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Number of subsequences in a given binary string divisible by 2
• Difficulty Level : Medium
• Last Updated : 13 May, 2021

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

Examples:

Input: str = “101”
Output:
“0” and “10” are the only subsequences
which are divisible by 2.
Input: str = “10010”
Output: 22

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

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 subsequences ending with 0. So, for every index i such that str[i] = ‘0’, find the number of subsequences ending at i. This value is equal to 2i (0-based indexing). Thus, the final answer will be equal to the summation of 2i 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 subsequences``int` `countSubSeq(string str, ``int` `len)``{``    ``// To store the final answer``    ``int` `ans = 0;` `    ``// Multiplier``    ``int` `mul = 1;` `    ``// Loop to find the answer``    ``for` `(``int` `i = 0; i < len; i++) {` `        ``// Condition to update the answer``        ``if` `(str[i] == ``'0'``)``            ``ans += mul;``        ``// updating multiplier``        ``mul *= 2;``    ``}` `    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``string str = ``"10010"``;``    ``int` `len = str.length();` `    ``cout << countSubSeq(str, len);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{` `// Function to return the count``// of the required subsequences``static` `int` `countSubSeq(String str, ``int` `len)``{``    ``// To store the final answer``    ``int` `ans = ``0``;` `    ``// Multiplier``    ``int` `mul = ``1``;` `    ``// Loop to find the answer``    ``for` `(``int` `i = ``0``; i < len; i++)``    ``{` `        ``// Condition to update the answer``        ``if` `(str.charAt(i) == ``'0'``)``            ``ans += mul;``            ` `        ``// updating multiplier``        ``mul *= ``2``;``    ``}``    ``return` `ans;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``String str = ``"10010"``;``    ``int` `len = str.length();` `    ``System.out.print(countSubSeq(str, len));``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implementation of the approach` `# Function to return the count``# of the required subsequences``def` `countSubSeq(strr, lenn):``    ` `    ``# To store the final answer``    ``ans ``=` `0` `    ``# Multiplier``    ``mul ``=` `1` `    ``# Loop to find the answer``    ``for` `i ``in` `range``(lenn):` `        ``# Condition to update the answer``        ``if` `(strr[i] ``=``=` `'0'``):``            ``ans ``+``=` `mul``            ` `        ``# updating multiplier``        ``mul ``*``=` `2` `    ``return` `ans` `# Driver code``strr ``=` `"10010"``lenn ``=` `len``(strr)` `print``(countSubSeq(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 subsequences``    ``static` `int` `countSubSeq(``string` `str, ``int` `len)``    ``{``        ``// To store the final answer``        ``int` `ans = 0;``    ` `        ``// Multiplier``        ``int` `mul = 1;``    ` `        ``// Loop to find the answer``        ``for` `(``int` `i = 0; i < len; i++)``        ``{``    ` `            ``// Condition to update the answer``            ``if` `(str[i] == ``'0'``)``                ``ans += mul;``                ` `            ``// updating multiplier``            ``mul *= 2;``        ``}``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``static` `public` `void` `Main ()``    ``{``        ``string` `str = ``"10010"``;``        ``int` `len = str.Length;``    ` `        ``Console.WriteLine(countSubSeq(str, len));``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``

Output:

`22`

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