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Xor base

C++

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std::vector<long long> calc_base(std::vector<long long> &v) {
    std::vector<long long> base;

    for (long long x : v) {
        for (long long b : base)
            x = std::min(x, b ^ x);
        if (x > 0)
            base.push_back(x);
    }

    return base;
}