Given two binary strings perform operation until B > 0 and print the result

Given two binary strings A and B of length N and M (up to 105). The task is to repeat the below process and find the answer.

Initialize ans = 0
while (B > 0)
    ans += A & B (bitwise AND)
    B = B / 2
print ans

Note: Answer can be very large so print Answer % 1000000007.

Examples:

Input: A = "1001", B = "10101"
Output: 11
1001 & 10101 = 1, ans = 1, B = 1010
1001 & 1010 = 8, ans = 9, B = 101
1001 & 101 = 1, ans = 10, B = 10
1001 & 10 = 0, ans = 10, B = 1
1001 & 1 = 1, ans = 11, B = 0

Input: A = "1010", B = "1101"
Output: 12


Approach: Since only B is getting affected in all the iterations and dividing a binary number by 2 means right shifting it by 1 bit, it can be observed that a bit in A will only be affected by the set bits in B which are on the left i.e. more significant than the current bit (including the current bit). For example, A = “1001” and B = “10101”, the least significant bit in A will only be affected by the set bits in B i.e. 3 bits in total and the most significant bit in A will only be affected by a single set bit in B i.e. the most significant bit in B as all the other set bits will not affect it in any iteration of the loop while performing bitwise AND, so the final result will be 20 * 3 + 23 * 1 = 3 + 8 = 11.

Below is the implementation of the above approach.

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mod (int)(1e9 + 7)
  
// Function to return the required result
ll BitOperations(string a, int n, string b, int m)
{
  
    // Reverse the strings
    reverse(a.begin(), a.end());
    reverse(b.begin(), b.end());
  
    // Count the number of set bits in b
    int c = 0;
    for (int i = 0; i < m; i++)
        if (b[i] == '1')
            c++;
  
    // To store the powers of 2
    ll power[n];
    power[0] = 1;
  
    // power[i] = pow(2, i) % mod
    for (int i = 1; i < n; i++)
        power[i] = (power[i - 1] * 2) % mod;
  
    // To store the final answer
    ll ans = 0;
    for (int i = 0; i < n; i++) {
        if (a[i] == '1') {
  
            // Add power[i] to the ans after
            // multiplying it with the number
            // of set bits in b
            ans += c * power[i];
            if (ans >= mod)
                ans %= mod;
        }
  
        // Divide by 2 means right shift b>>1
        // if b has 1 at right most side than
        // number of set bits will get decreased
        if (b[i] == '1')
            c--;
  
        // If no more set bits in b i.e. b = 0
        if (c == 0)
            break;
    }
  
    // Return the required answer
    return ans;
}
  
// Driver code
int main()
{
    string a = "1001", b = "10101";
    int n = a.length(), m = b.length();
  
    cout << BitOperations(a, n, b, m);
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG
{
      
static int mod = (int)(1e9 + 7);
  
// Function to return the required result
static int BitOperations(String a, 
            int n, String b, int m)
{
  
    // Reverse the strings
    char[] ch1 = a.toCharArray();
    reverse( ch1 );
    a = new String( ch1 );
    char[] ch2 = b.toCharArray();
    reverse( ch2 );
    b = new String( ch2 );
  
    // Count the number of set bits in b
    int c = 0;
    for (int i = 0; i < m; i++)
        if (b.charAt(i) == '1')
            c++;
  
    // To store the powers of 2
    int[] power = new int[n];
    power[0] = 1;
  
    // power[i] = pow(2, i) % mod
    for (int i = 1; i < n; i++)
        power[i] = (power[i - 1] * 2) % mod;
  
    // To store the final answer
    int ans = 0;
    for (int i = 0; i < n; i++) 
    {
        if (a.charAt(i) == '1'
        {
  
            // Add power[i] to the ans after
            // multiplying it with the number
            // of set bits in b
            ans += c * power[i];
            if (ans >= mod)
                ans %= mod;
        }
  
        // Divide by 2 means right shift b>>1
        // if b has 1 at right most side than
        // number of set bits will get decreased
        if (b.charAt(i) == '1')
            c--;
  
        // If no more set bits in b i.e. b = 0
        if (c == 0)
            break;
    }
  
    // Return the required answer
    return ans;
}
  
static void reverse(char a[]) 
    int i, k,n=a.length; 
    char t;
    for (i = 0; i < n / 2; i++) 
    
        t = a[i]; 
        a[i] = a[n - i - 1]; 
        a[n - i - 1] = t; 
    
}
  
// Driver code
public static void main(String[] args)
{
    String a = "1001", b = "10101";
    int n = a.length(), m = b.length();
  
    System.out.println(BitOperations(a, n, b, m));
}
}
  
// This code contributed by Rajput-Ji

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Python3

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# Python 3 implementation of the approach
mod = 1000000007
  
