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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "alg/monoid/add_pair.hpp" #include "ds/splaytree/splaytree_acted_set.hpp" // (所持金, 操作回数, query index) struct AS { using Monoid_A = Monoid_Add_Pair<int>; using A = Monoid_A::value_type; using S = tuple<int, int, int>; static S act(const S& s, const A& x) { auto [a, b, c] = s; return {a + x.fi, b + x.se, c}; } }; vc<int> solve_cf702F(vc<pair<int, int>> CQ, vc<int> query) { const int Q = len(query); sort(all(CQ), [&](auto& a, auto& b) -> bool { if (a.se != b.se) return a.se > b.se; return a.fi < b.fi; }); using T = tuple<int, int, int>; vc<T> dat(Q); FOR(q, Q) { int x = query[q]; dat[q] = {x, 0, q}; } sort(all(dat)); const int MAX = 500'000; SplayTree_ActedSet<AS> X(MAX); using np = decltype(X)::np; using S = typename AS::S; np root = X.new_node(dat); FOR(i, len(CQ)) { ll c = CQ[i].fi; np nm, nr; tie(root, nr) = X.split_max_right(root, [&](S& s) { return get<0>(s) < c; }); X.apply(nr, {-c, 1}); tie(nm, nr) = X.split_max_right(nr, [&](S& s) { return get<0>(s) < c; }); for (auto&& [aa, bb, cc]: X.get_all(nm)) assert(aa < c); for (auto&& [aa, bb, cc]: X.get_all(nr)) assert(aa >= c); for (auto [val, cnt, idx]: X.get_all(nm)) { ll t = val; auto [l_root, r_root] = X.split_max_right(root, [&](S& s) { return get<0>(s) < t; }); root = X.merge(l_root, X.new_node({val, cnt, idx})); root = X.merge(root, r_root); } root = X.merge(root, nr); } vc<int> ANS(Q); for (auto [val, cnt, idx]: X.get_all(root)) { ANS[idx] = cnt; } return ANS; } void test_1() { vc<pair<int, int>> CQ; CQ.eb(7, 5); CQ.eb(3, 5); CQ.eb(4, 3); vc<int> query = {13, 14}; vc<int> ANS = solve_cf702F(CQ, query); assert(ANS == vc<int>({2, 3})); } void test_2() { vc<pair<int, int>> CQ; CQ.eb(100, 500); CQ.eb(50, 499); vc<int> query = {50, 200, 150, 100}; vc<int> ANS = solve_cf702F(CQ, query); assert(ANS == vc<int>({1, 2, 2, 1})); } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test_1(); test_2(); solve(); return 0; }
#line 1 "test/1_mytest/cf702_F_splay.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template <typename T> T ceil(T x, T y) { return floor(x + y - 1, y); } template <typename T> T bmod(T x, T y) { return x - y * floor(x, y); } template <typename T> pair<T, T> divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 2 "alg/monoid/add_pair.hpp" template <typename E> struct Monoid_Add_Pair { using value_type = pair<E, E>; using X = value_type; static constexpr X op(const X &x, const X &y) { return {x.fi + y.fi, x.se + y.se}; } static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; } static constexpr X unit() { return {0, 0}; } static constexpr bool commute = true; }; #line 2 "ds/splaytree/splaytree.hpp" /* update でちゃんと prod が計算されてくれれば prod は op(lprod,x,rprod) でなくてもよい. */ // Node 型を別に定義して使う template <typename Node> struct SplayTree { Node *pool; const int NODES; int pid; using np = Node *; using X = typename Node::value_type; using A = typename Node::operator_type; vc<np> FREE; SplayTree(int NODES) : NODES(NODES), pid(0) { pool = new Node[NODES]; } ~SplayTree() { delete[] pool; } void free_subtree(np c) { if (!c) return; auto dfs = [&](auto &dfs, np c) -> void { if (c->l) dfs(dfs, c->l); if (c->r) dfs(dfs, c->r); FREE.eb(c); }; dfs(dfs, c); } void reset() { pid = 0; FREE.clear(); } np new_root() { return nullptr; } np new_node(const