coordinate compression

[Astral-23]

// Coodinate Compression // https://youtu.be/fR3W5IcBGLQ?t=8550

template <typename T> struct CC {
    bool initialized;
    vector<T> xs;
    T mx, Mx;
    CC(T mx, T Mx) : mx(mx), Mx(Mx) { initialized = false; }

    void add(T x, T width = 0) {
        for (T w = -width; w < 0; w++)
            if (x + w <= Mx && x >= mx - w) xs.push_back(x + w);
        for (T w = 0; w < width + 1; w++)
            if (x <= Mx - w && x + w >= mx) xs.push_back(x + w);
    }

    void add(vec<T> A, T width = 0) {
        for (T x : A) add(x, width);
    }

    void init() {
        sort(xs.begin(), xs.end());
        xs.erase(unique(xs.begin(), xs.end()), xs.end());
        initialized = true;
    }

    int operator()(T x) {//以下最大のindex
        if (!initialized) init();
        return upper_bound(xs.begin(), xs.end(), x) - xs.begin() - 1;
    }
    T operator[](int i) {
        if (!initialized) init();
        return xs[i];
    }
    int size() {
        if (!initialized) init();
        return xs.size();
    }
};