#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" // #include "../../template/template.hpp" // #include "../../segment-tree/rbst-segment-tree.hpp" // #include "../../misc/all.hpp" // #include "../../segment-tree/lazy-segment-tree.hpp" // #include "../../math/affine-transformation.hpp" #include "../../modint/montgomery-modint.hpp" using mint = LazyMontgomeryModInt<998244353>; using T = pair<mint, mint>; using E = Affine<mint>; T f(T a, T b) { return T(a.first + b.first, a.second + b.second); } T g(T a, E b) { return T(a.first * b.a + a.second * b.b, a.second); } E h(E a, E b) { return a * b; }; T ti() { return T{}; } E ei() { return E{}; } using namespace Nyaan; // すべての関数のテスト。ただしセグ木にぶたん系は別途 verify する void test(const int N = 100, const int Q = 100) { RBSTLazySegmentTree<int, T, E, f, g, h, ti, ei> seg1; LazySegmentTree seg2(N, f, g, h, ti(), ei()); ll MOD = 998244353; vector<function<void(void)>> funcs{ [&]() { // set_val int i = rng(0, N - 1); T x{rng(0, MOD - 1), 1}; seg1.set_val(i, x); seg2.set_val(i, x); }, [&]() { // set_val_fast int i = rng(0, N - 1); T x{rng(0, MOD - 1), 1}; seg1.set_val_fast(i, x); seg2.set_val(i, x); }, [&]() { // get_val int i = rng(0, N - 1); T v1 = seg1.get_val(i); T v2 = seg2.get_val(i); assert(v1 == v2 and "get_val"); }, [&]() { // apply_val int i = rng(0, N - 1); E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply_val(i, [&](T& t) { t = g(t, x); }); seg2.update(i, i + 1, x); }, [&]() { // apply_val_fast int i = rng(0, N - 1); E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply_val_fast(i, [&](T& t) { t = g(t, x); }); seg2.update(i, i + 1, x); }, [&]() { // erase int i = rng(0, N - 1); seg1.erase(i); seg2.set_val(i, T{}); }, [&]() { // apply int l = rng(0, N - 1); int r = rng(0, N - 1); if (l > r) swap(l, r); r++; E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply(l, r, x); seg2.update(l, r, x); }, [&]() { // fold int l = rng(0, N - 1); int r = rng(0, N - 1); if (l > r) swap(l, r); r++; auto v1 = seg1.fold(l, r); auto v2 = seg2.query(l, r); assert(v1 == v2 and "fold"); }, [&]() { // get_min_key, get_min_keyval int v1 = -1; while (true) { v1 = seg1.get_min_key(); if (v1 == -1) break; T val = seg2.get_val(v1); if (val.second == 1) break; if (val.second == 0) { seg1.erase(v1); seg2.set_val(v1, T{}); } else { assert(false and "get_min_key"); } } int v2 = -1; if (seg2.query(0, N).second != 0) { // [0, n) は非ゼロですか? int ng = 0, ok = N; while (ng + 1 < ok) { int m = (ng + ok) / 2; mint x = seg2.query(0, m).second; (x == 0 ? ng : ok) = m; } v2 = ok - 1; } assert(v1 == v2 && "get_min_key"); if (v1 == -1) { auto kv1 = seg1.get_min_keyval(); assert(kv1.second == T{} && "get_min_keyval"); } else { auto kv1 = seg1.get_min_keyval(); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "get_min_keyval"); } }, [&]() { // get_max_key, get_max_keyval int v1 = -1; while (true) { v1 = seg1.get_max_key(); if (v1 == -1) break; T val = seg2.get_val(v1); if (val.second == 1) break; if (val.second == 0) { seg1.erase(v1); seg2.set_val(v1, T{}); } else { assert(false and "get_max_key"); } } int v2 = -1; if (seg2.query(0, N).second != 0) { // [i, N) は非ゼロですか? int ok = 0, ng = N; while (ok + 1 < ng) { int m = (ng + ok) / 2; mint x = seg2.query(m, N).second; (x == 0 ? ng : ok) = m; } v2 = ok; } assert(v1 == v2 && "get_max_key"); if (v1 == -1) { auto kv1 = seg1.get_max_keyval(); assert(kv1.second == T{} && "get_max_keyval"); } else { auto kv1 = seg1.get_max_keyval(); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "get_mix_keyval"); } }, [&]() { // pop_min_key int v2 = -1; if (seg2.query(0, N).second != 0) { // [0, n) は非ゼロですか? int ng = 0, ok = N; while (ng + 1 < ok) { int m = (ng + ok) / 2; mint x = seg2.query(0, m).second; (x == 0 ? ng : ok) = m; } v2 = ok - 1; } if (v2 != -1) { pair<int, T> kv1; do { kv1 = seg1.pop_min_keyval(); } while (kv1.second.second == 0); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "pop_min_keyval"); seg2.set_val(v2, T{}); } }, [&]() { // pop_max_key int v2 = -1; if (seg2.query(0, N).second != 0) { // [i, N) は非ゼロですか? int ok = 0, ng = N; while (ok + 1 < ng) { int m = (ng + ok) / 2; mint x = seg2.query(m, N).second; (x == 0 ? ng : ok) = m; } v2 = ok; } if (v2 != -1) { pair<int, T> kv1; do { kv1 = seg1.pop_max_keyval(); } while (kv1.second.second == 0); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "pop_max_keyval"); seg2.set_val(v2, T{}); } }, }; rep(_, 10) { int qq = vector<ll>{0LL, rng(1, 10), rng(1, Q)}[rng(0, 2)]; rep(qnum, qq) { int c = rng(0, sz(funcs) - 1); // trc(c, "cmd"); funcs[c](); } { // make_array auto vec1 = seg1.make_array(); rep(i, sz(vec1) - 1) assert(vec1[i].fi < vec1[i + 1].fi); vector<pair<int, T>> vec2; rep(i, N) { T val = seg2.get_val(i); if (val != T{}) vec2.push_back({i, val}); } // trc(vec1); // trc(vec2); int i1 = 0, i2 = 0; while (i1 != sz(vec1) and i2 != sz(vec2)) { while (i1 != sz(vec1) and vec1[i1].second == T{}) i1++; if (i1 == sz(vec1)) break; assert(vec1[i1] == vec2[i2] and "make_array"); i1++, i2++; } while (i1 != sz(vec1) and vec1[i1].second == T{}) i1++; assert(i1 == sz(vec1) and i2 == sz(vec2) and "make_array"); // trc("make_array ok"); } seg1.clear(); rep(i, N) seg2.set_val(i, T{}); } } void test_tl(const int N = 5 * TEN(5), const int Q = 5 * TEN(5)) { ll MOD = 998244353; V<T> init; rep(i, N) init.emplace_back(rng(0, MOD - 1), rng(0, MOD - 1)); RBSTLazySegmentTree<int, T, E, f, g, h, ti, ei> seg1(init); LazySegmentTree seg2(init, f, g, h, ti(), ei()); vector<function<void(void)>> funcs{ [&]() { // apply int l = +rng(0, 10); int r = -rng(0, 10) + N; E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply(l, r, x); seg2.update(l, r, x); }, [&]() { // fold int l = +rng(0, 10); int r = -rng(0, 10) + N; auto v1 = seg1.fold(l, r); auto v2 = seg2.query(l, r); assert(v1 == v2 and "fold"); }, }; rep(qnum, Q) { int c = rng(0, sz(funcs) - 1); // trc(c, "cmd"); funcs[c](); } } void q() { rep(t, 10) test(10, TEN(4)); // rep(t, 10) test(100, TEN(4)); // rep(t, 2) test(TEN(4), TEN(2)); // test(10, TEN(4)); test(2, TEN(4)); test(1, TEN(4)); cerr << "test OK" << endl; Timer timer; test_tl(); cerr << "test_tl OK" << endl; cerr << "time : " << timer.elapsed() << endl; } void Nyaan::solve() { q(); int a, b; cin >> a >> b; cout << a + b << endl; }
#line 1 "verify/verify-unit-test/rbst-segment-tree.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" // #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 4 "verify/verify-unit-test/rbst-segment-tree.test.cpp" // #line 2 "segment-tree/rbst-segment-tree.hpp" #line 2 "internal/internal-type-traits.hpp" #line 4 "internal/internal-type-traits.hpp" using namespace std; namespace internal { template <typename T> using is_broadly_integral = typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>, true_type, false_type>::type; template <typename T> using is_broadly_signed = typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>, true_type, false_type>::type; template <typename T> using is_broadly_unsigned = typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template <typename T> \ constexpr bool x##_v = x<T>::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<typename T::var>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; #define ENABLE_HAS_VAR(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; } // namespace internal #line 4 "segment-tree/rbst-segment-tree.hpp" ENABLE_HAS_VAR(lazy); ENABLE_HAS_VAR(shift); template <typename Node, typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct RBSTSegmentTreeBase { protected: using Ptr = Node *; template <typename... Args> static Ptr _my_new(Args... args) { return new Node(args...); } static void _my_del(Ptr t) { delete t; } static int _count(const Ptr t) { return t ? t->cnt : 0; } static T _sum(const Ptr &t) { return t ? t->sum : ti(); } static uint64_t _rng() { static uint64_t x_ = 88172645463325252ULL; return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull; } static Ptr _merge(Ptr l, Ptr r) { if (!l || !r) return l ? l : r; if (int((_rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) { _push(l); l->r = _merge(l->r, r); return _update(l); } else { _push(r); r->l = _merge(l, r->l); return _update(r); } } static Ptr _build(int l, int r, const vector<pair<I, T>> &dat) { if (l == r) return nullptr; if (l + 1 == r) return _my_new(dat[l].first, dat[l].second); int m = (l + r) / 2; return _merge(_build(l, m, dat), _build(m, r, dat)); }; static void _push([[maybe_unused]] Ptr t) { if constexpr (has_lazy_v<Node>) { if (!t) return; if (t->lazy != ei()) { if (t->l) _propagate(t->l, t->lazy); if (t->r) _propagate(t->r, t->lazy); t->lazy = ei(); } } if constexpr (has_shift_v<Node>) { if (!t) return; if (t->shift != I{}) { if (t->l) _shift(t->l, t->shift); if (t->r) _shift(t->r, t->shift); t->shift = I{}; } } } static void _propagate([[maybe_unused]] Ptr t, [[maybe_unused]] const E &x) { if constexpr (has_lazy_v<Node>) { if (!t) return; t->lazy = h(t->lazy, x); t->val = g(t->val, x); t->sum = g(t->sum, x); } } static void _shift([[maybe_unused]] Ptr t, [[maybe_unused]] const I &sh) { if constexpr (has_shift_v<Node>) { if (!t) return; t->key += sh, t->shift += sh; } } static Ptr _update(Ptr t) { if (!t) return t; t->cnt = 1; t->sum = t->val; if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum); if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum); return t; } // key が k であるノードを探す, なければ nullptr static Ptr _find(Ptr t, I k) { while (t) { _push(t); if (k == t->key) return t; t = k < t->key ? t->l : t->r; } return nullptr; } static void _erase(Ptr &t, I k) { if (!t) return; _push(t); if (k == t->key) { Ptr tl = t->l, tr = t->r; _my_del(t); t = _merge(tl, tr); } else if (k < t->key) { _erase(t->l, k); _update(t); } else { _erase(t->r, k); _update(t); } } // [k 未満, k 以上] static pair<Ptr, Ptr> _split_by_key(Ptr t, I k) { if (!t) return {nullptr, nullptr}; _push(t); if (k == t->key) { Ptr tl = t->l; t->l = nullptr; return {tl, _update(t)}; } else if (k < t->key) { auto s = _split_by_key(t->l, k); t->l = s.second; return {s.first, _update(t)}; } else { auto s = _split_by_key(t->r, k); t->r = s.first; return {_update(t), s.second}; } } // [k 未満, k, k 超過] static array<Ptr, 3> _split_by_key3(Ptr t, I k) { if (!t) return {{nullptr, nullptr, nullptr}}; _push(t); if (k == t->key) { Ptr tl = t->l, tr = t->r; t->l = t->r = nullptr; return {{tl, _update(t), tr}}; } else if (k < t->key) { auto s = _split_by_key3(t->l, k); t->l = s[2]; return {{s[0], s[1], _update(t)}}; } else { auto s = _split_by_key3(t->r, k); t->r = s[0]; return {{_update(t), s[1], s[2]}}; } } // (-inf, i] の prod について check(prod) の (true / false) で切る template <typename C> static pair<Ptr, Ptr> _split_max_right(Ptr t, const C &check, T prod = ti()) { assert(check(prod)); if (!t) return {nullptr, nullptr}; _push(t); T p1 = f(prod, _sum(t->l)); if (check(p1)) { prod = p1; } else { auto s = _split_max_right(t->l, check, prod); t->l = s.second; return {s.first, _update(t)}; } prod = f(prod, t->val); if (!check(prod)) { Ptr tl = t->l; t->l = nullptr; return {tl, _update(t)}; } p1 = f(prod, _sum(t->r)); if (check(p1)) { return {t, nullptr}; } else { auto s = _split_max_right(t->r, check, prod); t->r = s.first; return {_update(t), s.second}; } } // [i, inf) の prod について check(prod) の (false / true) で切る template <typename C> static pair<Ptr, Ptr> _split_min_left(Ptr t, const C &check, T prod = ti()) { assert(check(prod)); if (!t) return {nullptr, nullptr}; _push(t); T p1 = f(_sum(t->r), prod); if (check(p1)) { prod = p1; } else { auto s = _split_min_left(t->r, check, prod); t->r = s.first; return {_update(t), s.second}; } prod = f(t->val, prod); if (!check(prod)) { Ptr tr = t->r; t->r = nullptr; return {_update(t), tr}; } p1 = f(_sum(t->l), prod); if (check(p1)) { return {nullptr, t}; } else { auto s = _split_min_left(t->l, check, prod); t->l = s.second; return {s.first, _update(t)}; } } // [l, inf) である地点に apply static void _apply_left(Ptr t, I l, const E &e) { if (!t) return; _push(t); if (t->key < l) { _apply_left(t->r, l, e); } else if (t->key == l) { t->val = g(t->val, e); _propagate(t->r, e); } else { _apply_left(t->l, l, e); t->val = g(t->val, e); _propagate(t->r, e); } _update(t); } // [-inf, r) である地点に apply static void _apply_right(Ptr t, I r, const E &e) { if (!t) return; _push(t); if (t->key < r) { _propagate(t->l, e); t->val = g(t->val, e); _apply_right(t->r, r, e); } else if (t->key == r) { _propagate(t->l, e); } else { _apply_right(t->l, r, e); } _update(t); } // [l, r) に apply static void _apply(Ptr t, I l, I r, const E &e) { if (!t) return; _push(t); if (t->key < l) { _apply(t->r, l, r, e); } else if (t->key == l) { t->val = g(t->val, e); _apply_right(t->r, r, e); } else if (t->key < r) { _apply_left(t->l, l, e); t->val = g(t->val, e); _apply_right(t->r, r, e); } else if (t->key == r) { _apply_left(t->l, l, e); } else { _apply(t->l, l, r, e); } _update(t); } // l 以上 static T _fold_left(Ptr t, I l) { if (!t) return ti(); _push(t); if (t->key < l) { return _fold_left(t->r, l); } else if (t->key == l) { return f(t->val, _fold_left(t->r, l)); } else { T tl = _fold_left(t->l, l); return f(f(tl, t->val), _sum(t->r)); } } // r 未満 static T _fold_right(Ptr t, I r) { if (!t) return ti(); _push(t); if (t->key < r) { T tr = _fold_right(t->r, r); return f(f(_sum(t->l), t->val), tr); } else if (t->key == r) { return _sum(t->l); } else { return _fold_right(t->l, r); } } static T _fold(Ptr t, I l, I r) { if (!t) return ti(); _push(t); if (t->key < l) { return _fold(t->r, l, r); } else if (t->key == l) { return f(t->val, _fold_right(t->r, r)); } else if (t->key < r) { T tl = _fold_left(t->l, l); T tr = _fold_right(t->r, r); return f(f(tl, t->val), tr); } else if (t->key == r) { return _fold_left(t->l, l); } else { return _fold(t->l, l, r); } } // t を根とする木の上で最小の key は? (t が空の場合は failed) static pair<I, T> _get_min_keyval(Ptr t, const I &failed) { if (!t) return {failed, ti()}; while (t->l) _push(t), t = t->l; return {t->key, t->val}; } // t を根とする木の上で最小の key は? (t が空の場合は failed) static pair<I, T> _get_max_keyval(Ptr t, const I &failed) { if (!t) return {failed, ti()}; while (t->r) _push(t), t = t->r; return {t->key, t->val}; } // t を根とする木のうち、[0, i の区間 fold が true になる最大の i