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z56MsV`H!t(?uPXJ{~X`*nLp!x_|Xsa{vUm%pV#g_`$*saFYyCM+{7fkKfT`mZJ$4b z?s10g{@--(|4sM)pR*UcPrJ`Pe?RX3{lWdu{kNEK5KX#ve{>kM2AO01+?}vZRz5ji1Gyb%8+qd7w z{d|`7|A#-;`~LUe)X!gh|3BHK^7-xPU(cSk-TU{F@9qAxy@Lzx5bi zt+En+^XJ|DX+PWlOz&?U#tOjNZ=dX*{T)8{ +using namespace std; + +/* macro helpers */ +#define __NARGS(...) std::tuple_size::value +#define __DECOMPOSE_S(a, x) auto x = a; +#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a; +constexpr void __() {} +#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __() +#define __as_typeof(container) decltype(container)::value_type + +/* type aliases */ +#if LONG_LONG_MAX != INT64_MAX +using ll = int64_t; +using ull = uint64_t; +#else +using ll = long long; +using ull = unsigned long long; +#endif +using int128 = __int128_t; +using uint128 = __uint128_t; +using pii = pair; +using pil = pair; +using pli = pair; +using pll = pair; + +/* constants */ +constexpr int INF = 0x3f3f3f3f; +constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL; +constexpr ll MDL = 1e9 + 7; +constexpr ll PRIME = 998'244'353; +constexpr ll MDL1 = 8784491; +constexpr ll MDL2 = PRIME; +constexpr int128 INT128_MAX = numeric_limits::max(); +constexpr uint128 UINT128_MAX = numeric_limits::max(); +constexpr int128 INT128_MIN = numeric_limits::min(); +constexpr uint128 UINT128_MIN = numeric_limits::min(); + +/* random */ + +mt19937 rd(chrono::duration_cast(chrono::system_clock::now().time_since_epoch()).count()); + +/* bit-wise operations */ +#define lowbit(x) ((x) & -(x)) +#define popcount(x) (__builtin_popcountll(ll(x))) +#define parity(x) (__builtin_parityll(ll(x))) +#define msp(x) (63LL - __builtin_clzll(ll(x))) +#define lsp(x) (__builtin_ctzll(ll(x))) + +/* arithmetic operations */ +#define mod(x, y) ((((x) % (y)) + (y)) % (y)) + +/* fast pairs */ +#define upair ull +#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1))) +#define u1(p) ((p) >> 32) +#define u2(p) ((p) & ((1ULL << 32) - 1)) +#define ult std::less +#define ugt std::greater + +#define ipair ull +#define imake(x, y) (umake(x, y)) +#define i1(p) (int(u1(ll(p)))) +#define i2(p) (ll(u2(p) << 32) >> 32) +struct ilt { + bool operator()(const ipair& a, const ipair& b) const { + if (i1(a) == i1(b)) return i2(a) < i2(b); + else return i1(a) < i1(b); + } +}; +struct igt { + bool operator()(const ipair& a, const ipair& b) const { + if (i1(a) == i1(b)) return i2(a) > i2(b); + else return i1(a) > i1(b); + } +}; + +/* conditions */ +#define loop while (1) +#define if_or(var, val) if (!(var == val)) var = val; else +#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;) +#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;) + +/* hash */ +struct safe_hash { + // https://codeforces.com/blog/entry/62393 + static uint64_t splitmix64(uint64_t x) { + // http://xorshift.di.unimi.it/splitmix64.c + x += 0x9e3779b97f4a7c15; + x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9; + x = (x ^ (x >> 27)) * 0x94d049bb133111eb; + return x ^ (x >> 31); + } + + size_t operator()(uint64_t x) const { + static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count(); + return splitmix64(x + FIXED_RANDOM); + } +}; + +struct pair_hash { + template + size_t operator()(const pair& a) const { + auto hash1 = safe_hash()(a.first); + auto hash2 = safe_hash()(a.second); + if (hash1 != hash2) { + return hash1 ^ hash2; + } + return