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# Maximize the number of times a character can be removed from substring 01 from given Binary String

• Difficulty Level : Hard
• Last Updated : 13 Jul, 2021

Given a binary string S of size N, the task is to find the maximum number of operations that can be performed on S, by selecting any substring “01” and removing any character from it in a single move, reducing the length of the string by 1.

Examples:

Input: S = “001111”, N = 6
Output: 5
Explanation:
One way to perform the operations is:

1. Select the substring “01” over the range [1, 2] and erase the S ( = ‘1’). The string modifies to “00111”.
2. Select the substring “01” over the range [1, 2] and erase the S ( = ‘1’). The string modifies to “0011”.
3. Select the substring “01” over the range [1, 2] and erase the S ( = ‘1’). The string modifies to “001”.
4. Select the substring “01” over the range [1, 2] and erase the S ( = ‘0’). The string modifies to “01”.
5. Select the substring “01” over the range [0, 1] and erase the S ( = ‘1’). The string modifies to “0”.
6. Now no characters can be removed.

Therefore, the total number of operations performed is 5, which is the maximum possible.

Input: S=”0101″, N=4
Output: 3

Approach: The given problem can be solved based on the following observations:

1. Any 1s present in the prefix of S cannot be removed because there are no 0s before them.
2. Any 0s present in the suffix of S cannot be removed because there are no 1s after them.
3. All other characters are removable.
4. If there are X removable characters, at most X-1 operations can be performed because, eventually, only a single character will remain which cannot be removed.

Follow the steps below to solve the problem:

• Initialize two variables, say X and Y as 0, which store the number of 0s in the suffix and the number of 1s in the prefix respectively, which cannot be removed.
• Iterate over the characters of the string S and perform the following steps:
• If the current character is ‘1′, increment Y by 1.
• Otherwise, stop traversing.
• Iterate over the characters of the string S in reverse order and perform the following steps:
• If the current character is 0, increment X by 1.
• Otherwise, stop traversing.
• If the sum of X and Y is equal to N, print 0 as there are no removable characters.
• Otherwise, print N-(X+Y)-1 as the answer.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the maximum moves``// that can be performed on a string``int` `maxOperations(string S, ``int` `N)``{``    ``// Stores 0s in suffix``    ``int` `X = 0;``    ``// Stores 1s in prefix``    ``int` `Y = 0;` `    ``// Iterate over the characters of``    ``// the string``    ``for` `(``int` `i = 0; i < N; i++) {``        ``if` `(S[i] == ``'0'``)``            ``break``;``        ``Y++;``    ``}``    ``// Iterate until i is greater than``    ``// or equal to 0``    ``for` `(``int` `i = N - 1; i >= 0; i--) {``        ``if` `(S[i] == ``'1'``)``            ``break``;``        ``X++;``    ``}` `    ``// If N is equal to x+y``    ``if` `(N == X + Y)``        ``return` `0;` `    ``// Return answer``    ``return` `N - (X + Y) - 1;``}``// Driver code``int` `main()``{``    ``// Input``    ``string S = ``"001111"``;``    ``int` `N = S.length();` `    ``// Function call``    ``cout << maxOperations(S, N) << endl;``    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;` `class` `GFG{` `// Function to find the maximum moves``// that can be performed on a string``static` `int` `maxOperations(String S, ``int` `N)``{``    ` `    ``// Stores 0s in suffix``    ``int` `X = ``0``;``    ` `    ``// Stores 1s in prefix``    ``int` `Y = ``0``;` `    ``// Iterate over the characters of``    ``// the string``    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ``if` `(S.charAt(i) == ``'0'``)``            ``break``;``            ` `        ``Y++;``    ``}``    ` `    ``// Iterate until i is greater than``    ``// or equal to 0``    ``for``(``int` `i = N - ``1``; i >= ``0``; i--)``    ``{``        ``if` `(S.charAt(i) == ``'1'``)``            ``break``;``            ` `        ``X++;``    ``}` `    ``// If N is equal to x+y``    ``if` `(N == X + Y)``        ``return` `0``;` `    ``// Return answer``    ``return` `N - (X + Y) - ``1``;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Input``    ``String S = ``"001111"``;``    ``int` `N = S.length();``    ` `    ``// Function call``    ``System.out.println(maxOperations(S, N));``}``}` `// This code is contributed by sanjoy_62`

## Python3

 `# Python3 program for the above approach` `# Function to find the maximum moves``# that can be performed on a string``def` `maxOperations(S, N):``    ` `    ``# Stores 0s in suffix``    ``X ``=` `0``    ` `    ``# Stores 1s in prefix``    ``Y ``=` `0` `    ``# Iterate over the characters of``    ``# the string``    ``for` `i ``in` `range``(N):``        ``if` `(S[i] ``=``=` `'0'``):``            ``break``        ` `        ``Y ``+``=` `1``        ` `    ``# Iterate until i is greater than``    ``# or equal to 0``    ``i ``=` `N ``-` `1``    ``while``(i >``=` `0``):``        ``if` `(S[i] ``=``=` `'1'``):``            ``break``        ` `        ``X ``+``=` `1` `    ``# If N is equal to x+y``    ``if` `(N ``=``=` `X ``+` `Y):``        ``return` `0` `    ``# Return answer``    ``return` `N ``-` `(X ``+` `Y) ``-` `1` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Input``    ``S ``=` `"001111"``    ``N ``=` `len``(S)` `    ``# Function call``    ``print``(maxOperations(S, N))``    ` `# This code is contributed by SURENDRA_GANGWAR`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{``    ` `// Function to find the maximum moves``// that can be performed on a string``static` `int` `maxOperations(String S, ``int` `N)``{``    ` `    ``// Stores 0s in suffix``    ``int` `X = 0;` `    ``// Stores 1s in prefix``    ``int` `Y = 0;` `    ``// Iterate over the characters of``    ``// the string``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ``if` `(S[i] == ``'0'``)``            ``break``;` `        ``Y++;``    ``}` `    ``// Iterate until i is greater than``    ``// or equal to 0``    ``for``(``int` `i = N - 1; i >= 0; i--)``    ``{``        ``if` `(S[i] == ``'1'``)``            ``break``;` `        ``X++;``    ``}` `    ``// If N is equal to x+y``    ``if` `(N == X + Y)``        ``return` `0;` `    ``// Return answer``    ``return` `N - (X + Y) - 1;``}` `// Driver code``static` `void` `Main()``{``    ` `    ``// Input``    ``String S = ``"001111"``;``    ``int` `N = S.Length;` `    ``// Function call``    ``Console.WriteLine(maxOperations(S, N));``}``}` `// This code is contributed by abhinavjain194`

## Javascript

 ``
Output
`5`

Time complexity: O(N)
Auxiliary Space: O(1)

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