Overflow error in Gomory Cutting Plane method

[nol0n]

How to reproduse

in application main.cpp

...
obv::Table table;
table.readFile("./test.txt"); // with problem given below

obv::lpalgs::simplexMethod(table);
obv::lpalgs::cuttingPlane(table);
std::cout << table << "\n\n";
...

Example

problem

max F = 1 * x1 + 15 * x2 + 24 * x3 + 3 * x4

3 * x1 +  4 * x2 +  1 * x3 +  2 * x4 <= 29
2 * x1 + 15 * x2 + 12 * x3 +  3 * x4 <= 61
3 * x1 +  5 * x2 +  2 * x3 + 14 * x4 <= 37
2 * x1 + 98 * x2 + 32 * x3 + 23 * x4 <= 57

format for input file

4  4
1 15 24  3
3  4  1  2 29
2 15 12  3 61
3  5  2 14 37
2 98 32 23 57

Expected answer

9 * x1 + x3 = 33

Now

It can't solve this problem because of integer overflow

[nol0n]

Fixed this method, at least I think so.

[nol0n]

After fixing other errors, this algorithm started causing overflow errors for integer values in rational numbers when trying to solve some problems, including this. The only fix I see is to use some library like GMP, but I'm not doing it because it will require me to rewrite everything. For now, the base cutting plane algorithm can't solve all problems (I think it will be correct to say it can solve some).

[nol0n]

And so... I decided to fix this issue by using BigInt class made by this kind man. It works for now, but I saw this issue and I think I'll also implement GMP variant later.