why transform all characters even if they are in final form ('c')? No sense

Instead custom lambda, you can use predefined std::multiplies()

any benefit from using auto && in this case?

with iteration from 1 to n you can save n-times on adding i+1

std::map dict should be const, also as mentioned std::vector v is redundant versus map keys

There is missing test at least for C++ that includes {INT_MAX, INT_MAX, INT_MAX, INT_MAX}
Its exotic case but possible and curretly code that overflows to -2 is passing

4 times only if e != w - short circuit of logical phrases in c++, but I agree it is not efficient

I suggest to exchange order on logic expression pred(*itr) && itr != arr.end().
In your variant program first will evaluate pred(*itr) that can be already == arr.end(), what means that you will calculate value for out of container data. In reversed version first will be evaluated that end of container was reached - it will give false and rest of AND conditions will be not evaluated due to so called shortcircuit of operator

What if n is negative?