は何か? // exclusive かつ (空 または[0,右]が真の場合) の場合は failed(inf) // inclusive かつ (空 または[0,0] が偽の場合) の場合は failed template <typename C, bool exclusive> static I _max_right(Ptr t, C check, const I &failed) { if (!t) return failed; _push(t); Ptr now = t; T prod_now = ti(); [[maybe_unused]] I prev = failed; while (true) { if (now->l != nullptr) { _push(now->l); auto pl = f(prod_now, now->l->sum); if (check(pl)) { prod_now = pl; } else { now = now->l; continue; } } auto pl = f(prod_now, now->val); if (!check(pl)) { if constexpr (exclusive) { return now->key; } else { return now->l ? _get_max_keyval(now->l, failed).first : prev; } } prod_now = pl; if (now->r == nullptr) { if constexpr (exclusive) { return failed; } else { return now->key; } } _push(now->r); if constexpr (!exclusive) prev = now->key; now = now->r; } } // t を根とする木のうち、i, inf) の区間 fold が true になる最小の i は何か? // inclusive かつ (空 または 存在しない) 場合は failed // exlucisve かつ (空 または [左, inf) が真) の場合は failed template <typename C, bool inclusive> static I _min_left(Ptr t, C check, const I &failed) { if (!t) return failed; _push(t); Ptr now = t; T prod_now = ti(); [[maybe_unused]] I prev = failed; while (true) { if (now->r != nullptr) { _push(now->r); auto pr = f(now->r->sum, prod_now); if (check(pr)) { prod_now = pr; } else { now = now->r; continue; } } auto pr = f(now->val, prod_now); if (!check(pr)) { if constexpr (inclusive) { return now->r ? _get_min_keyval(now->r, failed).first : prev; } else { return now->key; } } prod_now = pr; if (now->l == nullptr) { if constexpr (inclusive) { return now->key; } else { return failed; } } _push(now->l); if constexpr (inclusive) prev = now->key; now = now->l; } } static void _clear(Ptr t) { if (!t) return; if (t->l) _clear(t->l); if (t->r) _clear(t->r); _my_del(t); } static Ptr _deepcopy(Ptr t) { if (!t) return nullptr; Ptr u = _my_new(*t); if (u->l) u->l = _deepcopy(u->l); if (u->r) u->r = _deepcopy(u->r); return u; } static void _dump(Ptr t) { if (!t) return; _push(t); _dump(t->l); cerr << "## key = " << t->key << ","; cerr << "\tval = " << t->val << ", "; cerr << "\tsum = " << t->sum << ", "; cerr << "\tchild = "; cerr << "( "; if (t->l) cerr << t->l->key; if (!t->l) cerr << "nil"; cerr << ", "; if (t->r) cerr << t->r->key; if (!t->r) cerr << "nil"; cerr << " )" << endl; _dump(t->r); } static void _make_array(Ptr t, vector<pair<I, T>> &v) { if (!t) return; _push(t); if (t->l) _make_array(t->l, v); v.emplace_back(t->key, t->val); if (t->r) _make_array(t->r, v); } public: Ptr root; RBSTSegmentTreeBase() : root(nullptr) {} RBSTSegmentTreeBase(Ptr t) : root(t) {} RBSTSegmentTreeBase(const vector<T> xs, const vector<I> &vals = {}) { if (!vals.empty()) assert(xs.size() == vals.size()); int n = xs.size(); vector<pair<I, T>> dat(n); for (int i = 0; i < n; i++) dat[i] = {vals.empty() ? i : vals[i], xs[i]}; root = _build(0, n, dat); } RBSTSegmentTreeBase(RBSTSegmentTreeBase &&rhs) noexcept { root = rhs.root; } RBSTSegmentTreeBase(const RBSTSegmentTreeBase &rhs) { root = rhs.root; } ~RBSTSegmentTreeBase() = default; using RBST = RBSTSegmentTreeBase; RBST &operator=(RBST &&rhs) noexcept { root = rhs.root; return *this; } RBST &operator=(const RBST &rhs) { root = rhs.root; return *this; } RBST deepcopy() { return _deepcopy(root); } friend void swap(RBST &lhs, RBST &rhs) { swap(lhs.root, rhs.root); } void swap(RBST &rhs) { swap(root, rhs.root); } // destructive ordered _merge (max(lhs) < min(rhs)) friend RBST ordered_merge(RBST &lhs, RBST &rhs) { assert(lhs.get_max_key() < rhs.get_min_key()); return RBST{_merge(lhs.root, rhs.root)}; } // 1 点 値の書き換え void set_val(I i, T x) { auto s = _split_by_key3(root, i); if (s[1] == nullptr) { s[1] = _my_new(i, x); } else { s[1]->val = x; } root = _merge(_merge(s[0], _update(s[1])), s[2]); } // すでに要素が存在するときに値を set する。おそらく少し早い void set_val_fast(I i, T x) { static vector<Ptr> ps; ps.clear(); Ptr t = root; while (t) { _push(t); ps.push_back(t); if (i == t->key) break; t = i < t->key ? t->l : t->r; } if (!t) { set_val(i, x); return; } t->val = x; for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]); } // 1 点取得 T get_val(I i) { Ptr p = _find(root, i); return p ? p->val : ti(); } // 1 点 値の書き換え // func の返り値は void !!!!!!(参照された値を直接更新する) void apply_val(I i, const function<void(T &)> &func) { auto s = _split_by_key3(root, i); if (s[1] == nullptr) s[1] = _my_new(i); func(s[1]->val); root = _merge(_merge(s[0], _update(s[1])), s[2]); } // 1 点 値の書き換え 値が既に存在するときに早い // func の返り値は void !!!!!!