How to cyclically increment and decrement 26 latin characters in a loop - c++

Question

I want to increment or decrement characters, but have them cycle back to a when going beyond z and to z when going before a.
For example incrementing 'w' by 2 gives 'y' and decrementing 'w' by 2 gives 'u'.
Another example decrementing 'w' by 28 gives 'u' and decrementing 'a' by 256 gives 'e'.
I've figure out how to increment: char(int(A[i]+B-97)%26 +97) where B is the shift amount and A[i] is current character.

Answer 1

Don't overcomplicate. Use modulo to keep the increment or decrement amount in a range of 26 characters, then simply do a range check:
char cyclicIncrementDecrement(char ch, int amount)
{
int newValue = int(ch) + (amount % 26);
if (newValue < 'a') newValue += 26;
if (newValue > 'z') newValue -= 26;
return char(newValue);
}
This method of course assumes ch already is in range of 'a' to 'z'. If not, you need to handle that (put it in range or throw an exception or whatever is appropriate for your application).
Running this:
int main()
{
std::cout << cyclicIncrementDecrement('w', -2) << std::endl;
std::cout << cyclicIncrementDecrement('w', 2) << std::endl;
std::cout << cyclicIncrementDecrement('w', -28) << std::endl;
std::cout << cyclicIncrementDecrement('a', -256) << std::endl;
std::cout << cyclicIncrementDecrement('z', -256) << std::endl;
std::cout << cyclicIncrementDecrement('z', -51) << std::endl;
std::cout << cyclicIncrementDecrement('z', -52) << std::endl;
}
gives:
u
y
u
e
d
a
z

Answer 2

Using modular arithmetic, calculate your answer as modulo 26 and then add 'a' (ASCII 97) to your result.
char cyclic_increment(char ch, int n) {
int tmp = ((ch - 97) + n) % 26;
if (tmp < 0 )
tmp += 26;
return (char)(tmp + 97);
}
Alternatively, you could write the above (without an if) as:
char cyclic_increment(char ch, int n) {
return (((ch - 'a') + n) % 26 + 26) % 26 + 'a';
}

Answer 3

This handles both positive and negative offsets:
unsigned char az_cyclic(int in_ch)
{
constexpr int mod = 26; // There are 26 letters in the English alphabet
int offset = (in_ch - 'a') % mod; // (ASCII To zero-based offset) Mod_26 remainder
if (offset < 0) // If negative offset,
offset += mod; // normalize to positive. For example: -1 to 25
return 'a' + offset; // Normalize to ASCII
}
Use-cases:
int main()
{
unsigned char out_ch = '\0';
out_ch = az_cyclic('a' - 1); // 'z'
out_ch = az_cyclic('a' - 1 - 26); // 'z'
out_ch = az_cyclic('a' - 2); // 'y'
out_ch = az_cyclic('a' + 4); // 'e'
out_ch = az_cyclic('a' + 4 + 26); // 'e'
out_ch = az_cyclic('a' + 2); // 'c'
return 0;
}