X &x) { assert(!FREE.empty() || pid < NODES); np n = (FREE.empty() ? &(pool[pid++]) : POP(FREE)); Node::new_node(n, x); return n; } np new_node(const vc<X> &dat) { auto dfs = [&](auto &dfs, int l, int r) -> np { if (l == r) return nullptr; if (r == l + 1) return new_node(dat[l]); int m = (l + r) / 2; np l_root = dfs(dfs, l, m); np r_root = dfs(dfs, m + 1, r); np root = new_node(dat[m]); root->l = l_root, root->r = r_root; if (l_root) l_root->p = root; if (r_root) r_root->p = root; root->update(); return root; }; return dfs(dfs, 0, len(dat)); } u32 get_size(np root) { return (root ? root->size : 0); } np merge(np l_root, np r_root) { if (!l_root) return r_root; if (!r_root) return l_root; assert((!l_root->p) && (!r_root->p)); splay_kth(r_root, 0); // splay したので prop 済 r_root->l = l_root; l_root->p = r_root; r_root->update(); return r_root; } np merge3(np a, np b, np c) { return merge(merge(a, b), c); } np merge4(np a, np b, np c, np d) { return merge(merge(merge(a, b), c), d); } pair<np, np> split(np root, u32 k) { assert(!root || !root->p); if (k == 0) return {nullptr, root}; if (k == (root->size)) return {root, nullptr}; splay_kth(root, k - 1); np right = root->r; root->r = nullptr, right->p = nullptr; root->update(); return {root, right}; } tuple<np, np, np> split3(np root, u32 l, u32 r) { np nm, nr; tie(root, nr) = split(root, r); tie(root, nm) = split(root, l); return {root, nm, nr}; } tuple<np, np, np, np> split4(np root, u32 i, u32 j, u32 k) { np d; tie(root, d) = split(root, k); auto [a, b, c] = split3(root, i, j); return {a, b, c, d}; } // 部分木が区間 [l,r) に対応するようなノードを作って返す // そのノードが root になるわけではないので、 // このノードを参照した後にすぐに splay して根に持ち上げること void goto_between(np &root, u32 l, u32 r) { if (l == 0 && r == root->size) return; if (l == 0) { splay_kth(root, r); root = root->l; return; } if (r == root->size) { splay_kth(root, l - 1); root = root->r; return; } splay_kth(root, r); np rp = root; root = rp->l; root->p = nullptr; splay_kth(root, l - 1); root->p = rp; rp->l = root; rp->update(); root = root->r; } vc<X> get_all(const np &root) { vc<X> res; auto dfs = [&](auto &dfs, np root) -> void { if (!root) return; root->prop(); dfs(dfs, root->l); res.eb(root->get()); dfs(dfs, root->r); }; dfs(dfs, root); return res; } X get(np &root, u32 k) { assert(root == nullptr || !root->p); splay_kth(root, k); return root->get(); } void set(np &root, u32 k, const X &x) { assert(root != nullptr && !root->p); splay_kth(root, k); root->set(x); } void multiply(np &root, u32 k, const X &x) { assert(root != nullptr && !root->p); splay_kth(root, k); root->multiply(x); } X prod(np &root, u32 l, u32 r) { assert(root == nullptr || !root->p); using Mono = typename Node::Monoid_X; if (l == r) return Mono::unit(); assert(0 <= l && l < r && r <= root->size); goto_between(root, l, r); X res = root->prod; splay(root, true); return res; } X prod(np &root) { assert(root == nullptr || !root->p); using Mono = typename Node::Monoid_X; return (root ? root->prod : Mono::unit()); } void apply(np &root, u32 l, u32 r, const A &a) { if (l == r) return; assert(0 <= l && l < r && r <= root->size); goto_between(root, l, r); root->apply(a); splay(root, true); } void apply(np &root, const A &a) { if (!root) return; root->apply(a); } void reverse(np &root, u32 l, u32 r) { assert(root == nullptr || !root->p); if (l == r) return; assert(0 <= l && l < r && r <= root->size); goto_between(root, l, r); root->reverse(); splay(root, true); } void reverse(np root) { if (!root) return; root->reverse(); } void rotate(Node *n) { // n を根に近づける。