Maximum difference of zeros and ones in binary string

Difficulty Level : Medium
Last Updated : 06 May, 2021

Given a binary string of 0s and 1s. The task is to find the length of substring which is having 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

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The idea is to use Dynamic Programming to solve the problem.
Before that we will convert given binary string into integer array of value 1s and -1s, say arr[]. That can be easily done by traversing the given binary string and if ith index contain ‘0’ make -1 in corresponding position in array. Similarly, if ith index contain ‘1’, make 1 in the array.
Now, at each index i we need to make decision whether to take it or skip it. So, declare a 2D array of size n x 2, where n is the length of the given binary string, say dp[n][2].

dp[i][0] define the maximum value upto 
         index i, when we skip the i-th
         index element.
dp[i][1] define the maximum value upto 
         index i after taking the i-th
         index element.

Therefore, we can derive dp[i][] as:
dp[i][0] = max(dp[i+1][0], dp[i+1][1] + arr[i])
dp[i][1] = max(dp[i+1][1] + arr[i], 0)

For all ones we check this case explicitly.

C++

// CPP Program to find the length of
// substring with maximum difference of
// zeroes and ones in binary string.
#include <bits/stdc++.h>
#define MAX 100
using namespace std;
 
// Return true if there all 1s
bool allones(string s, int n)
{
    // Checking each index is 0 or not.
    int co = 0;
    for (int i = 0; i < s.size(); i++)
        co += (s[i] == '1');
 
    return (co == n);
}
 
// Find the length of substring with maximum
// difference of zeroes and ones in binary
// string
int findlength(int arr[], string s, int n,
              int ind, int st, int dp[][3])
{
    // If string is over.
    if (ind >= n)
        return 0;
 
    // If the state is already calculated.
    if (dp[ind][st] != -1)
        return dp[ind][st];
 
    if (st == 0)
        return dp[ind][st] = max(arr[ind] +
          findlength(arr, s, n, ind + 1, 1, dp),
          findlength(arr, s, n, ind + 1, 0, dp));
 
    else
        return dp[ind][st] = max(arr[ind] +
       findlength(arr, s, n, ind + 1, 1, dp), 0);
}
 
// Returns length of substring which is
// having maximum difference of number
// of 0s and number of 1s
int maxLen(string s, int n)
{
    // If all 1s return -1.
    if (allones(s, n))
        return -1;   
 
    // Else find the length.
    int arr[MAX] = { 0 };
    for (int i = 0; i < n; i++)
        arr[i] = (s[i] == '0' ? 1 : -1);   
 
    int dp[MAX][3];
    memset(dp, -1, sizeof dp);
    return findlength(arr, s, n, 0, 0, dp);
}
 
// Driven Program
int main()
{
    string s = "11000010001";
    int n = 11;
    cout << maxLen(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.Arrays;
 
class GFG
{
static final int MAX=100;
 
// Return true if there all 1s
static boolean allones(String s, int n)
{
    // Checking each index is 0 or not.
    int co = 0;
    for (int i = 0; i < s.length(); i++)
        if(s.charAt(i) == '1')
            co +=1;    
 
    return (co == n);
}
 
// Find the length of substring with maximum
// difference of zeroes and ones in binary
// string
static int findlength(int arr[], String s, int n,
                     int ind, int st, int dp[][])
{
    // If string is over.
    if (ind >= n)
        return 0;
 
    // If the state is already calculated.
    if (dp[ind][st] != -1)
        return dp[ind][st];
 
    if (st == 0)
        return dp[ind][st] = Math.max(arr[ind] +
                             findlength(arr, s, n,
                                   ind + 1, 1, dp),
                             findlength(arr, s, n,
                                   ind + 1, 0, dp));
 
    else
        return dp[ind][st] = Math.max(arr[ind] +
                             findlength(arr, s, n,
                               ind + 1, 1, dp), 0);
}
 
// Returns length of substring which is
// having maximum difference of number
// of 0s and number of 1s
static int maxLen(String s, int n)
{
    // If all 1s return -1.
    if (allones(s, n))
        return -1;
 
    // Else find the length.
    int arr[] = new int[MAX];
    for (int i = 0; i < n; i++)
        arr[i] = (s.charAt(i) == '0' ? 1 : -1);
 
    int dp[][] = new int[MAX][3];
    for (int[] row : dp)
            Arrays.fill(row, -1);
    return findlength(arr, s, n, 0, 0, dp);
}
 
// Driver code
public static void main (String[] args)
{
    String s = "11000010001";
    int n = 11;
    System.out.println(maxLen(s, n));
}
}
 
// This code is contributed by Anant Agarwal.

