#line 1 "main.cpp" #include #line 2 "/home/user/Library/utils/macros.hpp" #define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i)) #define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i)) #define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i)) #define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i)) #define ALL(x) std::begin(x), std::end(x) #line 6 "/home/user/Library/data_structure/segment_tree.hpp" /** * @brief Segment Tree / セグメント木 (monoids, 完全二分木) * @docs data_structure/segment_tree.md * @tparam Monoid (commutativity is not required) */ template struct segment_tree { typedef typename Monoid::value_type value_type; Monoid mon; int n; std::vector a; segment_tree() = default; segment_tree(int n_, const Monoid & mon_ = Monoid()) : mon(mon_) { n = 1; while (n < n_) n *= 2; a.resize(2 * n - 1, mon.unit()); } void point_set(int i, value_type b) { // 0-based assert (0 <= i and i < n); a[i + n - 1] = b; for (i = (i + n) / 2; i > 0; i /= 2) { // 1-based a[i - 1] = mon.mult(a[2 * i - 1], a[2 * i]); } } value_type range_get(int l, int r) { // 0-based, [l, r) assert (0 <= l and l <= r and r <= n); value_type lacc = mon.unit(), racc = mon.unit(); for (l += n, r += n; l < r; l /= 2, r /= 2) { // 1-based loop, 2x faster than recursion if (l % 2 == 1) lacc = mon.mult(lacc, a[(l ++) - 1]); if (r % 2 == 1) racc = mon.mult(a[(-- r) - 1], racc); } return mon.mult(lacc, racc); } value_type point_get(int i) { // 0-based assert (0 <= i and i < n); return a[i + n - 1]; } /** * @note O(min(n, (r - l) log n)) */ void range_set(int l, int r, value_type b) { assert (0 <= l and l <= r and r <= n); range_set(0, 0, n, l, r, b); } void range_set(int i, int il, int ir, int l, int r, value_type b) { if (l <= il and ir <= r and ir - il == 1) { // 0-based a[i] = b; } else if (ir <= l or r <= il) { // nop } else { range_set(2 * i + 1, il, (il + ir) / 2, l, r, b); range_set(2 * i + 2, (il + ir) / 2, ir, l, r, b); a[i] = mon.mult(a[2 * i + 1], a[2 * i + 2]); } } /** * @brief a fast & semigroup-friendly version constructor * @note $O(n)$ */ template segment_tree(InputIterator first, InputIterator last, const Monoid & mon_ = Monoid()) : mon(mon_) { int size = std::distance(first, last); n = 1; while (n < size) n *= 2; a.resize(2 * n - 1, mon.unit()); std::copy(first, last, a.begin() + (n - 1)); unsafe_rebuild(); } /** * @brief update a leaf node without updating ancestors * @note $O(1)$ */ void unsafe_point_set(int i, value_type b) { // 0-based assert (0 <= i and i < n); a[i + n - 1] = b; } /** * @brief re-build non-leaf nodes from leaf nodes * @note $O(n)$ */ void unsafe_rebuild() { REP_R (i, n - 1) { a[i] = mon.mult(a[2 * i + 1], a[2 * i + 2]); } } }; #line 4 "/home/user/Library/data_structure/lazy_propagation_segment_tree.hpp" #include #line 7 "/home/user/Library/data_structure/lazy_propagation_segment_tree.hpp" /** * @brief Lazy Propagation Segment Tree / 遅延伝播セグメント木 (monoids, 完全二分木) * @docs data_structure/lazy_propagation_segment_tree.md * @tparam MonoidX is a monoid * @tparam MonoidF is a monoid * @tparam Action is a function phi : F * X -> X where the partial applied phi(f, -) : X -> X is a homomorphism on X */ template struct lazy_propagation_segment_tree { static_assert (std::is_invocable_r::value, ""); typedef typename MonoidX::value_type value_type; typedef typename MonoidF::value_type operator_type; MonoidX mon_x; MonoidF mon_f; Action act; int n; std::vector a; std::vector f; lazy_propagation_segment_tree() = default; lazy_propagation_segment_tree(int n_, const MonoidX & mon_x_ = MonoidX(), const MonoidF & mon_f_ = MonoidF(), const Action & act_ = Action()) : mon_x(mon_x_), mon_f(mon_f_), act(act_) { n = 1; while (n < n_) n *= 2; a.resize(2 * n - 1, mon_x.unit()); f.resize(n - 1, mon_f.unit()); } template lazy_propagation_segment_tree(InputIterator first, InputIterator last, const MonoidX & mon_x_ = MonoidX(), const MonoidF & mon_f_ = MonoidF(), const Action & act_ = Action()) : mon_x(mon_x_), mon_f(mon_f_), act(act_) { int size = std::distance(first, last); n = 1; while (n < size) n *= 2; a.resize(2 * n - 1, mon_x.unit()); f.resize(n - 1, mon_f.unit()); std::copy(first, last, a.begin() + (n - 1)); REP_R (i, n - 1) { a[i] = mon_x.mult(a[2 * i + 1], a[2 * i + 2]); } } void point_set(int i, value_type b) { range_set(i, i + 1, b); } /** * @note O(min(n, (r - l) log n)) */ void range_set(int l, int r, value_type b) { assert (0 <= l and l <= r and r <= n); range_set(0, 0, n, l, r, b); } void range_set(int i, int il, int ir, int l, int r, value_type b) { if (l <= il and ir <= r and ir - il == 1) { // 0-based a[i] = b; } else if (ir <= l or r <= il) { // nop } else { range_apply(2 * i + 1, il, (il + ir) / 2, 0, n, f[i]); range_apply(2 * i + 2, (il + ir) / 2, ir, 0, n, f[i]); f[i] = mon_f.unit(); range_set(2 * i + 1, il, (il + ir) / 2, l, r, b); range_set(2 * i + 2, (il + ir) / 2, ir, l, r, b); a[i] = mon_x.mult(a[2 * i + 1], a[2 * i + 2]); } } void point_apply(int i, operator_type g) { range_apply(i, i + 1, g); } void range_apply(int l, int r, operator_type g) { assert (0 <= l and l <= r and r <= n); range_apply(0, 0, n, l, r, g); } void range_apply(int i, int il, int ir, int l, int r, operator_type g) { if (l <= il and ir <= r) { // 0-based a[i] = act(g, a[i]); if (i < f.size()) f[i] = mon_f.mult(g, f[i]); } else if (ir <= l or r <= il) { // nop } else { range_apply(2 * i + 1, il, (il + ir) / 2, 0, n, f[i]); range_apply(2 * i + 2, (il + ir) / 2, ir, 0, n, f[i]); f[i] = mon_f.unit(); // unnecessary if the oprator monoid is commutative range_apply(2 * i + 1, il, (il + ir) / 2, l, r, g); range_apply(2 * i + 2, (il + ir) / 2, ir, l, r, g); a[i] = mon_x.mult(a[2 * i + 1], a[2 * i + 2]); } } value_type point_get(int i) { return range_get(i, i + 1); } value_type range_get(int l, int r) { assert (0 <= l and l <= r and r <= n); if (l == 0 and r == n) return a[0]; value_type lacc = mon_x.unit(), racc = mon_x.unit(); for (int l1 = (l += n), r1 = (r += n) - 1; l1 > 1; l /= 2, r /= 2, l1 /= 2, r1 /= 2) { // 1-based loop, 2x faster than recursion if (l < r) { if (l % 2 == 1) lacc = mon_x.mult(lacc, a[(l ++) - 1]); if (r % 2 == 1) racc = mon_x.mult(a[(-- r) - 1], racc); } lacc = act(f[l1 / 2 - 1], lacc); racc = act(f[r1 / 2 - 1], racc); } return mon_x.mult(lacc, racc); } }; #line 4 "/home/user/Library/monoids/min.hpp" template struct min_monoid { typedef T value_type; value_type unit() const { return std::numeric_limits::max(); } value_type mult(value_type a, value_type b) const { return std::min(a, b); } }; #line 2 "/home/user/Library/monoids/plus.hpp" template struct plus_monoid { typedef T value_type; value_type unit() const { return value_type(); } value_type mult(value_type a, value_type b) const { return a + b; } }; #line 4 "/home/user/Library/monoids/plus_min_action.hpp" template struct plus_min_action { typename min_monoid::value_type operator () (typename plus_monoid::value_type f, typename min_monoid::value_type x) const { return (x == min_monoid().unit() ? x : f + x); } }; #line 8 "main.cpp" using namespace std; // struct mo_struct { // typedef int64_t value_type; // typedef int64_t result_type; // void add_right(int nr, value_type x_r) { // } // void add_left(int nl, value_type x_nl) { // } // void remove_right(int nr, value_type x_nr) { // } // void remove_left(int nl, value_type x_l) { // } // result_type query() { // return 