# 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.

`// 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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