Python3

# Python Program to find the length of
# substring with maximum difference of
# zeroes and ones in binary string.
MAX = 100
 
# Return true if there all 1s
def allones(s, n):
     
    # Checking each index
    # is 0 or not.
    co = 0
     
    for i in s:
        co += 1 if i == '1' else 0
 
    return co == n
 
# Find the length of substring with
# maximum difference of zeroes and
# ones in binary string
def findlength(arr, s, n, ind, st, dp):
     
    # If string is over
    if ind >= n:
        return 0
 
    # If the state is already calculated.
    if dp[ind][st] != -1:
        return dp[ind][st]
 
    if not st:
        dp[ind][st] = max(arr[ind] +
           findlength(arr, s, n, ind + 1, 1, dp),
            (findlength(arr, s, n, ind + 1, 0, dp)))
    else:
        dp[ind][st] = max(arr[ind] +
         findlength(arr, s, n, ind + 1, 1, dp), 0)
          
    return dp[ind][st]
 
# Returns length of substring which is
# having maximum difference of number
# of 0s and number of 1s
def maxLen(s, n):
     
    # If all 1s return -1.
    if allones(s, n):
        return -1
 
    # Else find the length.
    arr = [0] * MAX
    for i in range(n):
        arr[i] = 1 if s[i] == '0' else -1
 
    dp = [[-1] * 3 for _ in range(MAX)]
    return findlength(arr, s, n, 0, 0, dp)
 
# Driven Program
s = "11000010001"
n = 11
print(maxLen(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
{
    static int MAX = 100;
     
    // Return true if there all 1s
    public static bool allones(string s, int n)
    {
        // Checking each index is 0 or not.
        int co = 0;
        for (int i = 0; i < s.Length; i++)
            co += (s[i] == '1' ? 1 : 0);
 
        return (co == n);
    }
     
    // Find the length of substring with maximum
    // difference of zeroes and ones in binary
    // string
    public static int findlength(int[] arr, string s,
                    int n, int ind, int st, int[,] dp)
    {
        // If string is over.
        if (ind >= n)
            return 0;
     
        // If the state is already calculated.
        if (dp[ind,st] != -1)
            return dp[ind,st];
     
        if (st == 0)
            return dp[ind,st] = Math.Max(arr[ind] +
            findlength(arr, s, n, ind + 1, 1, dp),
            findlength(arr, s, n, ind + 1, 0, dp));
     
        else
            return dp[ind,st] = Math.Max(arr[ind] +
        findlength(arr, s, n, ind + 1, 1, dp), 0);
    }
     
    // Returns length of substring which is
    // having maximum difference of number
    // of 0s and number of 1s
    public static int maxLen(string s, int n)
    {
        // If all 1s return -1.
        if (allones(s, n))
            return -1;    
     
        // Else find the length.
        int[] arr = new int[MAX];
             
        for (int i = 0; i < n; i++)
            arr[i] = (s[i] == '0' ? 1 : -1);    
     
        int[,] dp = new int[MAX,3];
        for(int i = 0; i < MAX; i++)
            for(int j = 0; j < 3; j++)
                dp[i,j] = -1;
 
        return findlength(arr, s, n, 0, 0, dp);
    }
     
    // Driven Program
     
    static void Main()
    {
        string s = "11000010001";
        int n = 11;
        Console.Write(maxLen(s, n));
    }
    // This code is contributed by DrRoot_
}

Javascript

<script>
 
// Javascript Program to find the length of
// substring with maximum difference of
// zeroes and ones in binary string.
var MAX = 100;
 
// Return true if there all 1s
function allones( s,  n)
{
    // Checking each index is 0 or not.
    var co = 0;
    for (var i = 0; i < s.length; i++)
        co += (s[i] == '1');
 
    return (co == n);
}
 
// Find the length of substring with maximum
// difference of zeroes and ones in binary
// string
function findlength(arr, s, n, ind, st, dp)
{
    // If string is over.
    if (ind >= n)
        return 0;
 
    // If the state is already calculated.
    if (dp[ind][st] != -1)
        return dp[ind][st];
 
    if (st == 0)
        return dp[ind][st] = Math.max(arr[ind] +
          findlength(arr, s, n, ind + 1, 1, dp),
          findlength(arr, s, n, ind + 1, 0, dp));
 
    else
        return dp[ind][st] = Math.max(arr[ind] +
       findlength(arr, s, n, ind + 1, 1, dp), 0);
}
 
// Returns length of substring which is
// having maximum difference of number
// of 0s and number of 1s
function maxLen( s,  n)
{
    // If all 1s return -1.
    if (allones(s, n))
        return -1;   
 
    // Else find the length.
    var arr = Array(MAX).fill(0);
    for (var i = 0; i < n; i++)
        arr[i] = (s[i] == '0' ? 1 : -1);   
 
    var dp = Array.from(Array(MAX), ()=> Array(3).fill(-1));
    return findlength(arr, s, n, 0, 0, dp);
}
 
// Driven Program
var s = "11000010001";
var n = 11;
document.write( maxLen(s, n));
 
 
</script>