prop, update は rotate の外で行う。 Node *pp, *p, *c; p = n->p; pp = p->p; if (p->l == n) { c = n->r; n->r = p; p->l = c; } else { c = n->l; n->l = p; p->r = c; } if (pp && pp->l == p) pp->l = n; if (pp && pp->r == p) pp->r = n; n->p = pp; p->p = n; if (c) c->p = p; } void prop_from_root(np c) { if (!c->p) { c->prop(); return; } prop_from_root(c->p); c->prop(); } void splay(Node *me, bool prop_from_root_done) { // これを呼ぶ時点で、me の祖先(me を除く)は既に prop 済であることを仮定 // 特に、splay 終了時点で me は upd / prop 済である if (!prop_from_root_done) prop_from_root(me); me->prop(); while (me->p) { np p = me->p; np pp = p->p; if (!pp) { rotate(me); p->update(); break; } bool same = (p->l == me && pp->l == p) || (p->r == me && pp->r == p); if (same) rotate(p), rotate(me); if (!same) rotate(me), rotate(me); pp->update(), p->update(); } // me の update は最後だけでよい me->update(); } void splay_kth(np &root, u32 k) { assert(0 <= k && k < (root->size)); while (1) { root->prop(); u32 sl = (root->l ? root->l->size : 0); if (k == sl) break; if (k < sl) root = root->l; else { k -= sl + 1; root = root->r; } } splay(root, true); } // check(x), 左側のノード全体が check を満たすように切る template <typename F> pair<np, np> split_max_right(np root, F check) { if (!root) return {nullptr, nullptr}; assert(!root->p); np c = find_max_right(root, check); if (!c) { splay(root, true); return {nullptr, root}; } splay(c, true); np right = c->r; if (!right) return {c, nullptr}; right->p = nullptr; c->r = nullptr; c->update(); return {c, right}; } // check(x, cnt), 左側のノード全体が check を満たすように切る template <typename F> pair<np, np> split_max_right_cnt(np root, F check) { if (!root) return {nullptr, nullptr}; assert(!root->p); np c = find_max_right_cnt(root, check); if (!c) { splay(root, true); return {nullptr, root}; } splay(c, true); np right = c->r; if (!right) return {c, nullptr}; right->p = nullptr; c->r = nullptr; c->update(); return {c, right}; } // 左側のノード全体の prod が check を満たすように切る template <typename F> pair<np, np> split_max_right_prod(np root, F check) { if (!root) return {nullptr, nullptr}; assert(!root->p); np c = find_max_right_prod(root, check); if (!c) { splay(root, true); return {nullptr, root}; } splay(c, true); np right = c->r; if (!right) return {c, nullptr}; right->p = nullptr; c->r = nullptr; c->update(); return {c, right}; } template <typename F> np find_max_right(np root, const F &check) { // 最後に見つけた ok の点、最後に探索した点 np last_ok = nullptr, last = nullptr; while (root) { last = root; root->prop(); if (check(root->x)) { last_ok = root; root = root->r; } else { root = root->l; } } splay(last, true); return last_ok; } template <typename F> np find_max_right_cnt(np root, const F &check) { // 最後に見つけた ok の点、最後に探索した点 np last_ok = nullptr, last = nullptr; ll n = 0; while (root) { last = root; root->prop(); ll ns = (root->l ? root->l->size : 0); if (check(root->x, n + ns + 1)) { last_ok = root; n += ns + 1; root = root->r; } else { root = root->l; } } splay(last, true); return last_ok; } template <typename F> np find_max_right_prod(np root, const F &check) { using Mono = typename Node::Monoid_X; X prod = Mono::unit(); // 最後に見つけた ok の点、最後に探索した点 np last_ok = nullptr, last = nullptr; while (root) { last = root; root->prop(); np