Linked List addition in C++

list_add.cxx

#include <string>

class List {
    struct Node {
        Node* next;
        int   val;
        Node(int val, Node* next = nullptr)
            : next(next), val(val) {}
    };
    Node* head_;
    explicit List(Node* head) : head_(head) {}

public:
    List() : head_(nullptr) {}
    ~List() {
        while (head_) {
            Node* next = head_->next;
            delete head_;
            head_ = next;
        }
    }

    explicit List(const char* n) : head_(nullptr) {
        for (; *n != '\0'; ++n) {
            assert(*n >= '0' && *n <= '9');
            push(*n - '0');
        }
    }

    List& push(int n) {
        head_ = new Node(n, head_);
        return *this;
    }

    std::string to_string() const {
        std::string r;
        for (Node* p = head_; p; p = p->next)
            r += static_cast<char>(p->val + '0');
        std::reverse(r.begin(), r.end());
        return r;
    }

    List operator+(List const& b) const {
        Node *prev = nullptr, *l = head_, *r = b.head_;
        List ret;
        int carry = 0;
        for (; l && r; l = l->next, r = r->next)
            ret.append_carry(prev, carry += l->val + r->val);
        for (; l; l = l->next)
            ret.append_carry(prev, carry += l->val);
        for (; r; r = r->next)
            ret.append_carry(prev, carry += r->val);
        while (carry)
            ret.append_carry(prev, carry);
        return ret;
    }

private:
    const static int RADIX = 10;
    void append_carry(Node*& prev, int& carry) {
        Node* n = new Node(carry % RADIX);
        carry /= RADIX;
        if (prev  != nullptr) prev->next = n;
        if (head_ == nullptr) head_ = prev;
        prev = n;
    }
};


#include <iostream>

int main(void)
{
    std::cout << (List("123") + List("456")).to_string() << std::endl;
    std::cout << (List("123000") + List("456")).to_string() << std::endl;
    std::cout << (List("123") + List("456000")).to_string() << std::endl;
    return 0;
}