結果
問題 | No.992 最長増加部分列の数え上げ |
ユーザー | hashiryo |
提出日時 | 2024-10-11 18:49:38 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 42 ms / 2,000 ms |
コード長 | 8,594 bytes |
コンパイル時間 | 2,464 ms |
コンパイル使用メモリ | 214,356 KB |
実行使用メモリ | 8,180 KB |
最終ジャッジ日時 | 2024-10-11 18:49:46 |
合計ジャッジ時間 | 5,664 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 2 ms
5,248 KB |
testcase_03 | AC | 2 ms
5,248 KB |
testcase_04 | AC | 17 ms
5,248 KB |
testcase_05 | AC | 13 ms
5,248 KB |
testcase_06 | AC | 21 ms
5,248 KB |
testcase_07 | AC | 15 ms
5,248 KB |
testcase_08 | AC | 9 ms
5,248 KB |
testcase_09 | AC | 17 ms
5,248 KB |
testcase_10 | AC | 21 ms
5,248 KB |
testcase_11 | AC | 25 ms
5,248 KB |
testcase_12 | AC | 7 ms
5,248 KB |
testcase_13 | AC | 15 ms
5,248 KB |
testcase_14 | AC | 15 ms
5,248 KB |
testcase_15 | AC | 7 ms
5,248 KB |
testcase_16 | AC | 38 ms
6,144 KB |
testcase_17 | AC | 9 ms
5,248 KB |
testcase_18 | AC | 15 ms
5,248 KB |
testcase_19 | AC | 25 ms
5,248 KB |
testcase_20 | AC | 42 ms
6,400 KB |
testcase_21 | AC | 42 ms
6,400 KB |
testcase_22 | AC | 42 ms
6,400 KB |
testcase_23 | AC | 42 ms
6,656 KB |
testcase_24 | AC | 42 ms
6,400 KB |
testcase_25 | AC | 42 ms
6,528 KB |
testcase_26 | AC | 42 ms
6,656 KB |
testcase_27 | AC | 42 ms
6,400 KB |
testcase_28 | AC | 42 ms
6,528 KB |
testcase_29 | AC | 42 ms
6,400 KB |
testcase_30 | AC | 38 ms
8,096 KB |
testcase_31 | AC | 37 ms
8,072 KB |
testcase_32 | AC | 37 ms
8,104 KB |
testcase_33 | AC | 37 ms
8,176 KB |
testcase_34 | AC | 37 ms
8,180 KB |
testcase_35 | AC | 33 ms
7,968 KB |
testcase_36 | AC | 32 ms
7,964 KB |
testcase_37 | AC | 32 ms
7,968 KB |
testcase_38 | AC | 33 ms
7,972 KB |
testcase_39 | AC | 33 ms
7,968 KB |
testcase_40 | AC | 37 ms
7,968 KB |
testcase_41 | AC | 36 ms
7,844 KB |
testcase_42 | AC | 36 ms
7,972 KB |
testcase_43 | AC | 36 ms
7,972 KB |
testcase_44 | AC | 37 ms
7,848 KB |
ソースコード
// #define _GLIBCXX_DEBUG #include <bits/stdc++.h> // clang-format off std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;} std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;} std::ostream&operator<<(std::ostream&os,const __int128_t &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;} std::ostream&operator<<(std::ostream&os,const __uint128_t &u){if(!u)os<<"0";__uint128_t tmp=u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;} #define checkpoint() (void(0)) #define debug(...) (void(0)) #define debugArray(x,n) (void(0)) #define debugMatrix(x,h,w) (void(0)) // clang-format on #include <type_traits> template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) { std::make_signed_t<Uint> x= 1, y= 0, z= 0; for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q; return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod; } namespace math_internal { using namespace std; using u8= unsigned char; using u32= unsigned; using i64= long long; using u64= unsigned long long; using u128= __uint128_t; struct MP_Na { // mod < 2^32 u32 mod; constexpr MP_Na(): mod(0) {} constexpr MP_Na(u32 m): mod(m) {} constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; } constexpr inline u32 set(u32 n) const { return n; } constexpr inline u32 get(u32 n) const { return n; } constexpr inline u32 norm(u32 n) const { return n; } constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; } constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; } }; template <class u_t, class du_t, u8 B> struct MP_Mo { // mod < 2^32, mod < 2^62 u_t mod; constexpr MP_Mo(): mod(0), iv(0), r2(0) {} constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {} constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); } constexpr inline u_t set(u_t n) const { return mul(n, r2); } constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; } constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; } constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); } constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; } private: u_t iv, r2; static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; } constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); } }; using MP_Mo32= MP_Mo<u32, u64, 32>; using MP_Mo64= MP_Mo<u64, u128, 64>; struct MP_Br { // 2^20 < mod <= 2^41 u64 mod; constexpr MP_Br(): mod(0), x(0) {} constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {} constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); } static constexpr inline u64 set(u64 n) { return n; } constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; } constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; } constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); } constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; } private: u64 x; constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; } constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; } }; template <class du_t, u8 B> struct MP_D2B1 { // mod < 2^63, mod < 2^64 u64 mod; constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {} constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {} constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; } constexpr inline u64 set(u64 n) const { return n; } constexpr inline u64 get(u64 n) const { return n; } constexpr inline u64 norm(u64 n) const { return n; } constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; } constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; } private: u8 s; u64 d, v; constexpr inline u64 rem(const u128 &u) const { u128 q= (u >> 64) * v + u; u64 r= u64(u) - (q >> 64) * d - d; if (r > u64(q)) r+= d; if (r >= d) r-= d; return r; } }; using MP_D2B1_1= MP_D2B1<u64, 63>; using MP_D2B1_2= MP_D2B1<u128, 127>; template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) { for (u_t ret= md.set(1);; x= md.mul(x, x)) if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret; } } namespace math_internal { struct m_b {}; struct s_b: m_b {}; } template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>; template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>; namespace math_internal { template <class MP, u64 MOD> struct SB: s_b { protected: static constexpr MP md= MP(MOD); }; template <class U, class B> struct MInt: public B { using Uint= U; static constexpr inline auto mod() { return B::md.mod; } constexpr MInt(): x(0) {} template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {} constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {} constexpr MInt operator-() const { return MInt() - *this; } #define FUNC(name, op) \ constexpr MInt name const { \ MInt ret; \ return ret.x= op, ret; \ } FUNC(operator+(const MInt & r), B::md.plus(x, r.x)) FUNC(operator-(const MInt & r), B::md.diff(x, r.x)) FUNC(operator*(const MInt & r), B::md.mul(x, r.x)) FUNC(pow(u64 k), math_internal::pow(x, k, B::md)) #undef FUNC constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); } constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; } constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; } constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; } constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; } constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); } constexpr bool operator!=(const MInt &r) const { return !(*this == r); } constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); } constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); } constexpr inline Uint val() const { return B::md.get(x); } friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); } friend istream &operator>>(istream &is, MInt &r) { i64 v; return is >> v, r= MInt(v), is; } private: Uint x; }; template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>; template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>; } using math_internal::ModInt; template <class T> std::pair<std::vector<int>, std::vector<std::vector<int>>> longest_increasing_subsequence(const std::vector<T> &a) { int n= a.size(); std::vector<int> idx(n); std::vector<T> dp(n); int len= 0; for (int i= 0; i < n; ++i) { auto it= std::lower_bound(dp.begin(), dp.begin() + len, a[i]); if (*it= a[i]; (idx[i]= it - dp.begin()) == len) ++len; } std::vector<std::vector<int>> cand(len); for (int i= n; i--;) { if (idx[i] == len - 1 || (!cand[idx[i] + 1].empty() && a[i] < a[cand[idx[i] + 1].back()])) cand[idx[i]].emplace_back(i); else idx[i]= -1; } for (auto &c: cand) std::reverse(c.begin(), c.end()); return {idx, cand}; } using namespace std; signed main() { cin.tie(0); ios::sync_with_stdio(false); using Mint= ModInt<int(1e9 + 7)>; int N; cin >> N; vector<int> A(N); for (int i= 0; i < N; ++i) cin >> A[i]; auto [_, cand]= longest_increasing_subsequence(A); int k= cand.size(); vector<Mint> dp(cand[0].size(), 1); for (int i= 1; i < k; ++i) { int n= cand[i - 1].size(), m= cand[i].size(); vector<Mint> ndp(m); Mint sum= 0; for (int j= 0, l= 0, r= 0; j < m; ++j) { while (r < n && cand[i - 1][r] < cand[i][j]) sum+= dp[r++]; while (l < n && A[cand[i - 1][l]] >= A[cand[i][j]]) sum-= dp[l++]; ndp[j]= sum; } dp= std::move(ndp); } Mint ans= 0; for (auto x: dp) ans+= x; cout << ans << '\n'; return 0; }