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Also is the Java code for Garner's algorithm useful? Wouldn't a bigint implementation in pure C++ be more useful for the vast majority of CPers?

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I'm not sure Garner's algorithm is useful at all in competitive programming context... I would also probably prefer Python implementation.

I'm not sure Garner's algorithm is useful at all in competitive programming context... I would also probably prefer Python implementation.

Do we want to get rid of that section or just leave it if it doesn't hurt anything

@jxu
I think Garner's algorithm is fine. But we probably should replace the Java implementation with something else, e.g. C++ or Python.
In contests I usually was fine doing the computations with long long. It's quite typically that M is not too big, e.g. smaller than 1e9, then you can do all computations with 64 bit integers.

Although I've never used Garner's algorithm itself (bad time complexity, complicated).
I've always used this code:

struct Congruence
{
    long long a, m, totient_m;
};

class CRT
{
public:
    void add_congruence(long long a, long long m, long long totient_m) {
        congruences.push_back({a, m, totient_m});
    }

    long long get_unique_solution() {
        long long M = 1;
        for (const auto& c : congruences) {
            M *= c.m;
        }

        long long solution = 0;
        for (const auto& c : congruences) {
            auto b = M / c.m;
            solution = (solution + c.a * b % M * power(b, c.totient_m - 1, c.m)) % M;
        }
        return solution;
    }

    std::vector<Congruence> congruences;
};

Years ago I wrote some explanation to it here: https://discuss.codechef.com/t/problem-in-understanding-chineese-remainder-theorem/15899/2?u=afaxnraner