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#define PROBLEM "https://yukicoder.me/problems/no/1826" #include "my_template.hpp" #include "other/io.hpp" #include "ds/segtree/dynamic_segtree_sparse.hpp" #include "alg/monoid/max.hpp" void solve() { LL(N); vi X, Y, V; FOR(N) { LL(t, x, v); X.eb(t - x), Y.eb(t + x), V.eb(v); } auto I = argsort(X); X = rearrange(X, I), Y = rearrange(Y, I), V = rearrange(V, I); ll LIM = 1LL << 32; Dynamic_SegTree_Sparse<Monoid_Max<ll>, false> seg(N + 1, -LIM, LIM); using np = typename decltype(seg)::np; np root = nullptr; root = seg.set(root, 0, 0); FOR(i, N) { ll x = X[i], y = Y[i], v = V[i]; if (x < 0) continue; ll t = seg.prod(root, -LIM, y + 1) + v; root = seg.multiply(root, y, t); } print(root->prod); } signed main() { solve(); return 0; }
#line 1 "test/3_yukicoder/1826_2.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1826" #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_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } // (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 kth_bit(int k) { return T(1) << k; } template <typename T> bool has_kth_bit(T x, int k) { return x >> k & 1; } 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 1 "other/io.hpp" #define FASTIO #include <unistd.h> // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template <typename T> void rd_real(T &x) { string s; rd(s); x = stod(s); } template <typename T> void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template <class T, class U> void rd(pair<T, U> &p) { return rd(p.first), rd(p.second); } template <size_t N = 0, typename T> void rd_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); rd(x); rd_tuple<N + 1>(t); } } template <class... T> void rd(tuple<T...> &tpl) { rd_tuple(tpl); } template <size_t N = 0, typename T> void rd(array<T, N> &x) { for (auto &d: x) rd(d); } template <class T> void rd(vc<T> &x) { for (auto &d: x) rd(d); } void read() {} template <class H, class... T> void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template <typename T> void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template <typename T> void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template <class T, class U> void wt(const pair<T, U> val) { wt(val.first); wt(' '); wt(val.second); } template <size_t N = 0, typename T> void wt_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get<N>(t); wt(x); wt_tuple<N + 1>(t); } } template <class... T> void wt(tuple<T...> tpl) { wt_tuple(tpl); } template <class T, size_t S> void wt(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template <class T> void wt(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward<Tail>(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #if defined(LOCAL) #define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__) #define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME #define SHOW1(x) print(#x, "=", (x)), flush() #define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush() #define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush() #define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush() #define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush() #define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush() #else #define SHOW(...) #endif #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector<type> name(size); \ read(name) #define VV(type, name, h, w) \ vector<vector<type>> name(h, vector<type>(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); } void TIDAK(bool t = 1) { YES(!t); } #line 2 "ds/segtree/dynamic_segtree_sparse.hpp" // 常にほとんどの要素が unit であることが保証されるような動的セグ木 // したがって、default_prod の類は持たせられず、acted monoid も一般には扱えない // 追加 N 回のときノード数 N 以下が保証される template <typename Monoid, bool PERSISTENT> struct Dynamic_SegTree_Sparse { using MX = Monoid; using X = typename MX::value_type; struct Node { ll idx; Node *l, *r; X prod, x; }; const int NODES; const ll L0, R0; Node *pool; int pid; using np = Node *; vc<np> FREE; Dynamic_SegTree_Sparse(int NODES, ll L0, ll R0) : NODES(NODES), L0(L0), R0(R0), pid(0) { pool = new Node[NODES]; } ~Dynamic_SegTree_Sparse() { delete[] pool; } // 木 dp のマージのときなどに使用すると MLE 回避できることがある // https://codeforces.com/problemset/problem/671/D void free_subtree(np c) { 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); } np new_root() { return nullptr; } np new_node(ll idx, const X x) { if (!FREE.empty()) { np c = POP(FREE); c->idx = idx, c->l = c->r = nullptr; c->prod = c->x = x; return c; } assert(pid < NODES); pool[pid].idx = idx; pool[pid].l = pool[pid].r = nullptr; pool[pid].x = pool[pid].prod = x; return &(pool[pid++]); } X prod(np root, ll l, ll r) { assert(L0 <= l && l <= r && r <= R0); if (l == r) return MX::unit(); X x = MX::unit(); prod_rec(root, L0, R0, l, r, x); return x; } X prod_all(np root) { return prod(root, L0, R0); } np set(np root, ll i, const X &x) { assert(L0 <= i && i < R0); return set_rec(root, L0, R0, i, x); } np multiply(np root, ll i, const X &x) { assert(L0 <= i && i < R0); return multiply_rec(root, L0, R0, i, x); } template <typename F> ll max_right(np root, F check, ll L) { assert(L0 <= L && L <= R0 && check(MX::unit())); X x = MX::unit(); return max_right_rec(root, check, L0, R0, L, x); } template <typename F> ll min_left(np root, F check, ll R) { assert(L0 <= R && R <= R0 && check(MX::unit())); X x = MX::unit(); return min_left_rec(root, check, L0, R0, R, x); } void reset() { pid = 0; FREE.clear(); } vc<pair<ll, X>> get_all(np root) { vc<pair<ll, X>> res; auto dfs = [&](auto &dfs, np c) -> void { if (!c) return; dfs(dfs, c->l); res.eb(c->idx, c->x); dfs(dfs, c->r); }; dfs(dfs, root); return res; } X get(np root, ll idx) { auto dfs = [&](auto &dfs, np c) -> X { if (!c) return Monoid::unit(); if (idx == c->idx) return c->x; if (idx < (c->idx)) return dfs(dfs, c->l); return dfs(dfs, c->r); }; return dfs(dfs, root); } private: void update(np c) { c->prod = c->x; if (c->l) c->prod = MX::op(c->l->prod, c->prod); if (c->r) c->prod = MX::op(c->prod, c->r->prod); } np copy_node(np c) { if (!c || !PERSISTENT) return c; assert(pid < NODES); pool[pid].idx = c->idx; pool[pid].l = c->l; pool[pid].r = c->r; pool[pid].x = c->x; pool[pid].prod = c->prod; return &(pool[pid++]); } np set_rec(np c, ll l, ll r, ll i, X x) { if (!c) { c = new_node(i, x); return c; } c = copy_node(c); if (c->idx == i) { c->x = x; update(c); return c; } ll m = (l + r) / 2; if (i < m) { if (c->idx < i) swap(c->idx, i), swap(c->x, x); c->l = set_rec(c->l, l, m, i, x); } if (m <= i) { if (i < c->idx) swap(c->idx, i), swap(c->x, x); c->r = set_rec(c->r, m, r, i, x); } update(c); return c; } np multiply_rec(np c, ll l, ll r, ll i, X x) { if (!c) { c = new_node(i, x); return c; } c = copy_node(c); if (c->idx == i) { c->x = MX::op(c->x, x); update(c); return c; } ll m = (l + r) / 2; if (i < m) { if (c->idx < i) swap(c->idx, i), swap(c->x, x); c->l = multiply_rec(c->l, l, m, i, x); } if (m <= i) { if (i < c->idx) swap(c->idx, i), swap(c->x, x); c->r = multiply_rec(c->r, m, r, i, x); } update(c); return c; } void prod_rec(np c, ll l, ll r, ll ql, ll qr, X &x) { chmax(ql, l); chmin(qr, r); if (ql >= qr || !c) return; if (l == ql && r == qr) { x = MX::op(x, c->prod); return; } ll m = (l + r) / 2; prod_rec(c->l, l, m, ql, qr, x); if (ql <= (c->idx) && (c->idx) < qr) x = MX::op(x, c->x); prod_rec(c->r, m, r, ql, qr, x); } template <typename F> ll max_right_rec(np c, const F &check, ll l, ll r, ll ql, X &x) { if (!c || r <= ql) return R0; if (check(MX::op(x, c->prod))) { x = MX::op(x, c->prod); return R0; } ll m = (l + r) / 2; ll k = max_right_rec(c->l, check, l, m, ql, x); if (k != R0) return k; if (ql <= (c->idx)) { x = MX::op(x, c->x); if (!check(x)) return c->idx; } return max_right_rec(c->r, check, m, r, ql, x); } template <typename F> ll min_left_rec(np c, const F &check, ll l, ll r, ll qr, X &x) { if (!c || qr <= l) return L0; if (check(MX::op(c->prod, x))) { x = MX::op(c->prod, x); return L0; } ll m = (l + r) / 2; ll k = min_left_rec(c->r, check, m, r, qr, x); if (k != L0) return k; if (c->idx < qr) { x = MX::op(c->x, x); if (!check(x)) return c->idx + 1; } return min_left_rec(c->l, check, l, m, qr, x); } }; #line 2 "alg/monoid/max.hpp" template <typename E> struct Monoid_Max { using X = E; using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); } static constexpr X unit() { return -infty<E>; } static constexpr bool commute = true; }; #line 6 "test/3_yukicoder/1826_2.test.cpp" void solve() { LL(N); vi X, Y, V; FOR(N) { LL(t, x, v); X.eb(t - x), Y.eb(t + x), V.eb(v); } auto I = argsort(X); X = rearrange(X, I), Y = rearrange(Y, I), V = rearrange(V, I); ll LIM = 1LL << 32; Dynamic_SegTree_Sparse<Monoid_Max<ll>, false> seg(N + 1, -LIM, LIM); using np = typename decltype(seg)::np; np root = nullptr; root = seg.set(root, 0, 0); FOR(i, N) { ll x = X[i], y = Y[i], v = V[i]; if (x < 0) continue; ll t = seg.prod(root, -LIM, y + 1) + v; root = seg.multiply(root, y, t); } print(root->prod); } signed main() { solve(); return 0; }