0; // } // }; template std::vector run_mo_algorithm(Mo mo, const std::vector& values, const std::vector >& queries) { int n = values.size(); int m = queries.size(); // sort queries int sq_n = sqrt(n); std::vector order(m); iota(ALL(order), 0); sort(ALL(order), [&](int i, int j) { int l_i, r_i; std::tie(l_i, r_i) = queries[i]; int l_j, r_j; std::tie(l_j, r_j) = queries[j]; return make_pair(l_i / sq_n, r_i) < make_pair(l_j / sq_n, r_j); }); // compute queries vector ans(m); int l = 0; int r = 0; for (int j : order) { int nl, nr; std::tie(nl, nr) = queries[j]; for (; r < nr; ++ r) mo.add_right(r + 1, values[r]); for (; nl < l; -- l) mo.add_left(l - 1, values[l - 1]); for (; nr < r; -- r) mo.remove_right(r - 1, values[r - 1]); for (; l < nl; ++ l) mo.remove_left(l + 1, values[l]); ans[j] = mo.query(); } return ans; } struct mo_struct { typedef int64_t value_type; typedef int64_t result_type; private: typedef segment_tree > plus_segtree_type; typedef lazy_propagation_segment_tree, plus_monoid, plus_min_action > plus_min_segtree_type; // input int n; const vector& a; // static unordered_map compress; int k; vector dp_l; vector dp_r; // dynamic int l; int r; int64_t value_lr; plus_segtree_type segtree_l; plus_min_segtree_type segtree_m; plus_segtree_type segtree_r; public: mo_struct(const vector& a_) : n(a_.size()) , a(a_) { // static compress vector sorted_a = a; sort(ALL(sorted_a)); for (int64_t a_i : sorted_a) { compress.emplace(a_i, compress.size()); } k = compress.size(); // static left dp_l.resize(n + 1); segtree_l = plus_segtree_type(k); segtree_l.range_set(0, k, 0); REP (i, n) { dp_l[i + 1] = dp_l[i] + segtree_l.range_get(compress[a[i]] + 1, k); segtree_l.point_set(compress[a[i]], segtree_l.point_get(compress[a[i]]) + 1); } segtree_l = plus_segtree_type(k); segtree_l.range_set(0, k, 0); // static right dp_r.resize(n + 1); segtree_r = plus_segtree_type(k); segtree_r.range_set(0, k, 0); REP_R (i, n) { dp_r[i] = dp_r[i + 1] + segtree_r.range_get(0, compress[a[i]]); segtree_r.point_set(compress[a[i]], segtree_r.point_get(compress[a[i]]) + 1); } // dynamic l = 0; r = 0; value_lr = 0; segtree_m = plus_min_segtree_type(k); segtree_m.range_set(0, k, 0); REP (i, n) { segtree_m.range_apply(compress[a[i]] + 1, k, 1); } } void add_right(int nr, int64_t x_r) { assert (nr == r + 1); int y = compress[x_r]; value_lr -= segtree_l.range_get(y + 1, k); segtree_m.range_apply(y + 1, k, -1); segtree_r.point_set(y, segtree_r.point_get(y) - 1); r = nr; } void add_left(int nl, int64_t x_nl) { assert (nl == l - 1); int y = compress[x_nl]; value_lr -= segtree_r.range_get(0, y); segtree_l.point_set(y, segtree_l.point_get(y) - 1); segtree_m.range_apply(0, y, -1); l = nl; } void remove_right(int nr, int64_t x_nr) { assert (nr == r - 1); int y = compress[x_nr]; value_lr += segtree_l.range_get(y + 1, k); segtree_m.range_apply(y + 1, k, 1); segtree_r.point_set(y, segtree_r.point_get(y) + 1); r = nr; } void remove_left(int nl, int64_t x_l) { assert (nl == l + 1); int y = compress[x_l]; value_lr += segtree_r.range_get(0, y); segtree_l.point_set(y, segtree_l.point_get(y) + 1); segtree_m.range_apply(0, y, 1); l = nl; } int64_t query() { int64_t ans = 0; ans += dp_l[l]; ans += dp_r[r]; ans += value_lr; ans += (int64_t)(r - l) * segtree_m.range_get(0, k); return ans; } }; vector solve(int n, int q, const vector& a, const vector >& queries) { return run_mo_algorithm(mo_struct(a), a, queries); } int main() { int n, q; cin >> n >> q; vector a(n); REP (i, n) { cin >> a[i]; } vector > queries(q); REP (i, q) { int l, r; cin >> l >> r; -- l; queries[i] = make_pair(l, r); } auto ans = solve(n, q, a, queries); REP (i, q) { cout << ans[i] << endl; } return 0; }