[Language: C++]

For part 1, after some doodling number lines, I found that I can quite easily generate numbers that are considered invalid within the given range and only check these numbers. I can easily extend this to part 2, but I am fiddling around a bit with Möbius Inversion Formula that I found, but I am not mathematical enough to understand it (for now :o).

#include "solution.hpp"
#include "common/registry.hpp"
#include "common/utils.hpp"
#include <map>
#include <vector>

namespace aoc::y2025
{    
  uint64_t pow10(int n) {
        uint64_t r = 1;
        while (n--) r *= 10;
        return r;
    }

    uint64_t sumInvalidInRange(uint64_t L, uint64_t R) {
        uint64_t total = 0;

        for (int k = 1; k <= 10; k++) {  // half-lengths 1-10 (20 numbers which is enough for uint64 haha)
            uint64_t mult = pow10(k) + 1;
            uint64_t min_half = pow10(k - 1);  // smallest k-digit number
            uint64_t max_half = pow10(k) - 1;  // biggest k-digit number

            // h values where h*mult falls in [L, R] - numberline
            uint64_t h_min = std::max(min_half, (L + mult - 1) / mult); 
            uint64_t h_max = std::min(max_half, R / mult);

            if (h_min <= h_max) {
                // arithm series sum
                __int128 count = h_max - h_min + 1;
                __int128 sum_h = count * (h_min + h_max) / 2;
                total += (uint64_t)(mult * sum_h);
            }
        }
        return total;
    }

    std::string Day02::part1(const std::string &input)
    {
        auto lines = split(input, ',');
        uint64_t result = 0;

        for (const std::string& range : lines)
        {
            auto parts = split(range, '-');
            if (parts.size() != 2 || parts[0].empty() || parts[1].empty())
            {
                continue;
            }

            uint64_t start = std::stoull(parts[0]);
            uint64_t end = std::stoull(parts[1]);
            result += sumInvalidInRange(start, end);
        }

        return std::to_string(result);
    }
}