(参照された値を直接更新する) void apply_val_fast(I i, const function<void(T &)> &func) { static vector<Ptr> ps; ps.clear(); Ptr t = root; while (t) { _push(t); ps.push_back(t); if (i == t->key) break; t = i < t->key ? t->l : t->r; } if (!t) { apply_val(i, func); return; } func(t->val); for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]); } // 頂点の削除 virtual void erase(I i) { _erase(root, i); } // 範囲作用 void apply(I l, I r, const E &e) { if (l >= r) return; _apply(root, l, r, e); } void apply_all(const E &e) { _propagate(root, e); } // 範囲取得 T fold(I l, I r) { if (l >= r) return ti(); return _fold(root, l, r); } T fold_all() { return _sum(root); } void shift(const I &sh) { _shift(root, sh); } // key 最小を取得 I get_min_key(I failed = -1) { return _get_min_keyval(root, failed).first; } // key 最大を取得 I get_max_key(I failed = -1) { return _get_max_keyval(root, failed).first; } // (key, val) 最小を取得 pair<I, T> get_min_keyval(I failed = -1) { return _get_min_keyval(root, failed); } // (key, val) 最大を取得 pair<I, T> get_max_keyval(I failed = -1) { return _get_max_keyval(root, failed); } // (key, val) 最小を pop pair<I, T> pop_min_keyval(I failed = -1) { assert(root != nullptr); auto kv = _get_min_keyval(root, failed); erase(kv.first); return kv; } // (key, val) 最大を取得 pair<I, T> pop_max_keyval(I failed = -1) { assert(root != nullptr); auto kv = _get_max_keyval(root, failed); erase(kv.first); return kv; } // n 未満の i のうち、[i, n) の区間 fold が true になる最小の i は何か? // (存在しない場合は failed を返す) template <typename C> I min_left(I n, C check, I failed) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _min_left<C, true>(x, check, failed); root = _merge(x, y); return res; } // n 未満の i のうち、(i, n) の区間 fold が true になる最小の i は何か? // (空だったり (左端, n) が 真の場合は minus_infty を返す) template <typename C> I min_left_exclusive(I n, C check, I minus_infty) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _min_left<C, false>(x, check, minus_infty); root = _merge(x, y); return res; } // n 以上の i のうち、[n, i) の区間 fold が true になる最大の i は何か? // (空だったり [n, 右端] が true の場合は infty を返す) template <typename C> I max_right(I n, C check, I infty) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _max_right<C, true>(y, check, infty); root = _merge(x, y); return res; } // n 以上の i のうち、[n, i] の区間 fold が true になる最大の i は何か? // (存在しない場合は failed を返す) template <typename C> I max_right_inclusive(I n, C check, I failed) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _max_right<C, false>(y, check, failed); root = _merge(x, y); return res; } // (key 未満, key 以上) で分割 // 呼び出し後のオブジェクトは空のセグ木になる pair<RBST, RBST> split_by_key(const I &key) { auto [x, y] = _split_by_key(root, key); root = nullptr; return make_pair(RBST{x}, RBST{y}); } // [i, inf) の区間積が (false, true) になる境界で分割 // 呼び出し後のオブジェクトは空のセグ木になる template <typename C> pair<RBST, RBST> split_min_left(const C &check) { assert(check(ti()) == true); auto [x, y] = _split_min_left(root, check); root = nullptr; return make_pair(RBST{x}, RBST{y}); } // (-inf, i] の区間積が (true, false) になる境界で分割 // 呼び出し後のオブジェクトは空のセグ木になる template <typename C> pair<RBST, RBST> split_max_right(const C &check) { assert(check(ti()) == true); auto [x, y] = _split_max_right(root, check); root = nullptr; return make_pair(RBST{x}, RBST{y}); } void clear() { _clear(root), root = nullptr; } int size() { return _count(root); } bool empty() { return !root; } void dump() { cerr << "***** dump start *****" << endl; _dump(root); cerr << "****** dump end ******" << endl; } // 列を配列に変換して返す vector<pair<I, T>> make_array() { vector<pair<I, T>> res; _make_array(root, res); return res; } }; namespace RBSTSegmentTreeImpl { bool _ei() { return false; } template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct ShiftableLazySegNode { ShiftableLazySegNode *l, *r; I key, shift; T val, sum; E lazy; int cnt; ShiftableLazySegNode(const I &i, const T &t = ti()) : l(), r(), key(i), shift(I{}), val(t), sum(t), lazy(ei()), cnt(1) {} }; template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> using RBSTShiftableLazySegmentTree = RBSTSegmentTreeBase<ShiftableLazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E, f, g, h, ti, ei>; template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct LazySegNode { LazySegNode *l, *r; I key; T val, sum; E lazy; int cnt; LazySegNode(const I &i, const T &t = ti()) : l(), r(), key(i), val(t), sum(t), lazy(ei()), cnt(1) {} }; template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> using RBSTLazySegmentTree = RBSTSegmentTreeBase<LazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E, f, g, h, ti, ei>; template <typename I, typename T, T (*f)(T, T), T (*ti)()> struct SegNode { SegNode *l, *r; I key; T val, sum; int cnt; SegNode(const I &i, const T &t = ti()) : l(), r(), key(i), val(t), sum(t), cnt(1) {} }; template <typename I, typename T, T (*f)(T, T), T (*ti)()> using RBSTSegmentTree = RBSTSegmentTreeBase<SegNode<I, T, f, ti>, I, T, bool, f, nullptr, nullptr, ti, _ei>; } // namespace RBSTSegmentTreeImpl using RBSTSegmentTreeImpl::RBSTLazySegmentTree; using