# Function to return the required result
def BitOperations(a, n, b, m):
      
    # Reverse the strings
    a = a[::-1]
    b = b[::-1]
      
    # Count the number of set
    # bits in b
    c = 0
    for i in range(m):
        if (b[i] == '1'):
            c += 1
  
    # To store the powers of 2
    power = [None] * n
    power[0] = 1
  
    # power[i] = pow(2, i) % mod
    for i in range(1, n):
        power[i] = (power[i - 1] * 2) % mod
  
    # To store the final answer
    ans = 0
    for i in range(0, n):
        if (a[i] == '1'):
              
            # Add power[i] to the ans after
            # multiplying it with the number
            # of set bits in b
            ans += c * power[i]
            if (ans >= mod):
                ans %= mod
  
        # Divide by 2 means right shift b>>1
        # if b has 1 at right most side than
        # number of set bits will get decreased
        if (b[i] == '1'):
            c -= 1
              
        # If no more set bits in b i.e. b = 0
        if (c == 0):
            break
  
    # Return the required answer
    return ans
  
# Driver code
if __name__ == '__main__':
    a = "1001"
    b = "10101"
    n = len(a)
    m = len(b)
  
    print(BitOperations(a, n, b, m))
  
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
using System;
using System.Collections;
  
class GFG
{
      
static int mod = (int)(1e9 + 7);
  
// Function to return the required result
static int BitOperations(string a, 
            int n, string b, int m)
{
  
    // Reverse the strings
    char[] ch1 = a.ToCharArray();
    Array.Reverse( ch1 );
    a = new string( ch1 );
    char[] ch2 = b.ToCharArray();
    Array.Reverse( ch2 );
    b = new string( ch2 );
  
    // Count the number of set bits in b
    int c = 0;
    for (int i = 0; i < m; i++)
        if (b[i] == '1')
            c++;
  
    // To store the powers of 2
    int[] power = new int[n];
    power[0] = 1;
  
    // power[i] = pow(2, i) % mod
    for (int i = 1; i < n; i++)
        power[i] = (power[i - 1] * 2) % mod;
  
    // To store the final answer
    int ans = 0;
    for (int i = 0; i < n; i++) 
    {
        if (a[i] == '1'
        {
  
            // Add power[i] to the ans after
            // multiplying it with the number
            // of set bits in b
            ans += c * power[i];
            if (ans >= mod)
                ans %= mod;
        }
  
        // Divide by 2 means right shift b>>1
        // if b has 1 at right most side than
        // number of set bits will get decreased
        if (b[i] == '1')
            c--;
  
        // If no more set bits in b i.e. b = 0
        if (c == 0)
            break;
    }
  
    // Return the required answer
    return ans;
}
  
// Driver code
static void Main()
{
    string a = "1001", b = "10101";
    int n = a.Length, m = b.Length;
  
    Console.WriteLine(BitOperations(a, n, b, m));
}
}
  
// This code is contributed by mits

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PHP

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<?php
// PHP implementation of the approach 
$GLOBALS['mod'] = (1e9 + 7);
  
// Function to return the required result 
function BitOperations($a, $n, $b, $m
{
  
    // Reverse the strings 
    $a = strrev($a);
    $b = strrev($b); 
  
    // Count the number of set bits in b 
    $c = 0; 
    for ($i = 0; $i < $m; $i++) 
        if ($b[$i] == '1'
            $c++; 
  
    # To store the powers of 2 
    $power = array() ; 
    $power[0] = 1; 
  
    // power[i] = pow(2, i) % mod 
    for ($i = 1; $i < $n; $i++) 
        $power[$i] = ($power[$i - 1] * 2) % 
                      $GLOBALS['mod']; 
  
    // To store the final answer 
    $ans = 0; 
    for ($i = 0; $i < $n; $i++) 
    
        if ($a[$i] == '1'
        
  
            // Add power[i] to the ans after 
            // multiplying it with the number 
            // of set bits in b 
            $ans += $c * $power[$i]; 
            if ($ans >= $GLOBALS['mod']) 
                $ans %= $GLOBALS['mod']; 
        
  
        // Divide by 2 means right shift b>>1 
        // if b has 1 at right most side than 
        // number of set bits will get decreased 
        if ($b[$i] == '1'
            $c--; 
  
        // If no more set bits in b i.e. b = 0 
        if ($c == 0) 
            break
    
  
    // Return the required answer 
    return $ans
  
// Driver code 
$a = "1001";
$b = "10101"
$n = strlen($a);
$m = strlen($b); 
  
echo BitOperations($a, $n, $b, $m); 
  
// This code is contributed by Ryuga
?>

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Output:

11


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