# Maximum difference of zeros and ones in binary string

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
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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].

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

Therefore, we can derive dp[i][] as:
dp[i] = max(dp[i+1], dp[i+1] + arr[i])
dp[i] = max(dp[i+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 ` `#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[]) ` `{ ` `    ``// 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]; ` `    ``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_ ` `} `

Output :

```6
```

Maximum difference of zeros and ones in binary string | Set 2 (O(n) time)

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