#line 1 "test/yuki/1435_SegTree-BinarySearch.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1435" #line 2 "other/template.hpp" #include #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define REP_SELECTER(a, b, c, d, e, ...) e #define REP1_0(b, c) REP1_1(b, c) #define REP1_1(b, c) for (ll REP_COUNTER_ ## c = 0; REP_COUNTER_ ## c < (ll)(b); ++ REP_COUNTER_ ## c) #define REP1(b) REP1_0(b, __COUNTER__) #define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i) #define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i) #define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c)) #define rep(...) REP_SELECTER(__VA_ARGS__, REP4, REP3, REP2, REP1) (__VA_ARGS__) #define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i) #define RREP3(i, a, b) for (ll i = (ll)(a) - 1; i >= (ll)(b); --i) #define RREP4(i, a, b, c) for (ll i = (ll)(a) - 1; i >= (ll)(b); i -= (ll)(c)) #define rrep(...) REP_SELECTER(__VA_ARGS__, RREP4, RREP3, RREP2) (__VA_ARGS__) #define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i) #define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i) #define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c)) #define reps(...) REP_SELECTER(__VA_ARGS__, REPS4, REPS3, REPS2) (__VA_ARGS__) #define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i) #define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i) #define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c)) #define rreps(...) REP_SELECTER(__VA_ARGS__, RREPS4, RREPS3, RREPS2) (__VA_ARGS__) #define each_for(...) for (auto&& __VA_ARGS__) #define each_const(...) for (const auto& __VA_ARGS__) #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #if __cplusplus >= 201402L #define CONSTEXPR constexpr #else #define CONSTEXPR #endif #ifdef __cpp_if_constexpr #define IF_CONSTEXPR constexpr #else #define IF_CONSTEXPR #endif using ll = long long; using ull = unsigned long long; using ld = long double; using PLL = std::pair; template using prique = std::priority_queue, std::greater>; template class infinity { public: static constexpr T value = std::numeric_limits::max() / 2; static constexpr T mvalue = std::numeric_limits::min() / 2; static constexpr T max = std::numeric_limits::max(); static constexpr T min = std::numeric_limits::min(); }; #if __cplusplus <= 201402L template constexpr T infinity::value; template constexpr T infinity::mvalue; template constexpr T infinity::max; template constexpr T infinity::min; #endif #if __cplusplus >= 201402L template constexpr T INF = infinity::value; #endif constexpr ll inf = infinity::value; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; template std::ostream& operator<<(std::ostream& ost, const std::pair& p) { return ost << p.first << ' ' << p.second; } template std::istream& operator>>(std::istream& ist, std::pair& p) { return ist >> p.first >> p.second; } template::value>::type* = nullptr> auto operator<<(std::ostream& ost, const Container& cont) -> decltype(cont.begin(), cont.end(), ost) { for (auto itr = cont.begin(); itr != cont.end(); ++itr) { if (itr != cont.begin()) ost << ' '; ost << *itr; } return ost; } template::value>::type* = nullptr> auto operator>>(std::istream& ist, Container& cont) -> decltype(cont.begin(), cont.end(), ist) { for (auto itr = cont.begin(); itr != cont.end(); ++itr) ist >> *itr; return ist; } template inline constexpr bool chmin(T &a, const U &b) noexcept { return a > b ? a = b, true : false; } template inline constexpr bool chmax(T &a, const U &b) noexcept { return a < b ? a = b, true : false; } inline CONSTEXPR ll gcd(ll a, ll b) noexcept { while (b) { const ll c = a; a = b; b = c % b; } return a; } inline CONSTEXPR ll lcm(ll a, ll b) noexcept { return a / gcd(a, b) * b; } inline CONSTEXPR bool is_prime(ll N) noexcept { if (N <= 1) return false; for (ll i = 2; i * i <= N; ++i) { if (N % i == 0) return false; } return true; } inline std::vector prime_factor(ll N) noexcept { std::vector res; for (ll i = 2; i * i <= N; ++i) { while (N % i == 0) { res.push_back(i); N /= i; } } if (N != 1) res.push_back(N); return res; } inline CONSTEXPR ll my_pow(ll a, ll b) noexcept { ll res = 1; while (b) { if (b & 1) res *= a; b >>= 1; a *= a; } return res; } inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) noexcept { a %= mod; ll res = 1; while (b) { if (b & 1) (res *= a) %= mod; b >>= 1; (a *= a) %= mod; } return res; } PLL extGCD(ll a, ll b) noexcept { if (b == 0) return PLL{1, 0}; PLL p = extGCD(b, a % b); std::swap(p.first, p.second); p.second -= p.first * (a / b); if (p.first < 0) { p.first += b; p.second -= a; } return p; } ll mod_inv(ll a, ll mod) noexcept { const PLL p = extGCD(a, mod); assert(p.first * a + p.second * mod == 1); return p.first; } PLL ChineseRemainder(ll b1, ll m1, ll b2, ll m2) noexcept { const PLL p = extGCD(m1, m2); const ll g = p.first * m1 + p.second * m2; const ll l = m1 / g * m2; if ((b2 - b1) % g != 0) return PLL{-1, -1}; const ll x = (b2 - b1) / g * p.first % (m2 / g); return {(x * m1 + b1 + l) % l, l}; } PLL ChineseRemainders(const std::vector& b, const std::vector& m) noexcept { PLL res{0, 1}; rep (i, b.size()) { res = ChineseRemainder(res.first, res.second, b[i], m[i]); if (res.first == -1) return res; } return res; } template class RecLambda { private: F f; public: explicit constexpr RecLambda(F&& f_) : f(std::forward(f_)) {} template constexpr auto operator()(Args&&... args) const -> decltype(f(*this, std::forward(args)...)) { return f(*this, std::forward(args)...); } }; template inline constexpr RecLambda rec_lambda(F&& f) { return RecLambda(std::forward(f)); } template struct multi_dim_vector { using type = std::vector::type>; }; template struct multi_dim_vector { using type = T; }; template constexpr std::vector make_vec(int n, Arg&& arg) { return std::vector(n, std::forward(arg)); } template constexpr typename multi_dim_vector::type make_vec(int n, Args&&... args) { return typename multi_dim_vector::type (n, make_vec(std::forward(args)...)); } inline CONSTEXPR int popcnt(ull x) { #if __cplusplus >= 202002L return std::popcount(x); #endif x = (x & 0x5555555555555555) + ((x >> 1 ) & 0x5555555555555555); x = (x & 0x3333333333333333) + ((x >> 2 ) & 0x3333333333333333); x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4 ) & 0x0f0f0f0f0f0f0f0f); x = (x & 0x00ff00ff00ff00ff) + ((x >> 8 ) & 0x00ff00ff00ff00ff); x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff); return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff); } template> class presser { protected: std::vector dat; Comp cmp; bool sorted = false; public: presser() : presser(Comp()) {} presser(const Comp& cmp) : cmp(cmp) {} presser(const std::vector& vec, const Comp& cmp = Comp()) : dat(vec), cmp(cmp) {} presser(std::vector&& vec, const Comp& cmp = Comp()) : dat(std::move(vec)), cmp(cmp) {} presser(std::initializer_list il, const Comp& cmp = Comp()) : dat(il.begin(), il.end()), cmp(cmp) {} void reserve(int n) { assert(!sorted); dat.reserve(n); } void push_back(const T& v) { assert(!sorted); dat.push_back(v); } void push_back(T&& v) { assert(!sorted); dat.push_back(std::move(v)); } void push(const std::vector& vec) { assert(!sorted); dat.reserve(dat.size() + vec.size()); std::copy(all(vec), std::back_inserter(dat)); } int build() { assert(!sorted); sorted = true; std::sort(all(dat), cmp); dat.erase(std::unique(all(dat), [&](const T& a, const T& b) -> bool { return !cmp(a, b) && !cmp(b, a); }), dat.end()); return dat.size(); } const T& operator[](int k) const& { assert(sorted); assert(0 <= k && k < (int)dat.size()); return dat[k]; } T operator[](int k) && { assert(sorted); assert(0 <= k && k < (int)dat.size()); return std::move(dat[k]); } int get_index(const T& val) const { assert(sorted); return static_cast(std::lower_bound(all(dat), val, cmp) - dat.begin()); } std::vector pressed(const std::vector& vec) const { assert(sorted); std::vector res(vec.size()); rep (i, vec.size()) res[i] = get_index(vec[i]); return res; } void press(std::vector& vec) const { static_assert(std::is_integral::value, "template argument must be convertible from int type"); assert(sorted); each_for (i : vec) i = get_index(i); } int size() const { assert(sorted); return dat.size(); } const std::vector& data() const& { return dat; } std::vector data() && { return std::move(dat); } }; #line 2 "data-struct/segment/SegmentTree.hpp" #line 2 "other/bitop.hpp" #line 4 "other/bitop.hpp" namespace bitop { #define KTH_BIT(b, k) (((b) >> (k)) & 1) #define POW2(k) (1ull << (k)) inline ull next_combination(int n, ull x) { if (n == 0) return 1; ull a = x & -x; ull b = x + a; return (x & ~b) / a >> 1 | b; } #define rep_comb(i, n, k) for (ull i = (1ull << (k)) - 1; i < (1ull << (n)); i = bitop::next_combination((n), i)) inline CONSTEXPR int msb(ull x) { int res = x ? 