tmp = root->r; root->r = nullptr; root->update(); X lprod = Mono::op(prod, root->prod); root->r = tmp; root->update(); if (check(lprod)) { prod = lprod; last_ok = root; root = root->r; } else { root = root->l; } } splay(last, true); return last_ok; } }; #line 2 "ds/splaytree/splaytree_acted_set.hpp" namespace SplayTreeNodes { template <typename ActedSet> struct Node_AS { using Monoid_A = typename ActedSet::Monoid_A; using A = typename ActedSet::A; using S = typename ActedSet::S; using value_type = S; using operator_type = A; using np = Node_AS *; np p, l, r; S x; A lazy; u32 size; bool rev; static void new_node(np n, const S &x) { n->p = n->l = n->r = nullptr; n->x = x; n->lazy = Monoid_A::unit(); n->size = 1; n->rev = 0; } void update() { size = 1; if (l) { size += l->size; } if (r) { size += r->size; } } void prop() { if (lazy != Monoid_A::unit()) { if (l) { l->apply(lazy); } if (r) { r->apply(lazy); } lazy = Monoid_A::unit(); } if (rev) { if (l) { l->rev ^= 1; swap(l->l, l->r); } if (r) { r->rev ^= 1; swap(r->l, r->r); } rev = 0; } } // update, prop 以外で呼ばれるものは、splay 後であることが想定されている。 // したがってその時点で update, prop 済であることを仮定してよい。 S get() { return x; } void set(const S &xx) { x = xx; update(); } void apply(const A &a) { x = ActedSet::act(x, a); lazy = Monoid_A::op(lazy, a); } void reverse() { swap(l, r); rev ^= 1; } }; template <typename ActedSet> using SplayTree_ActedSet = SplayTree<Node_AS<ActedSet>>; } // namespace SplayTreeNodes using SplayTreeNodes::SplayTree_ActedSet; #line 5 "test/1_mytest/cf702_F_splay.test.cpp" // (所持金, 操作回数, query index) struct AS { using Monoid_A = Monoid_Add_Pair<int>; using A = Monoid_A::value_type; using S = tuple<int, int, int>; static S act(const S& s, const A& x) { auto [a, b, c] = s; return {a + x.fi, b + x.se, c}; } }; vc<int> solve_cf702F(vc<pair<int, int>> CQ, vc<int> query) { const int Q = len(query); sort(all(CQ), [&](auto& a, auto& b) -> bool { if (a.se != b.se) return a.se > b.se; return a.fi < b.fi; }); using T = tuple<int, int, int>; vc<T> dat(Q); FOR(q, Q) { int x = query[q]; dat[q] = {x, 0, q}; } sort(all(dat)); const int MAX = 500'000; SplayTree_ActedSet<AS> X(MAX); using np = decltype(X)::np; using S = typename AS::S; np root = X.new_node(dat); FOR(i, len(CQ)) { ll c = CQ[i].fi; np nm, nr; tie(root, nr) = X.split_max_right(root, [&](S& s) { return get<0>(s) < c; }); X.apply(nr, {-c, 1}); tie(nm, nr) = X.split_max_right(nr, [&](S& s) { return get<0>(s) < c; }); for (auto&& [aa, bb, cc]: X.get_all(nm)) assert(aa < c); for (auto&& [aa, bb, cc]: X.get_all(nr)) assert(aa >= c); for (auto [val, cnt, idx]: X.get_all(nm)) { ll t = val; auto [l_root, r_root] = X.split_max_right(root, [&](S& s) { return get<0>(s) < t; }); root = X.merge(l_root, X.new_node({val, cnt, idx})); root = X.merge(root, r_root); } root = X.merge(root, nr); } vc<int> ANS(Q); for (auto [val, cnt, idx]: X.get_all(root)) { ANS[idx] = cnt; } return ANS; } void test_1() { vc<pair<int, int>> CQ; CQ.eb(7, 5); CQ.eb(3, 5); CQ.eb(4, 3); vc<int> query = {13, 14}; vc<int> ANS = solve_cf702F(CQ, query); assert(ANS == vc<int>({2, 3})); } void test_2() { vc<pair<int, int>> CQ; CQ.eb(100, 500); CQ.eb(50, 499); vc<int> query = {50, 200, 150, 100}; vc<int> ANS = solve_cf702F(CQ, query); assert(ANS == vc<int>({1, 2, 2, 1})); } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test_1(); test_2(); solve(); return 0; }