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Copy set bits in a range

  • Difficulty Level : Medium
  • Last Updated : 29 May, 2018

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.




// 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; 
}

Output :

Modified x is 14

 

Method 2 (Copy all bits using one bit mask)






// 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;
}

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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