0 : -1; if (x & 0xFFFFFFFF00000000) x &= 0xFFFFFFFF00000000, res += 32; if (x & 0xFFFF0000FFFF0000) x &= 0xFFFF0000FFFF0000, res += 16; if (x & 0xFF00FF00FF00FF00) x &= 0xFF00FF00FF00FF00, res += 8; if (x & 0xF0F0F0F0F0F0F0F0) x &= 0xF0F0F0F0F0F0F0F0, res += 4; if (x & 0xCCCCCCCCCCCCCCCC) x &= 0xCCCCCCCCCCCCCCCC, res += 2; return res + ((x & 0xAAAAAAAAAAAAAAAA) ? 1 : 0); } inline CONSTEXPR int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; } } #line 2 "other/monoid.hpp" #line 4 "other/monoid.hpp" namespace Monoid { template struct Sum { using value_type = T; static constexpr T op(const T& a, const T& b) { return a + b; } static constexpr T id() { return T{0}; } static constexpr T inv(const T& a, const T& b) { return a - b; } static constexpr T get_inv(const T& a) { return -a; } }; template::max> struct Min { using value_type = T; static constexpr T op(const T& a, const T& b) { return a > b ? b : a; } static constexpr T id() { return max_value; } }; template::min> struct Max { using value_type = T; static constexpr T op(const T& a, const T& b) { return a < b ? b : a;} static constexpr T id() { return min_value; } }; template struct Assign { using value_type = T; static constexpr T op(const T&, const T& b) { return b; } }; template::max> struct AssignMin { using M = Min; using E = Assign; static constexpr T op(const T& a, const T&) { return a; } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T&) { return a; } }; template::min> struct AssignMax { using M = Max; using E = Assign; static constexpr T op(const T& a, const T&) { return a; } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T&) { return a; } }; template struct AssignSum { using M = Sum; using E = Assign; static constexpr T op(const T& a, const T&) { return a; } static constexpr T mul(const T& a, int b) { return a * b; } static constexpr T mul_op(const T& a, int b, const T&) { return a * b; } }; template::max> struct AddMin { using M = Min; using E = Sum; static constexpr T op(const T& a, const T& b) { return b + a; } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T& c) { return c + a; } }; template::min> struct AddMax { using M = Max; using E = Sum; static constexpr T op(const T& a, const T& b) { return b + a; } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T& c) { return c + a; } }; template struct AddSum { using M = Sum; using E = Sum; static constexpr T op(const T& a, const T& b) { return b + a; } static constexpr T mul(const T& a, int b) { return a * b; } static constexpr T mul_op(const T& a, int b, const T& c) { return c + a * b; } }; template::max> struct ChminMin { using M = Min; using E = Min; static constexpr T op(const T& a, const T& b) { return std::min(b, a); } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T& c) { return std::min(c, a); } }; template::min> struct ChminMax { using M = Max; using E = Min; static constexpr T op(const T& a, const T& b) { return std::min(b, a); } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T& c) { return std::min(c, a); } }; template::max> struct ChmaxMin { using M = Min; using E = Max; static constexpr T op(const T& a, const T& b) { return std::max(b, a); } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T& c) { return std::max(c, a); } }; template::min> struct ChmaxMax { using M = Max; using E = Max; static constexpr T op(const T& a, const T& b) { return std::max(b, a); } static constexpr T mul(const T& a, int) { return a; } static constexpr T mul_op(const T& a, int, const T& c) { return std::max(c, a); } }; template struct ReverseMonoid { using value_type = typename M::value_type; static value_type op(const value_type& a, const value_type& b) { return M::op(b, a); } static value_type id() { return M::id(); } static value_type get_inv(const value_type& a) { return M::get_inv(a); } }; template struct AttachEffector { using M = M_; using E = M_; using T = typename M_::value_type; static T op(const T& a, const T& b) { return M_::op(b, a); } }; template struct AttachMonoid { using M = E_; using E = E_; using T = typename E_::value_type; static T op(const T& a, const T& b) { return E_::op(b, a); } }; template class has_id : public std::false_type {}; template class has_id : public std::true_type {}; template class has_inv : public std::false_type {}; template class has_inv : public std::true_type {}; template class has_get_inv : public std::false_type {}; template class has_get_inv : public std::true_type {}; template class has_mul : public std::false_type {}; template class has_mul : public std::true_type {}; template class has_mul_op : public std::false_type {}; template class has_mul_op : public std::true_type {}; template class is_semigroup : public std::false_type {};; template class is_semigroup(), (void)T::op)> : public std::true_type {}; template class is_monoid : public std::false_type {};; template class is_monoid(), (void)T::op, (void)T::id)> : public std::true_type {}; template class is_group : public std::false_type {};; template class is_group(), (void)T::op, (void)T::id, (void)T::get_inv)> : public std::true_type {}; template class is_action : public std::true_type {}; template class is_action(), std::declval(), (void)T::op)> : public std::false_type {}; } // namespace Monoid #line 6 "data-struct/segment/SegmentTree.hpp" template class SegmentTree { protected: using T = typename M::value_type; int n, ori; std::vector data; public: SegmentTree() : SegmentTree(0) {} SegmentTree(int n) : SegmentTree(std::vector(n, M::id())) {} SegmentTree(const std::vector& v) { init(v); } void init(const std::vector& v) { ori = v.size(); n = 1 << bitop::ceil_log2(ori); data.assign(n << 1, M::id()); rep (i, ori) data[n + i] = v[i]; rrep (i, n, 1) data[i] = M::op(data[i << 1], data[i << 1 ^ 1]); } template void update(int k, const Upd& upd) { assert(0 <= k && k < ori); k += n; data[k] = upd(data[k]); while (k >>= 1) data[k] = M::op(data[k << 1], data[k << 1 ^ 1]); } void set(int k, T x) { update(k, [&](T) -> T { return x; }); } void apply(int k, T x) { update(k, [&](T a) -> T { return M::op(a, x); }); } T prod(int l, int r) const { assert(0 <= l && l <= r && r <= ori); l += n; r += n; T lsm = M::id(), rsm = M::id(); while (l < r) { if (l & 1) lsm = M::op(lsm, data[l++]); if (r & 1) rsm = M::op(data[--r], rsm); l >>= 1; r >>= 1; } return M::op(lsm, rsm); } T all_prod() const { return data[1]; } T get(int k) const { return data[k + n]; } template int max_right(int l, const Cond& cond) const { assert(0 <= l && l <= ori); assert(cond(M::id())); if (l == ori) return ori; l += n; T sm = M::id(); do { while ((l & 1) == 0) l >>= 1; if (!cond(M::op(sm, data[l]))) { while (l < n) { l <<= 1; if (cond(M::op(sm, data[l]))) sm = M::op(sm, data[l++]); } return l - n; } sm = M::op(sm, data[l++]); } while ((l & -l) != l); return ori; } template int min_left(int r, const Cond& cond) const { assert(0 <= r && r <= ori); assert(cond(M::id())); if (r == 0) return 0; r += n; T sm = M::id(); do { --r; while ((r & 1) && r > 1) r >>= 1; if (!cond(M::op(data[r], sm))) { while (r < n) { r = r << 1 ^ 1; if (cond(M::op(data[r], sm))) sm = M::op(data[r--], sm); } return r + 1 - n; } sm = M::op(data[r], sm); } while ((r & -r) != r); return 0; } }; // verified with test/aoj/DSL/DSL_2_A-RMQ.test.cpp template::max> using RangeMinimumQuery = SegmentTree>; template::min> using RangeMaximumQuery = SegmentTree>; // verified with test/aoj/DSL/DSL_2_B-RSQ.test.cpp template using RangeSumQuery = SegmentTree>; /** * @brief SegmentTree(セグメント木) * @docs docs/SegmentTree.md */ #line 4 "test/yuki/1435_SegTree-BinarySearch.test.cpp" using namespace std; int main() { struct Mmm { typedef struct value_type { int m1, m2, M; } T; static T op(T a, T b) { int v[4] = {a.m1, a.m2, b.m1, b.m2}; sort(all(v)); return {v[0], v[1], max(a.M, b.M)}; } static T id() { return {infinity::value, infinity::value, infinity::mvalue}; } }; int N; cin >> N; vector A(N); cin >> A; vector B(N); rep (i, N) { B[i].m1 = B[i].M = A[i]; B[i].m2 = infinity::value; } SegmentTree seg(B); ll ans1 = 0, ans2 = 0; rep (i, N) { ll idx = seg.max_right(i, [&](const auto& v) { return v.M <= v.m1 + v.m2; }); ans1 += idx - i - 1; } reps (i, N) { ll idx = seg.min_left(i, [&](const auto& v) { return v.M <= v.m1 + v.m2; }); ans2 += i - idx - 1; } assert(ans1 == ans2); cout << ans1 << endl; }