Here's one approach:
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <algorithm>
#include <numeric>
#include <array>
#include <string>
#include <locale>
struct lexcmp {
lexcmp() { std::iota(order_.begin(), order_.end(), std::int_fast8_t{}); }
explicit lexcmp(std::string const& order) {
assert(order.size() == order_.size());
for (std::size_t i{}; i != order_.size(); ++i) {
char const order_letter = order[i];
assert(std::isalpha(order_letter, std::locale::classic()));
assert(std::islower(order_letter, std::locale::classic()));
order_[i] = order_letter - 'a';
}
auto unique_order_letters = [this]{
auto order = order_;
std::sort(order.begin(), order.end());
return order.end() - std::unique(order.begin(), order.end()) == 0;
};
assert(unique_order_letters());
}
bool operator ()(std::string const& a, std::string const& b) const {
auto const a_len = a.size(), b_len = b.size();
std::size_t i{};
for (auto const len = std::min(a_len, b_len); i != len; ++i) {
if (auto const diff = order_[a[i] - 'a'] - order_[b[i] - 'a']) {
return diff < 0;
}
}
return i == a_len && i != b_len;
}
private:
std::array<std::int_fast8_t, 26> order_;
};
Online Demo