String with additive sequence

// C++ program to check whether a string
// makes an additive sequence or not
#include <bits/stdc++.h>
using namespace std;

// Checks whether num is valid or not, by
// checking first character and size
bool isValid(string num)
{
    if (num.size() > 1 && num[0] == '0')
        return false;
    return true;
}

// returns int value at pos string, if pos is
// out of bound then returns 0
int val(string a, int pos)
{
    if (pos >= a.length())
        return 0;

    //  converting character to integer
    return (a[pos] - '0');
}

// add two number in string form and return
// result as a string
string addString(string a, string b)
{
    string sum = "";
    int i = a.length() - 1;
    int j = b.length() - 1;
    int carry = 0;

    //  loop until both string get processed
    while (i >= 0 || j >= 0)
    {
        int t = val(a, i) + val(b, j) + carry;
        sum += (t % 10 + '0');
        carry = t / 10;
        i--;    j--;
    }
    if (carry)
        sum += (carry + '0');
    reverse(sum.begin(), sum.end());
    return sum;
}

//  Recursive method to check c = a + b
bool checkAddition(list<string>& res, string a,
                             string b, string c)
{
    //  both first and second number should be valid
    if (!isValid(a) || !isValid(b))
        return false;
    string sum = addString(a, b);

    //  if sum is same as c then direct return
    if (sum == c)
    {
        res.push_back(sum);
        return true;
    }

    /*  if sum size is greater than c, then no
        possible sequence further OR if c is not
        prefix of sum string, then no possible
        sequence further  */
    if (c.size() <= sum.size() ||
        sum != c.substr(0, sum.size()))
        return false;
    else
    {
        res.push_back(sum);
        
        //  next recursive call will have b as first
        //  number, sum as second number and string
        //  c as third number after removing prefix
        //  sum string from c
        return checkAddition(res, b, sum,
                             c.substr(sum.size()));
    }
}

//  Method returns additive sequence from string as
// a list
list<string> additiveSequence(string num)
{
    list<string> res;
    int l = num.length();

    // loop until l/2 only, because if first
    // number is larger,then no possible sequence
    // later
    for (int i = 1; i <= l/2; i++)
    {
        for (int j = 1; j <= (l - i)/2; j++)
        {
            if (checkAddition(res, num.substr(0, i),
                              num.substr(i, j),
                              num.substr(i + j)))
            {
                // adding first and second number at
                // front of result list
                res.push_front(num.substr(i, j));
                res.push_front(num.substr(0, i));
                return res;
            }
        }
    }

    // If code execution reaches here, then string
    // doesn't have any additive sequence
    res.clear();
    return res;
}

//  Method to print result list
void printResult(list<string> res)
{
    for (auto it = res.begin(); it != res.end(); it++)
        cout << *it << " ";
    cout << endl;
}

//  Driver code to test above methods
int main()
{
    string num = "235813";
    list<string> res = additiveSequence(num);
    printResult(res);

    num = "199100199";
    res = additiveSequence(num);
    printResult(res);
    return 0;
}