hash1; + } +}; + +/* build data structures */ +#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];) +#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];) +#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);) +#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};) +#define adj(ch, n) __AS_PROCEDURE(vector> ch((n) + 1);) +#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);) +#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);) +template pair> discretize(Iterator __first, Iterator __last) { + set st(__first, __last); + size_t N = 0; + map mp; + for (auto&& x : st) mp[x] = ++N; + return {N, mp}; +} +template pair> unordered_discretize(Iterator __first, Iterator __last) { + set st(__first, __last); + size_t N = 0; + unordered_map mp; + for (auto&& x : st) mp[x] = ++N; + return {N, mp}; +} + +/* io */ +#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL)) +template void __read(T& x) { cin >> x; } +template void __read(T& x, U&... args) { cin >> x; __read(args...); } +#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);) +#define readvec(type, a, n) __AS_PROCEDURE(vector a(n); for (int i = 0; i < (n); ++i) cin >> a[i];) +#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;) +#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;) +#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;) +template ostream& operator<<(ostream& out, const pair& p) { + out << "{" << p.first << ", " << p.second << "}"; + return out; +} +template +void print_tuple_impl(std::basic_ostream& os, const Tuple& t, std::index_sequence) { + using swallow = int[]; // guaranties left to right order + (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get(t)), 0)... }; +} +template +decltype(auto) operator<<(std::basic_ostream& os, const std::tuple& t) { + os << "{"; + print_tuple_impl(os, t, std::index_sequence_for{}); + return os << "}"; +} +template ostream& operator<<(ostream& out, const vector& vec) { + for (auto&& i : vec) out << i << ' '; + return out; +} +std::ostream& operator<<(std::ostream& dest, const int128& value) { + // https://stackoverflow.com/a/25115163/23881100 + std::ostream::sentry s( dest ); + if ( s ) { + uint128 tmp = value < 0 ? -value : value; + char buffer[ 128 ]; + char* d = std::end( buffer ); + do { + -- d; + *d = "0123456789"[ tmp % 10 ]; + tmp /= 10; + } while ( tmp != 0 ); + if ( value < 0 ) { + -- d; + *d = '-'; + } + int len = std::end( buffer ) - d; + if ( dest.rdbuf()->sputn( d, len ) != len ) { + dest.setstate( std::ios_base::badbit ); + } + } + return dest; +} + +/* pops */ +#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();) +#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();) +#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();) + +/* math */ +constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); } + +void __exgcd(ll a, ll b, ll& x, ll& y) { + if (b == 0) { + x = 1, y = 0; + return; + } + __exgcd(b, a % b, y, x); + y -= a / b * x; +} + +ll inverse(ll a, ll b) { + ll x, y; + __exgcd(a, b, x, y); + return mod(x, b); +} + +vector> decompose(ll x) { + vector> res; + for (int i = 2; i * i <= x; i++) { + if (x % i == 0) { + int cnt = 0; + ll pw = 1; + while (x % i == 0) ++cnt, x /= i, pw *= i; + res.emplace_back(i, cnt, pw); + } + } + if (x != 1) { + res.emplace_back(x, 1, x); + } + return res; +} + +/* string algorithms */ +vector calc_next(string t) { // pi function of t + int