Given an integer N. The task is to count the numbers of pairs of integers A and B such that A + B + N = A ^ B ^ N and A and B are less than N.
Input: N = 2
For N = 2
2 XOR 0 XOR 0 = 2+0+0
2 XOR 0 XOR 1 = 2+0+1
2 XOR 0 XOR 2 != 2+0+2
2 XOR 1 XOR 0 = 2+1+0
2 XOR 1 XOR 1 != 2+1+1
2 XOR 1 XOR 2 != 2+1+2
2 XOR 2 XOR 0 != 2+2+0
2 XOR 2 XOR 1 != 2+2+1
2 XOR 2 XOR 2 != 2+2+2
So (0, 0), (0, 1) and (1, 0) are the required pairs. So the output is 3.
Input: N = 4
To make the sum of three numbers equal to the xor of three number with one of the number given we can do following:-
- Represent the fixed number in binary form.
- Traverse the binary expansion of the fixed number.
- If you find a 1 there is only one condition i.e. you take the other two number’s binary bits as 0 and 0.
- If you find a 0 there will be three conditions i.e. either you can have binary bits as (0, 0), (1, 0)
or (0, 1).
- The following above triplets of bits will never go for a carry so they are valid.
- So the answer will be 3^(number of zeros in binary representation).
Below is the implementation of the above approach:
Time Complexity: O(Number of unset_bits)
- Find three element from given three arrays such that their sum is X | Set 2
- Number of quadruples where the first three terms are in AP and last three terms are in GP
- Count numbers whose sum with x is equal to XOR with x
- Equal Sum and XOR
- Check if Sum and XOR of all elements of array is equal
- Count ways to generate pairs having Bitwise XOR and Bitwise AND equal to X and Y respectively
- XOR of two numbers after making length of their binary representations equal
- Count numbers whose difference with N is equal to XOR with N
- Count numbers whose XOR with N is equal to OR with N
- Absolute difference between the XOR of Non-Prime numbers and Prime numbers of an Array
- Count subarrays with sum equal to its XOR value
- Minimum insertions to make XOR of an Array equal to half of its sum
- Maximum sum of Bitwise XOR of all elements of two equal length subsets
- Find a number X such that (X XOR A) is minimum and the count of set bits in X and B are equal
- Find XOR of two number without using XOR operator
- Given a set, find XOR of the XOR's of all subsets.
- Choose X such that (A xor X) + (B xor X) is minimized
- Find K numbers with sum equal to N and sum of their squares maximized
- Find two numbers from their sum and XOR
- Count ordered pairs of positive numbers such that their sum is S and XOR is K
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