_0] = i
    return res
 
# driver code
str = "101001000"
print("Length of longest balanced"
     " sub string = ",stringLen(str))
 
# This code is contributed by "Sharad_Bhardwaj"

C#




// C# Code for finding the length of
// the longest balanced substring
using System;
using System.Collections.Generic;
 
class GFG
{
public static void Main(string[] args)
{
    string str = "101001000";
 
    // Create a map to store differences
    //between counts of 1s and 0s.
    Dictionary<int,
               int> map = new Dictionary<int,
                                         int>();
     
    // Initially difference is 0;
    map[0] = -1;
    int res = 0;
    int count_0 = 0, count_1 = 0;
    for (int i = 0; i < str.Length;i++)
    {
        // Keep track of count of 0s and 1s
        if (str[i] == '0')
        {
            count_0++;
        }
        else
        {
            count_1++;
        }
 
        // If difference between current counts
        // already exists, then substring between
        // previous and current index has same
        // no. of 0s and 1s. Update result if this
        // substring is more than current result.
        if (map.ContainsKey(count_1 - count_0))
        {
            res = Math.Max(res, (i - map[count_1 -
                                         count_0]));
        }
 
        // If the current difference is
        // seen first time.
        else
        {
            map[count_1 - count_0] = i;
        }
 
    }
 
    Console.WriteLine("Length of longest balanced" +
                            " sub string = " + res);
}
}
 
// This code is contributed by Shrikant13

Javascript




<script>
 
// Javascript Code for finding the length of
// the longest balanced substring
     
    let str = "101001000";
    // Create a map to store differences
    // between counts of 1s and 0s.
    let map = new Map();
      
    // Initially difference is 0;
            map.set(0, -1);
            let res =0;
            let count_0 = 0, count_1 = 0;
            for(let i=0; i<str.length;i++)
            {
                // Keep track of count of 0s and 1s
                if(str[i]=='0')
                    count_0++;
                else
                    count_1++;
  
        // If difference between current counts
        // already exists, then substring between
        // previous and current index has same
        // no. of 0s and 1s. Update result if this
        // substring is more than current result.
  
                if(map.has(count_1-count_0))
                    res =
                    Math.max(res, (i -
                    map.get(count_1-count_0)));
      
        // If the current difference
        // is seen first time.
                else
                    map.set(count_1-count_0,i);
                  
            }
              
            document.write(
            "Length of longest balanced sub string = "+res
            );
     
 
// This code is contributed by unknown2108
 
</script>

Output

Length of longest balanced sub string = 6

Time Complexity: O(n)

Extended Problem: Largest subarray with equal number of 0s and 1s

This article is contributed by Shivam Pradhan (anuj_charm) and ASIPU PAWAN KUMAR. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. 


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