RBSTSegmentTreeImpl::RBSTSegmentTree; using RBSTSegmentTreeImpl::RBSTShiftableLazySegmentTree; /** * @brief RBST-based Dynamic Lazy Segment Tree */ #line 6 "verify/verify-unit-test/rbst-segment-tree.test.cpp" // #line 2 "misc/all.hpp" #line 2 "misc/fastio.hpp" #line 8 "misc/fastio.hpp" using namespace std; #line 12 "misc/fastio.hpp" namespace fastio { static constexpr int SZ = 1 << 17; static constexpr int offset = 64; char inbuf[SZ], outbuf[SZ]; int in_left = 0, in_right = 0, out_right = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; void load() { int len = in_right - in_left; memmove(inbuf, inbuf + in_left, len); in_right = len + fread(inbuf + len, 1, SZ - len, stdin); in_left = 0; } void flush() { fwrite(outbuf, 1, out_right, stdout); out_right = 0; } void skip_space() { if (in_left + offset > in_right) load(); while (inbuf[in_left] <= ' ') in_left++; } void single_read(char& c) { if (in_left + offset > in_right) load(); skip_space(); c = inbuf[in_left++]; } void single_read(string& S) { skip_space(); while (true) { if (in_left == in_right) load(); int i = in_left; for (; i != in_right; i++) { if (inbuf[i] <= ' ') break; } copy(inbuf + in_left, inbuf + i, back_inserter(S)); in_left = i; if (i != in_right) break; } } template <typename T, enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr> void single_read(T& x) { if (in_left + offset > in_right) load(); skip_space(); char c = inbuf[in_left++]; [[maybe_unused]] bool minus = false; if constexpr (internal::is_broadly_signed_v<T>) { if (c == '-') minus = true, c = inbuf[in_left++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = inbuf[in_left++]; } if constexpr (internal::is_broadly_signed_v<T>) { if (minus) x = -x; } } void rd() {} template <typename Head, typename... Tail> void rd(Head& head, Tail&... tail) { single_read(head); rd(tail...); } void single_write(const char& c) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = c; } void single_write(const bool& b) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = b ? '1' : '0'; } void single_write(const string& S) { flush(), fwrite(S.data(), 1, S.size(), stdout); } void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); } template <typename T, enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr> void single_write(const T& _x) { if (out_right > SZ - offset) flush(); if (_x == 0) { outbuf[out_right++] = '0'; return; } T x = _x; if constexpr (internal::is_broadly_signed_v<T>) { if (x < 0) outbuf[out_right++] = '-', x = -x; } constexpr int buffer_size = sizeof(T) * 10 / 4; char buf[buffer_size]; int i = buffer_size; while (x >= 10000) { i -= 4; memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; } if (x < 100) { if (x < 10) { outbuf[out_right] = '0' + x; ++out_right; } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; outbuf[out_right] = '0' + q; outbuf[out_right + 1] = '0' + r; out_right += 2; } } else { if (x < 1000) { memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3); out_right += 3; } else { memcpy(outbuf + out_right, pre.num + (x << 2), 4); out_right += 4; } } memcpy(outbuf + out_right, buf + i, buffer_size - i); out_right += buffer_size - i; } void wt() {} template <typename Head, typename... Tail> void wt(const Head& head, const Tail&... tail) { single_write(head); wt(forward<const Tail>(tail)...); } template <typename... Args> void wtn(const Args&... x) { wt(forward<const Args>(x)...); wt('\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::skip_space; using fastio::wt; using fastio::wtn; #line 2 "misc/rng.hpp" #line 2 "internal/internal-seed.hpp" #line 4 "internal/internal-seed.hpp" using namespace std; namespace internal { unsigned long long non_deterministic_seed() { unsigned long long m = chrono::duration_cast<chrono::nanoseconds>( chrono::high_resolution_clock::now().time_since_epoch()) .count(); m ^= 9845834732710364265uLL; m ^= m << 24, m ^= m >> 31, m ^= m << 35; return m; } unsigned long long deterministic_seed() { return 88172645463325252UL; } // 64 bit の seed 値を生成 (手元では seed 固定) // 連続で呼び出すと同じ値が何度も返ってくるので注意 // #define RANDOMIZED_SEED するとシードがランダムになる unsigned long long seed() { #if defined(NyaanLocal) && !defined(RANDOMIZED_SEED) return deterministic_seed(); #else return non_deterministic_seed(); #endif } } // namespace internal #line 4 "misc/rng.hpp" namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = internal::seed(); return _x ^= _x << 7, _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % u64(r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % u64(r - l); } // choose n numbers from [l, r) without overlapping vector<i64> randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set<i64> s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector<i64> ret; for (auto& x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } // [l, r) double rnd(double l, double r) { assert(l < r); return l + rnd() * (r - l); } template <typename T> void randshf(vector<T>& v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; #line 2 "misc/timer.hpp" #line 4 "misc/timer.hpp" using namespace std; struct Timer { chrono::high_resolution_clock::time_point st; Timer() { reset(); } void reset() { st = chrono::high_resolution_clock::now(); } long long elapsed() { auto ed = chrono::high_resolution_clock::now(); return chrono::duration_cast<chrono::milliseconds>(ed - st).count(); } long long operator()() { return elapsed(); } }; #line 8 "verify/verify-unit-test/rbst-segment-tree.test.cpp" // #line 2 "segment-tree/lazy-segment-tree.hpp" // LazySegmentTree template <typename T, typename E, typename F, typename G, typename H> struct LazySegmentTree { int n, height; F f; G g; H h; T ti; E ei; vector<T> dat; vector<E> laz; LazySegmentTree(int _n, F _f, G _g, H _h, T _ti, E _ei) : f(_f), g(_g), h(_h), ti(_ti), ei(_ei) { init(_n); } LazySegmentTree(const vector<T> &v, F _f, G _g, H _h, T _ti, E _ei) : f(_f), g(_g), h(_h), ti(_ti), ei(_ei) { init((int)v.size()); build(v); } void init(int _n) { n = 1; height = 0; while (n < _n) n <<= 1, height++; dat.assign(2 * n, ti); laz.assign(2 * n, ei); } void build(const vector<T> &v) { int _n = v.size(); init(_n); for (int i = 0; i < _n; i++) dat[n + i] = v[i]; for (int i = n - 1; i; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]); } inline T reflect(int k) { return laz[k] == ei ? dat[k] : g(dat[k], laz[k]); } inline void eval(int k) { if (laz[k] == ei) return; laz[(k << 1) | 0] = h(laz[(k << 1) | 0], laz[k]); laz[(k << 1) | 1] = h(laz[(k << 1) | 1], laz[k]); dat[k] = reflect(k); laz[k] = ei; } inline void thrust(int k) { for (int i = height; i; i--) eval(k >> i); } inline void recalc(int k) { while (k >>= 1) dat[k] = f(reflect((k << 1) | 0), reflect((k << 1) | 1)); } void update(int a, int b, E x) { if (a >= b) return; thrust(a += n); thrust(b += n - 1); for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) { if (l & 1) laz[l] = h(laz[l], x), l++; if (r & 1) --r, laz[r] = h(laz[r], x); } recalc(a); recalc(b); } void set_val(int a, T x) { thrust(a += n); dat[a] = x; laz[a] = ei; recalc(a); } T get_val(int a) { thrust(a += n); return reflect(a); } T query(int a, int b) { if (a >= b) return ti; thrust(a += n); thrust(b += n - 1); T vl = ti, vr = ti; for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) { if (l & 1) vl = f(vl, reflect(l++)); if (r & 1) vr = f(reflect(--r), vr); } return f(vl, vr); } }; #line 10 "verify/verify-unit-test/rbst-segment-tree.test.cpp" // #line 2 "math/affine-transformation.hpp" template <typename mint> struct Affine { mint a, b; constexpr Affine() : a(1), b(0) {} constexpr Affine(mint _a, mint _b) : a(_a), b(_b) {} mint operator()(mint x) { return a * x + b; } // R(L(x)) friend Affine operator*(const Affine& l, const Affine& r) { return Affine(l.a * r.a, l.b * r.a + r.b); } bool operator==(const Affine& r) const { return a == r.a && b == r.b; } bool operator!=(const Affine& r) const { return a != r.a || b != r.b; } friend ostream& operator<<(ostream& os, const Affine& r) { os << "( " << r.a << ", " << r.b << " )"; return os; } }; /** * @brief アフィン変換 */ #line 2 "modint/montgomery-modint.hpp" template <uint32_t mod> struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt<mod>(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; #line 13 "verify/verify-unit-test/rbst-segment-tree.test.cpp" using mint = LazyMontgomeryModInt<998244353>; using T = pair<mint, mint>; using E = Affine<mint>; T f(T a, T b) { return T(a.first + b.first, a.second + b.second); } T g(T a, E b) { return T(a.first * b.a + a.second * b.b, a.second); } E h(E a, E b) { return a * b; }; T ti() { return T{}; } E ei() { return E{}; } using namespace Nyaan; // すべての関数のテスト。ただしセグ木にぶたん系は別途 verify する void test(const int N = 100, const int Q = 100) { RBSTLazySegmentTree<int, T, E, f, g, h, ti, ei> seg1; LazySegmentTree seg2(N, f, g, h, ti(), ei()); ll MOD = 998244353; vector<function<void(void)>> funcs{ [&]() { // set_val int i = rng(0, N - 1); T x{rng(0, MOD - 1), 1}; seg1.set_val(i, x); seg2.set_val(i, x); }, [&]() { // set_val_fast int i = rng(0, N - 1); T x{rng(0, MOD - 1), 1}; seg1.set_val_fast(i, x); seg2.set_val(i, x); }, [&]() { // get_val int i = rng(0, N - 1); T v1 = seg1.get_val(i); T v2 = seg2.get_val(i); assert(v1 == v2 and "get_val"); }, [&]() { // apply_val int i = rng(0, N - 1); E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply_val(i, [&](T& t) { t = g(t, x); }); seg2.update(i, i + 1, x); }, [&]() { // apply_val_fast int i = rng(0, N - 