n = (int)t.length(); + vector pi(n); + for (int i = 1; i < n; i++) { + int j = pi[i - 1]; + while (j > 0 && t[i] != t[j]) j = pi[j - 1]; + if (t[i] == t[j]) j++; + pi[i] = j; + } + return pi; +} +vector calc_z(string t) { // z function of t + int m = t.length(); + vector z; + z.push_back(m); + pair prev = {1, -1}; + for (int i = 1; i < m; ++i) { + if (z[i - prev.first] + i <= prev.second) { + z.push_back(z[i - prev.first]); + } else { + int j = max(i, prev.second + 1); + while (j < m && t[j] == t[j - i]) ++j; + z.push_back(j - i); + prev = {i, j - 1}; + } + } + return z; +} +vector kmp(string s, string t) { // find all t in s + string cur = t + '#' + s; + int sz1 = s.size(), sz2 = t.size(); + vector v; + vector lps = calc_next(cur); + for (int i = sz2 + 1; i <= sz1 + sz2; i++) { + if (lps[i] == sz2) v.push_back(i - 2 * sz2); + } + return v; +} +int period(string s) { // find the length of shortest recurring period + int n = s.length(); + auto z = calc_z(s); + for (int i = 1; i <= n / 2; ++i) { + if (n % i == 0 && z[i] == n - i) { + return i; + } + } + return n; +} +///////////////////////////////////////////////////////// + +#define SINGLE_TEST_CASE +// #define DUMP_TEST_CASE 7219 + +void dump() {} + +void dump_ignore() {} + +template struct MLL { + ll val; + MLL(ll v = 0) : val(mod(v, mdl)) {} + friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); } + friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); } + friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); } + friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); } + friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); } + friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; } + friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; } + void operator+=(const MLL& rhs) { val = (*this + rhs).val; } + void operator-=(const MLL& rhs) { val = (*this - rhs).val; } + void operator*=(const MLL& rhs) { val = (*this * rhs).val; } + void operator/=(const MLL& rhs) { val = (*this / rhs).val; } + void operator%=(const MLL& rhs) { val = (*this % rhs).val; } +}; + +template +ostream& operator<<(ostream& out, const MLL& num) { + return out << num.val; +} + +template +istream& operator>>(istream& in, MLL& num) { + return in >> num.val; +} + +constexpr int MAXN = 6e5 + 10; +MLL fact[MAXN], pw[MAXN]; +void prep() { + fact[0] = 1, pw[0] = 1; + for (int i = 1; i < MAXN; ++i) { + fact[i] = fact[i - 1] * i; + pw[i] = pw[i - 1] * 2; + } +} + +void solve() { + read(int, k); + int n = 1 << k; + vector a(n, -1); + for (int i = 0; i < n; ++i) { + read(int, x); + if (x == -1) { + ;; + } else { + a[x - 1] = i; + } + } + MLL res = 1; + for (int i = 0; i < k; ++i) { + int tot = 1 << k - i; + unordered_set left, right; + int cnt = 0; + for (int j = 0; j < tot / 2; ++j) { + if (a[j] == -1) continue; + if (left.count(a[j] >> i) or left.count((a[j] >> i) ^ 1)) { + cout << 0 << '\n'; + return; + } + left.emplace(a[j] >> i); + } + for (int j = tot / 2; j < tot; ++j) { + if (a[j] == -1) continue; + if (left.count(a[j] >> i) or right.count(a[j] >> i) or right.count((a[j] >> i) ^ 1)) { + cout << 0 << '\n'; + return; + } + right.emplace(a[j] >> i); + cnt += 1; + } + int to_swap = tot / 2; + for (int j = 0; j < tot / 2; ++j) { + if (left.count(j << 1) or left.count((j << 1) + 1) or right.count(j << 1) or right.count((j << 1) + 1)) { + to_swap -= 1; + } + } + res = (res * fact[tot / 2 - cnt]) * pw[to_swap]; + } + cout << res << '\n'; +} + +int main() { +#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__) + assert(false && "incompatible compiler variant detected."); +#endif + untie, cout.tie(NULL); + prep(); +#ifdef SINGLE_TEST_CASE + solve(); +#else + read(int, t); + for (int i = 0; i < t; ++i) { +#ifdef DUMP_TEST_CASE + if (t < (DUMP_TEST_CASE)) { + solve(); + } else if (i + 1 == (DUMP_TEST_CASE)) { + dump(); + } else { + dump_ignore(); + } +#else + solve(); +#endif + } +#endif +} diff --git a/src/bin/cf-1839d.cc b/src/bin/cf-1839d.cc new file mode 100644 index 0000000..bfdc1e4 --- /dev/null +++ b/src/bin/cf-1839d.cc @@ -0,0 +1,351 @@ +#ifdef ONLINE_JUDGE +#pragma GCC optimize("Ofast") +#endif +///////////////////////////////////////////////////////// +/** + * Useful Macros + * by subcrip + * (requires C++17) + */ + +#include +using namespace std; + +/* macro helpers */ +#define __NARGS(...) std::tuple_size::value +#define __DECOMPOSE_S(a, x) auto x = a; +#define __DECOMPOSE_N(a, ...) auto [__VA_ARGS__] = a; +constexpr void __() {} +#define __AS_PROCEDURE(...) __(); __VA_ARGS__; __() +#define __as_typeof(container) decltype(container)::value_type + +/* type aliases */ +#if LONG_LONG_MAX != INT64_MAX +using ll = int64_t; +using ull = uint64_t; +#else +using ll = long long; +using ull = unsigned long long; +#endif +using int128 = __int128_t; +using uint128 = __uint128_t; +using pii = pair; +using pil = pair; +using pli = pair; +using pll = pair; + +/* constants */ +constexpr int INF = 0x3f3f3f3f; +constexpr ll INFLL = 0x3f3f3f3f3f3f3f3fLL; +constexpr ll MDL = 1e9 + 7; +constexpr ll PRIME = 998'244'353; +constexpr ll MDL1 = 8784491; +constexpr ll MDL2 = PRIME; +constexpr int128 INT128_MAX = numeric_limits::max(); +constexpr uint128 UINT128_MAX = numeric_limits::max(); +constexpr int128 INT128_MIN = numeric_limits::min(); +constexpr uint128 UINT128_MIN = numeric_limits::min(); + +/* random */ + +mt19937 rd(chrono::duration_cast(chrono::system_clock::now().time_since_epoch()).count()); + +/* bit-wise operations */ +#define lowbit(x) ((x) & -(x)) +#define popcount(x) (__builtin_popcountll(ll(x))) +#define parity(x) (__builtin_parityll(ll(x))) +#define msp(x) (63LL - __builtin_clzll(ll(x))) +#define lsp(x) (__builtin_ctzll(ll(x))) + +/* arithmetic operations */ +#define mod(x, y) ((((x) % (y)) + (y)) % (y)) + +/* fast pairs */ +#define upair ull +#define umake(x, y) (ull(x) << 32 | (ull(y) & ((1ULL << 32) - 1))) +#define u1(p) ((p) >> 32) +#define u2(p) ((p) & ((1ULL << 32) - 1)) +#define ult std::less +#define ugt std::greater + +#define ipair ull +#define imake(x, y) (umake(x, y)) +#define i1(p) (int(u1(ll(p)))) +#define i2(p) (ll(u2(p) << 32) >> 32) +struct ilt { + bool operator()(const ipair& a, const ipair& b) const { + if (i1(a) == i1(b)) return i2(a) < i2(b); + else return i1(a) < i1(b); + } +}; +struct igt { + bool operator()(const ipair& a, const ipair& b) const { + if (i1(a) == i1(b)) return i2(a) > i2(b); + else return i1(a) > i1(b); + } +}; + +/* conditions */ +#define loop while (1) +#define if_or(var, val) if (!