LEETCODE WEEKLY 409 T3

namespace atcoder
{

template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
struct lazy_segtree {
    int ceil_pow2(int n)
    {
        int x = 0;
        while ((1U << x) < (unsigned int) (n))
            x++;
        return x;
    }

  public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S> &v) : _n(int(v.size()))
    {
        log = ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++)
            d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x)
    {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--)
            push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++)
            update(p >> i);
    }

    S get(int p)
    {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--)
            push(p >> i);
        return d[p];
    }

    S prod(int l, int r)
    {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r)
            return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l)
                push(l >> i);
            if (((r >> i) << i) != r)
                push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1)
                sml = op(sml, d[l++]);
            if (r & 1)
                smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f)
    {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--)
            push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++)
            update(p >> i);
    }
    void apply(int l, int r, F f)
    {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r)
            return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l)
                push(l >> i);
            if (((r >> i) << i) != r)
                push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1)
                    all_apply(l++, f);
                if (r & 1)
                    all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l)
                update(l >> i);
            if (((r >> i) << i) != r)
                update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l)
    {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g)
    {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n)
            return _n;
        l += size;
        for (int i = log; i >= 1; i--)
            push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0)
                l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r)
    {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g)
    {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0)
            return 0;
        r += size;
        for (int i = log; i >= 1; i--)
            push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2))
                r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f)
    {
        d[k] = mapping(f, d[k]);
        if (k < size)
            lz[k] = composition(f, lz[k]);
    }
    void push(int k)
    {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

} // namespace atcoder
using a2i = array<int, 2>;
using atcoder::lazy_segtree;
using S = a2i;
S op(S a, S b) {return a2i{a[0] + b[0], a[1] + b[1]};}
using F = int;
S e() {return {0, 0};}
S mapping(F f, S r) {
    if (f == 0)
        return r;
    return S{r[1], r[1]};
}
F id() {return 0;}
F composite(F f, F g) {
    if (f == 0) return g;
    if (g == 0) return f;
    return 1;
}

class Solution {
public:
    vector<int> shortestDistanceAfterQueries(int n, vector<vector<int>>& qs) {
        int m = qs.size();
        vector<int> ret(m);
        int len = n - 1;

        lazy_segtree<S, op, e, F, mapping, composite, id> seg(n);
        for (int i = 0; i < n; ++i) seg.set(i, {0, 1});

        for (int i = 0; i < m; ++i) {
            int u = qs[i][0], v = qs[i][1];

            int marked = seg.prod(u + 1, v)[0];
            // cout << "marked: " << marked << '\n';
            len -= v - u - 1 - marked;

            seg.apply(u + 1, v, 1);

            ret[i] = len;
        }

        return ret;
    }
};