XOR Exchange Variable

The usual procedure for exchanging two variables, A/b, is

int temp;

Temp=a

A=b;

B=temp;

the 3rd temporary variable temp above is required .

Using the following method, for a given two integers a, a, the following XOR operation can achieve A/b exchange without the help of the 3rd temporary variable:

A = a ^ b;
b = a ^ b;
A = a ^ b;

This exchange of two variables without the help of the 3rd temporary variable process, the implementation is mainly based on the following properties of the XOR operation:

1. Any one of the variable X and its own XOR operation, the result is 0, that is, x^x=0

2. any one of the variables X and 0 is an XOR operation, the result is unchanged, that is, x^0=x

3. The XOR operation has the binding, namely a^b^c= (a^b) ^c=a^ (b^c)

4. The XOR operation is exchangeable, i.e. A^b=b^a

Analysis:

First step: a = a ^ b;

The result of a variable after completion is a ^ b

Step Two: b = a ^ b;

At this point, a to the right of the assignment number is the value of a ^ B, then the assignment number to the right of a with a ^ B replaced,

Get (a ^ b) ^ B=a ^ (b ^ b) =a ^0=a,

That is, after the second operation, the value in B is a, which is b=a, and a is changed to B.

Step three: a = a ^ b;

At this time the assignment number to the right of a save is still a ^ B value, and the assignment number to the right of B is already a,

Replace the assignment number to the right of the B, respectively,

That is, the assignment number to the right a ^ b= (a ^ b) ^ A=a ^ b^ a=a ^ a^ b=0^ b=b, the value assigned to a, that is a=b

That is, after the third operation, the value in A is B, which is a=b, and B is changed to a.

This completes the exchange of two variables, a, B, as in the three steps above, without the need for a 3rd temporary variable procedure.

This process is equivalent to the following process:

A=a+b

B=a-b;

A=a-b;

The precondition is that the value of the a+b cannot overflow.

XOR Exchange Variable