Given two numbers and . Find the values of X and Y in the equations.
- A = X + Y
- B = X xor Y
The task is to make X as minimum as possible. If it is not possible to find any valid values for X and Y then print -1.
Input : A = 12, B = 8 Output : X = 2, Y = 10 Input : A = 12, B = 9 Output : -1
Let’s take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then one can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, Y = X + B. Taking into account that X + Y = X + X + B = A, one can obtain the following formulas for finding X and Y:
- X = (A – B) / 2
- Y = X + B = (A + B) / 2
One should also notice that if A < B or A and B have different parity, then the answer doesn’t exist and output is -1. If X and (A – X) not equal to X then the answer is also -1.
Below is the implementation of the above approach :
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- Linear Diophantine Equations
- Number of solutions to Modular Equations
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