(var == val)) var = val; else +#define continue_or(var, val) __AS_PROCEDURE(if (var == val) continue; var = val;) +#define break_or(var, val) __AS_PROCEDURE(if (var == val) break; var = val;) + +/* hash */ +struct safe_hash { + // https://codeforces.com/blog/entry/62393 + static uint64_t splitmix64(uint64_t x) { + // http://xorshift.di.unimi.it/splitmix64.c + x += 0x9e3779b97f4a7c15; + x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9; + x = (x ^ (x >> 27)) * 0x94d049bb133111eb; + return x ^ (x >> 31); + } + + size_t operator()(uint64_t x) const { + static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count(); + return splitmix64(x + FIXED_RANDOM); + } +}; + +struct pair_hash { + template + size_t operator()(const pair& a) const { + auto hash1 = safe_hash()(a.first); + auto hash2 = safe_hash()(a.second); + if (hash1 != hash2) { + return hash1 ^ hash2; + } + return hash1; + } +}; + +/* build data structures */ +#define unordered_counter(from, to) __AS_PROCEDURE(unordered_map<__as_typeof(from), size_t, safe_hash> to; for (auto&& x : from) ++to[x];) +#define counter(from, to, cmp) __AS_PROCEDURE(map<__as_typeof(from), size_t, cmp> to; for (auto&& x : from) ++to[x];) +#define pa(a) __AS_PROCEDURE(__typeof(a) pa; pa.push_back({}); for (auto&&x : a) pa.push_back(pa.back() + x);) +#define sa(a) __AS_PROCEDURE(__typeof(a) sa(a.size() + 1); {int n = a.size(); for (int i = n - 1; i >= 0; --i) sa[i] = sa[i + 1] + a[i];};) +#define adj(ch, n) __AS_PROCEDURE(vector> ch((n) + 1);) +#define edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v), ch[v].push_back(u);) +#define Edge(ch, u, v) __AS_PROCEDURE(ch[u].push_back(v);) +template pair> discretize(Iterator __first, Iterator __last) { + set st(__first, __last); + size_t N = 0; + map mp; + for (auto&& x : st) mp[x] = ++N; + return {N, mp}; +} +template pair> unordered_discretize(Iterator __first, Iterator __last) { + set st(__first, __last); + size_t N = 0; + unordered_map mp; + for (auto&& x : st) mp[x] = ++N; + return {N, mp}; +} + +/* io */ +#define untie __AS_PROCEDURE(ios_base::sync_with_stdio(0), cin.tie(NULL)) +template void __read(T& x) { cin >> x; } +template void __read(T& x, U&... args) { cin >> x; __read(args...); } +#define read(type, ...) __AS_PROCEDURE(type __VA_ARGS__; __read(__VA_ARGS__);) +#define readvec(type, a, n) __AS_PROCEDURE(vector a(n); for (int i = 0; i < (n); ++i) cin >> a[i];) +#define putvec(a) __AS_PROCEDURE(for (auto&& x : a) cout << x << ' '; cout << endl;) +#define debug(x) __AS_PROCEDURE(cerr << #x" = " << (x) << endl;) +#define debugvec(a) __AS_PROCEDURE(cerr << #a" = "; for (auto&& x : a) cerr << x << ' '; cerr << endl;) +template ostream& operator<<(ostream& out, const pair& p) { + out << "{" << p.first << ", " << p.second << "}"; + return out; +} +template +void print_tuple_impl(std::basic_ostream& os, const Tuple& t, std::index_sequence) { + using swallow = int[]; // guaranties left to right order + (void)swallow { 0, (void(os << (Index == 0 ? "" : ", ") << std::get(t)), 0)... }; +} +template +decltype(auto) operator<<(std::basic_ostream& os, const std::tuple& t) { + os << "{"; + print_tuple_impl(os, t, std::index_sequence_for{}); + return os << "}"; +} +template ostream& operator<<(ostream& out, const vector& vec) { + for (auto&& i : vec) out << i << ' '; + return out; +} +std::ostream& operator<<(std::ostream& dest, const int128& value) { + // https://stackoverflow.com/a/25115163/23881100 + std::ostream::sentry s( dest ); + if ( s ) { + uint128 tmp = value < 0 ? -value : value; + char buffer[ 128 ]; + char* d = std::end( buffer ); + do { + -- d; + *d = "0123456789"[ tmp % 10 ]; + tmp /= 10; + } while ( tmp != 0 ); + if ( value < 