1); E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply_val_fast(i, [&](T& t) { t = g(t, x); }); seg2.update(i, i + 1, x); }, [&]() { // erase int i = rng(0, N - 1); seg1.erase(i); seg2.set_val(i, T{}); }, [&]() { // apply int l = rng(0, N - 1); int r = rng(0, N - 1); if (l > r) swap(l, r); r++; E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply(l, r, x); seg2.update(l, r, x); }, [&]() { // fold int l = rng(0, N - 1); int r = rng(0, N - 1); if (l > r) swap(l, r); r++; auto v1 = seg1.fold(l, r); auto v2 = seg2.query(l, r); assert(v1 == v2 and "fold"); }, [&]() { // get_min_key, get_min_keyval int v1 = -1; while (true) { v1 = seg1.get_min_key(); if (v1 == -1) break; T val = seg2.get_val(v1); if (val.second == 1) break; if (val.second == 0) { seg1.erase(v1); seg2.set_val(v1, T{}); } else { assert(false and "get_min_key"); } } int v2 = -1; if (seg2.query(0, N).second != 0) { // [0, n) は非ゼロですか? int ng = 0, ok = N; while (ng + 1 < ok) { int m = (ng + ok) / 2; mint x = seg2.query(0, m).second; (x == 0 ? ng : ok) = m; } v2 = ok - 1; } assert(v1 == v2 && "get_min_key"); if (v1 == -1) { auto kv1 = seg1.get_min_keyval(); assert(kv1.second == T{} && "get_min_keyval"); } else { auto kv1 = seg1.get_min_keyval(); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "get_min_keyval"); } }, [&]() { // get_max_key, get_max_keyval int v1 = -1; while (true) { v1 = seg1.get_max_key(); if (v1 == -1) break; T val = seg2.get_val(v1); if (val.second == 1) break; if (val.second == 0) { seg1.erase(v1); seg2.set_val(v1, T{}); } else { assert(false and "get_max_key"); } } int v2 = -1; if (seg2.query(0, N).second != 0) { // [i, N) は非ゼロですか? int ok = 0, ng = N; while (ok + 1 < ng) { int m = (ng + ok) / 2; mint x = seg2.query(m, N).second; (x == 0 ? ng : ok) = m; } v2 = ok; } assert(v1 == v2 && "get_max_key"); if (v1 == -1) { auto kv1 = seg1.get_max_keyval(); assert(kv1.second == T{} && "get_max_keyval"); } else { auto kv1 = seg1.get_max_keyval(); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "get_mix_keyval"); } }, [&]() { // pop_min_key int v2 = -1; if (seg2.query(0, N).second != 0) { // [0, n) は非ゼロですか? int ng = 0, ok = N; while (ng + 1 < ok) { int m = (ng + ok) / 2; mint x = seg2.query(0, m).second; (x == 0 ? ng : ok) = m; } v2 = ok - 1; } if (v2 != -1) { pair<int, T> kv1; do { kv1 = seg1.pop_min_keyval(); } while (kv1.second.second == 0); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "pop_min_keyval"); seg2.set_val(v2, T{}); } }, [&]() { // pop_max_key int v2 = -1; if (seg2.query(0, N).second != 0) { // [i, N) は非ゼロですか? int ok = 0, ng = N; while (ok + 1 < ng) { int m = (ng + ok) / 2; mint x = seg2.query(m, N).second; (x == 0 ? ng : ok) = m; } v2 = ok; } if (v2 != -1) { pair<int, T> kv1; do { kv1 = seg1.pop_max_keyval(); } while (kv1.second.second == 0); auto kv2 = make_pair(v2, seg2.get_val(v2)); assert(kv1 == kv2 && "pop_max_keyval"); seg2.set_val(v2, T{}); } }, }; rep(_, 10) { int qq = vector<ll>{0LL, rng(1, 10), rng(1, Q)}[rng(0, 2)]; rep(qnum, qq) { int c = rng(0, sz(funcs) - 1); // trc(c, "cmd"); funcs[c](); } { // make_array auto vec1 = seg1.make_array(); rep(i, sz(vec1) - 1) assert(vec1[i].fi < vec1[i + 1].fi); vector<pair<int, T>> vec2; rep(i, N) { T val = seg2.get_val(i); if (val != T{}) vec2.push_back({i, val}); } // trc(vec1); // trc(vec2); int i1 = 0, i2 = 0; while (i1 != sz(vec1) and i2 != sz(vec2)) { while (i1 != sz(vec1) and vec1[i1].second == T{}) i1++; if (i1 == sz(vec1)) break; assert(vec1[i1] == vec2[i2] and "make_array"); i1++, i2++; } while (i1 != sz(vec1) and vec1[i1].second == T{}) i1++; assert(i1 == sz(vec1) and i2 == sz(vec2) and "make_array"); // trc("make_array ok"); } seg1.clear(); rep(i, N) seg2.set_val(i, T{}); } } void test_tl(const int N = 5 * TEN(5), const int Q = 5 * TEN(5)) { ll MOD = 998244353; V<T> init; rep(i, N) init.emplace_back(rng(0, MOD - 1), rng(0, MOD - 1)); RBSTLazySegmentTree<int, T, E, f, g, h, ti, ei> seg1(init); LazySegmentTree seg2(init, f, g, h, ti(), ei()); vector<function<void(void)>> funcs{ [&]() { // apply int l = +rng(0, 10); int r = -rng(0, 10) + N; E x{rng(0, MOD - 1), rng(0, MOD - 1)}; seg1.apply(l, r, x); seg2.update(l, r, x); }, [&]() { // fold int l = +rng(0, 10); int r = -rng(0, 10) + N; auto v1 = seg1.fold(l, r); auto v2 = seg2.query(l, r); assert(v1 == v2 and "fold"); }, }; rep(qnum, Q) { int c = rng(0, sz(funcs) - 1); // trc(c, "cmd"); funcs[c](); } } void q() { rep(t, 10) test(10, TEN(4)); // rep(t, 10) test(100, TEN(4)); // rep(t, 2) test(TEN(4), TEN(2)); // test(10, TEN(4)); test(2, TEN(4)); test(1, TEN(4)); cerr << "test OK" << endl; Timer timer; test_tl(); cerr << "test_tl OK" << endl; cerr << "time : " << timer.elapsed() << endl; } void Nyaan::solve() { q(); int a, b; cin >> a >> b; cout << a + b << endl; }