Problem

We need to sum big numbers and we require your help.

Write a function that returns the sum of two numbers. The input numbers are strings and the function must return a string.

Example

add("123", "321"); -> "444"
add("11", "99");   -> "110"

Notes

The input numbers are big.
The input is a string of only digits
The numbers are positives

Solution

In arithmetic, addition can be performed by aligning the addends vertically and add the colums, starting from the unit colum (on the right). $$ \begin{aligned} 105 \\ +\quad6\\ \hline 111\\ \end{aligned} $$ To simulate the steps, traverse two adden-strings from the last position, add their digits then append the sum to the result string. Because of the length difference and right alignment, the position is length - i for i in range 1 to length

Initialize carry = 0 to store the extra digit if a column exceeds 9, this is then transferred to the next column or appended into the result string after calculated all the colums.

#include <string>

std::string add(const std::string& a, const std::string& b) {
    std::string res = "";
    int len_a = a.length(), len_b = b.length(), n = std::max(len_a, len_b);
    int carry = 0;

    for(int i = 1; i <= n; i++){
        if(i <= lenA)
            carry += a[lenA - i] - '0';
        if(i <= lenB)
            carry += b[lenB - i] - '0';
        res.insert(res.begin(), carry % 10 + '0');
        carry /= 10;
    }
    res.insert(res.begin(), carry + '0');

    while(res.length() > 1 && res.front() == '0')
        res.erase(res.begin());
    return res;
}

Thank you for reading.

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