Adding Big Numbers

• Time : $O(max(|a|,|b|))$
• Space : $O(|a| + |b|)$

#include <string>

std::string add(const std::string& a, const std::string& b) {
    std::string ca = a, cb = b;
    std::reverse(std::begin(ca), std::end(ca));
    std::reverse(std::begin(cb), std::end(cb));
    std::string res = "";
    int carry = 0, i = 0;
    while(i < ca.length() and i < cb.length()) {
        int now = carry + ca[i] - '0' + cb[i] - '0';
        res.push_back(now % 10 + '0');
        carry = now / 10;
        i += 1;
    }
    while(i < ca.length()) {
        int now = carry + ca[i] - '0';
        res.push_back(now % 10 + '0');
        carry = now / 10;
        i += 1;
    }
    while(i < cb.length()) {
        int now = carry + cb[i] - '0';
        res.push_back(now % 10 + '0');
        carry = now / 10;
        i += 1;
    }
    if(carry) res.push_back(carry + '0');
    std::reverse(std::begin(res), std::end(res));
    return res;
}