# Number of sub-strings in a given binary string divisible by 2

Given a binary string str of length N, the task is to find the count of substrings of str which are divisible by 2. Leading zeros in a substring is allowed.

Examples:

Input: str = “101”
Output: 2
“0” and “10” are the only substrings
which are divisible by 2.

Input: str = “10010”
Output: 10

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive approach: A naive approach will be to generate all possible substrings and check if they are divisible by 2. The time complexity for this will be O(N3).

Efficient approach: It can be observed that any binary number is divisible by 2 only if it ends with a 0. Now, the task is to just count the number of substrings ending with 0. So, for every index i such that str[i] = ‘0’, find the number of substrings ending at i. This value is equal to (i + 1) (0-based indexing). Thus, the final answer will be equal to the summation of (i + 1) for all i such that str[i] = ‘0’.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the count ` `// of the required substrings ` `int` `countSubStr(string str, ``int` `len) ` `{ ` `    ``// To store the final answer ` `    ``int` `ans = 0; ` ` `  `    ``// Loop to find the answer ` `    ``for` `(``int` `i = 0; i < len; i++) { ` ` `  `        ``// Condition to update the answer ` `        ``if` `(str[i] == ``'0'``) ` `            ``ans += (i + 1); ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str = ``"10010"``; ` `    ``int` `len = str.length(); ` ` `  `    ``cout << countSubStr(str, len); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GFG  ` `{ ` `     `  `    ``// Function to return the count  ` `    ``// of the required substrings  ` `    ``static` `int` `countSubStr(String str, ``int` `len)  ` `    ``{  ` `        ``// To store the final answer  ` `        ``int` `ans = ``0``;  ` `     `  `        ``// Loop to find the answer  ` `        ``for` `(``int` `i = ``0``; i < len; i++)  ` `        ``{  ` `     `  `            ``// Condition to update the answer  ` `            ``if` `(str.charAt(i) == ``'0'``)  ` `                ``ans += (i + ``1``);  ` `        ``}  ` `        ``return` `ans;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args) ` `    ``{  ` `        ``String str = ``"10010"``;  ` `        ``int` `len = str.length();  ` `     `  `        ``System.out.println(countSubStr(str, len));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to return the count ` `# of the required substrrings ` `def` `countSubStr(strr, lenn): ` `     `  `    ``# To store the final answer ` `    ``ans ``=` `0` ` `  `    ``# Loop to find the answer ` `    ``for` `i ``in` `range``(lenn): ` ` `  `        ``# Condition to update the answer ` `        ``if` `(strr[i] ``=``=` `'0'``): ` `            ``ans ``+``=` `(i ``+` `1``) ` ` `  `    ``return` `ans ` ` `  `# Driver code ` `strr ``=` `"10010"` `lenn ``=` `len``(strr) ` ` `  `print``(countSubStr(strr, lenn)) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG  ` `{  ` `     `  `    ``// Function to return the count  ` `    ``// of the required substrings  ` `    ``static` `int` `countSubStr(``string` `str, ``int` `len)  ` `    ``{  ` `        ``// To store the final answer  ` `        ``int` `ans = 0;  ` `     `  `        ``// Loop to find the answer  ` `        ``for` `(``int` `i = 0; i < len; i++)  ` `        ``{  ` `     `  `            ``// Condition to update the answer  ` `            ``if` `(str[i] == ``'0'``)  ` `                ``ans += (i + 1);  ` `        ``}  ` `        ``return` `ans;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main ()  ` `    ``{  ` `        ``string` `str = ``"10010"``;  ` `        ``int` `len = str.Length;  ` `     `  `        ``Console.WriteLine(countSubStr(str, len));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by AnkitRai01  `

Output:

```10
```

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Improved By : mohit kumar 29, AnkitRai01