Given a non-negative integer N, the task is to find count of non-negative integers
less than or equal to N whose bitwise OR and sum with N are equal.
Input : N = 3 Output : 1 0 is the only number in [0, 3] that satisfies given property. (0 + 3) = (0 | 3) Input : 10 Output : 4 (0 + 10) = (0 | 10) (Both are 10) (1 + 10) = (1 | 10) (Both are 11) (4 + 10) = (4 | 10) (Both are 14) (5 + 10) = (5 | 10) (Both are 15)
A simple solution is to traverse all numbers from 0 to N and do bitwise OR and SUM with N, if both are equal increment counter.
Time complexity = O(N).
An efficient solution is to follow following steps.
1. Find count of zero bit in N.
2. Return pow(2,count).
The idea is based on the fact that bitwise OR and sum of a number x with N are equal, if and only if
bitwise AND of x with N will is 0
Let, N=10 =10102. Bitwise AND of a number with N will be 0, if number contains zero bit with all respective set bit(s) of N and either zero bit or set bit with all respective zero bit(s) of N (because, 0&0=1&0=0). e.g. bit : 1 0 1 0 position: 4 3 2 1 Bitwise AND of any number with N will be 0, if the number has following bit pattern 1st position can be either 0 or 1 (2 ways) 2nd position can be 1 (1 way) 3rd position can be either 0 or 1 (2 ways) 4th position can be 1 (1 way) Total count = 2*1*2*1 = 22 = 4.
Total time complexity of above solution will be O(log2(N)).
This article is contributed by Viranjan Kumar Akela. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Find N distinct numbers whose bitwise Or is equal to K
- Largest set with bitwise OR equal to n
- Maximum subset with bitwise OR equal to k
- Minimum Bitwise OR operations to make any two array elements equal
- Bitwise AND of all the odd numbers from 1 to N
- Total pairs in an array such that the bitwise AND, bitwise OR and bitwise XOR of LSB is 1
- Check whether bitwise OR of N numbers is Even or Odd
- Check whether bitwise AND of N numbers is Even or Odd
- Numbers that are bitwise AND of at least one non-empty sub-array
- Maximum possible Bitwise OR of the two numbers from the range [L, R]
- Russian Peasant (Multiply two numbers using bitwise operators)
- Rearrange array elements such that Bitwise AND of first N - 1 elements is equal to last element
- Leftover element after performing alternate Bitwise OR and Bitwise XOR operations on adjacent pairs
- Find subsequences with maximum Bitwise AND and Bitwise OR
- Equal Sum and XOR of three Numbers
Improved By : jit_t