What is the idea behind ^= 32, that converts lowercase letters to upper and vice versa?

Question

I was solving some problem on codeforces. Normally I first check if the character is upper or lower English letter then subtract or add 32 to convert it to the

Answer 1

This uses the fact than ASCII values have been chosen by really smart people.

foo ^= 32;

This flips the 6th lowest bit¹ of foo (the uppercase flag of ASCII sort of), transforming an ASCII upper case to a lower case and vice-versa.

+---+------------+------------+
|   | Upper case | Lower case |  32 is 00100000
+---+------------+------------+
| A | 01000001   | 01100001   |
| B | 01000010   | 01100010   |
|            ...              |
| Z | 01011010   | 01111010   |
+---+------------+------------+

Example

'A' ^ 32

    01000001 'A'
XOR 00100000 32
------------
    01100001 'a'

And by property of XOR, 'a' ^ 32 == 'A'.

Notice

C++ is not required to use ASCII to represent characters. Another variant is EBCDIC. This trick only works on ASCII platforms. A more portable solution would be to use std::tolower and std::toupper, with the offered bonus to be locale-aware (it does not automagically solve all your problems though, see comments):

bool case_incensitive_equal(char lhs, char rhs)
{
    return std::tolower(lhs, std::locale{}) == std::tolower(rhs, std::locale{}); // std::locale{} optional, enable locale-awarness
}

assert(case_incensitive_equal('A', 'a'));

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¹⁾ As 32 is 1 << 5 (2 to the power 5), it flips the 6th bit (counting from 1).