Copy set bits in a range

Given two numbers x and y, and a range [l, r] where 1 <= l, r <= 32. The task is consider set bits of y in range [l, r] and set these bits in x also. Examples : 

Input  : x = 10, y = 13, l = 2, r = 3
Output : x = 14
Binary representation of 10 is 1010 and 
that of y is 1101. There is one set bit
in y at 3’rd position (in given range). 
After we copy this bit to x, x becomes 1110
which is binary representation of 14.

Input  : x = 8, y = 7, l = 1, r = 2
Output : x = 11

Source : D E Shaw Interview

Method 1 (One by one copy bits)
We can one by one find set bits of y by traversing given range. For every set bit, we OR it to existing bit of x, so that the becomes set in x, if it was not set. Below is C++ implementation.

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// C++ program to rearrange array in alternating
// C++ program to copy set bits in a given
// range [l, r] from y to x.
#include <bits/stdc++.h>
using namespace std;
  
// Copy set bits in range [l, r] from y to x.
// Note that x is passed by reference and modified
// by this function.
void copySetBits(unsigned &x, unsigned y,
                 unsigned l, unsigned r)
{
   // l and r must be between 1 to 32
   // (assuming ints are stored using
   //  32 bits)
   if (l < 1 || r > 32)
      return ;
  
   // Travers in given range
   for (int i=l; i<=r; i++)
   {
       // Find a mask (A number whose
       // only set bit is at i'th position)
       int mask = 1 << (i-1);
  
       // If i'th bit is set in y, set i'th
       // bit in x also.
       if (y & mask)
          x = x | mask;
   }
}
  
// Driver code
int main()
{
   unsigned x = 10, y = 13, l = 2, r = 3;
   copySetBits(x, y, l, r);
   cout << "Modified x is " << x;
   return 0; 
}

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Output : 




Modified x is 14


 


Method 2 (Copy all bits using one bit mask)











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// C++ program to copy set bits in a given 


// range [l, r] from y to x. 


#include <bits/stdc++.h> 


using namespace std; 


  


// Copy set bits in range [l, r] from y to x. 


// Note that x is passed by reference and modified 


// by this function. 


void copySetBits(unsigned &x, unsigned y, 


                 unsigned l, unsigned r) 


{ 


    // l and r must be between 1 to 32 


    if (l < 1 || r > 32) 


        return ; 


  


    // get the length of the mask 


    int maskLength = (1<<(r-l+1)) - 1; 


  


    // Shift the mask to the required position 


    // "&" with y to get the set bits at between 


    // l ad r in y 


    int mask = ((maskLength)<<(l-1)) & y ; 


    x = x | mask; 


} 


  


// Driver code 


int main() 


{ 


   unsigned x = 10, y = 13, l = 2, r = 3; 


   copySetBits(x, y, l, r); 


   cout << "Modified x is " << x; 


   return 0; 


} 



















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Output : 


Modified x is 14


Thanks to Ashish Rathi for suggesting this solution in a comment.


This article is contributed by Rishi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above


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