Question

how to swap two numbers inplace without using any additional space?

Answer 1

If you have 2 variables a and b: (each variable occupies its own memory address)

a = a xor b
b = a xor b
a = a xor b

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There are also some other variations to this problem but they will fail if there is overflow:

a=a+b
b=a-b
a=a-b

a=a*b
b=a/b
a=a/b

The plus and minus variation may work if you have custom types that have + and – operators that make sense.

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Note: To avoid confusion, if you have only 1 variable, and 2 references or pointers to it, then all of the above will fail. A check should be made to avoid this.

Unlike a lot of people are saying it does not matter if you have 2 different numbers. It only matters that you have 2 distinct variables where the number exists in 2 different memory addresses.

I.e. this is perfectly valid:

int a = 3;
int b = 3;

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

assert(a == b);
assert(a == 3);