0 ) { + -- d; + *d = '-'; + } + int len = std::end( buffer ) - d; + if ( dest.rdbuf()->sputn( d, len ) != len ) { + dest.setstate( std::ios_base::badbit ); + } + } + return dest; +} + +/* pops */ +#define poptop(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.top(); q.pop();) +#define popback(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.back(); q.pop_back();) +#define popfront(q, ...) __AS_PROCEDURE(auto [__VA_ARGS__] = q.front();q.pop_front();) + +/* math */ +constexpr inline int lg2(ll x) { return x == 0 ? -1 : sizeof(ll) * 8 - 1 - __builtin_clzll(x); } + +void __exgcd(ll a, ll b, ll& x, ll& y) { + if (b == 0) { + x = 1, y = 0; + return; + } + __exgcd(b, a % b, y, x); + y -= a / b * x; +} + +ll inverse(ll a, ll b) { + ll x, y; + __exgcd(a, b, x, y); + return mod(x, b); +} + +vector> decompose(ll x) { + vector> res; + for (int i = 2; i * i <= x; i++) { + if (x % i == 0) { + int cnt = 0; + ll pw = 1; + while (x % i == 0) ++cnt, x /= i, pw *= i; + res.emplace_back(i, cnt, pw); + } + } + if (x != 1) { + res.emplace_back(x, 1, x); + } + return res; +} + +/* string algorithms */ +vector calc_next(string t) { // pi function of t + int n = (int)t.length(); + vector pi(n); + for (int i = 1; i < n; i++) { + int j = pi[i - 1]; + while (j > 0 && t[i] != t[j]) j = pi[j - 1]; + if (t[i] == t[j]) j++; + pi[i] = j; + } + return pi; +} +vector calc_z(string t) { // z function of t + int m = t.length(); + vector z; + z.push_back(m); + pair prev = {1, -1}; + for (int i = 1; i < m; ++i) { + if (z[i - prev.first] + i <= prev.second) { + z.push_back(z[i - prev.first]); + } else { + int j = max(i, prev.second + 1); + while (j < m && t[j] == t[j - i]) ++j; + z.push_back(j - i); + prev = {i, j - 1}; + } + } + return z; +} +vector kmp(string s, string t) { // find all t in s + string cur = t + '#' + s; + int sz1 = s.size(), sz2 = t.size(); + vector v; + vector lps = calc_next(cur); + for (int i = sz2 + 1; i <= sz1 + sz2; i++) { + if (lps[i] == sz2) v.push_back(i - 2 * sz2); + } + return v; +} +int period(string s) { // find the length of shortest recurring period + int n = s.length(); + auto z = calc_z(s); + for (int i = 1; i <= n / 2; ++i) { + if (n % i == 0 && z[i] == n - i) { + return i; + } + } + return n; +} +///////////////////////////////////////////////////////// + +// #define SINGLE_TEST_CASE +// #define DUMP_TEST_CASE 7219 + +void dump() {} + +void dump_ignore() {} + +void prep() {} + +void solve() { + read(int, n); + vector a(n + 2); + for (int i = 1; i <= n; ++i) { + cin >> a[i]; + } + a[n + 1] = INF; + vector> dp(n + 2, vector(n + 1, INF)); + dp[0][0] = 0; + for (int i = 1; i <= n + 1; ++i) { + if (a[i] > a[i - 1]) { + for (int k = 0; k <= n; ++k) { + dp[i][k] = min(dp[i][k], dp[i - 1][k]); + } + } + for (int j = i - 1; ~j; --j) { + for (int k = 0; k < n; ++k) { + if (a[i] > a[j]) { + dp[i][k + 1] = min(dp[i][k + 1], dp[j][k] + i - j - 1); + } + } + } + } + int res = INF; + for (int i = 1; i <= n; ++i) { + res = min(res, dp[n + 1][i]); + cout << res << " \n"[i == n]; + } +} + +int main() { +#if __cplusplus < 201703L || defined(_MSC_VER) && !defined(__clang__) + assert(false && "incompatible compiler variant detected."); +#endif + untie, cout.tie(NULL); + prep(); +#ifdef SINGLE_TEST_CASE + solve(); +#else + read(int, t); + for (int i = 0; i < t; ++i) { +#ifdef DUMP_TEST_CASE + if (t < (DUMP_TEST_CASE)) { + solve(); + } else if (i + 1 == (DUMP_TEST_CASE)) { + dump(); + } else { + dump_ignore(); + } +#else + solve(); +#endif + } +#endif +} diff --git a/src/bin/ctext_out.cc b/src/bin/ctext_out.cc index 18b3f8b..225946c 100644 --- a/src/bin/ctext_out.cc +++ b/src/bin/ctext_out.cc @@ -292,197 +292,86 @@ void dump() {} void dump_ignore() {} -void prep() {} - -template> class segtree { -private: - using size_type = uint64_t; - using info_type = Addable_Info_t; - using tag_type = Tag_t; - size_type _max; - vector d; - vector b; - - void pull(size_type p) { - d[p] = d[p * 2] + d[p * 2 + 1]; - } - - void push(size_type p, size_type left_len, size_type right_len) { - d[p * 2].apply(b[p], left_len), d[p * 2 + 1].apply(b[p], right_len); - b[p * 2].apply(b[p]), b[p * 2 + 1].apply(b[p]); - b[p] = tag_type(); - } - - void set(size_type s, size_type t, size_type p, size_type x, const info_type& c) { - if (s == t) { - d[p] = c; - return; - } - size_type m = s + (t - s >> 1); - if (s != t) push(p, m - s + 1, t - m); - if (x <= m) set(s, m, p * 2, x, c); - else set(m + 1, t, p * 2 + 1, x, c); - d[p] = d[p * 2] + d[p * 2 + 1]; - } - - void range_apply(size_type s, size_type t, size_type p, size_type l, size_type r, const tag_type& c) { - if (l <= s && t <= r) { - d[p].apply(c, t - s + 1); - b[p].apply(c); - return; - } - size_type m = s + (t - s >> 1); - push(p, m - s + 1, t - m); - if (l <= m) range_apply(s, m, p * 2, l, r, c); - if (r > m) range_apply(m + 1, t, p * 2 + 1, l, r, c); - pull(p); - } - - info_type range_query(size_type s, size_type t, size_type p, size_type l, size_type r) { - if (l <= s && t <= r) { - return d[p]; - } - size_type m = s + (t - s >> 1); - info_type res = {}; - push(p, m - s + 1, t - m); - if (l <= m) res = res + range_query(s, m, p * 2, l, r); - if (r > m) res = res + range_query(m + 1, t, p * 2 + 1, l, r); - return res; - } - - void build(const Sequence& a, size_type s, size_type t, size_type p) { - if (s == t) { - d[p] = a[s]; - return; - } - int m = s + (t - s >> 1); - build(a, s, m, p * 2); - build(a, m + 1, t, p * 2 + 1); - pull(p); - } -public: - segtree(size_type __max) : d(4 * __max), b(4 * __max), _max(__max - 1) {} - segtree(const Sequence& a) : segtree(a.size()) { - build(a, {}, _max, 1); - } - - void set(size_type i, const info_type& c) { - set({}, _max, 1, i, c); - } - - void range_apply(size_type l, size_type r, const tag_type& c) { - range_apply({}, _max, 1, l, r, c); - } - - void apply(size_type i, const tag_type& c) { - range_apply(i, i, c); - } - - info_type range_query(size_type l, size_type r) { - return range_query({}, _max, 1, l, r); - } - - info_type query(size_type i) { - return range_query(i, i); - } - - Sequence serialize() { - Sequence res = {}; - for (size_type i = 0; i <= _max; ++i) { - res.push_back(query(i)); - } - return res; - } - - const vector& get_d() { - return d; - } +template struct MLL { + ll val; + MLL(ll v = 0) : val(mod(v, mdl)) {} + friend MLL operator+(const MLL& lhs, const MLL& rhs) { return mod(lhs.val + rhs.val, mdl); } + friend MLL operator-(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - rhs.val, mdl); } + friend MLL operator*(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * rhs.val, mdl); } + friend MLL operator/(const MLL& lhs, const MLL& rhs) { return mod(lhs.val * mod(inverse(rhs.val, mdl), mdl), mdl); } + friend MLL operator%(const MLL& lhs, const MLL& rhs) { return mod(lhs.val - (lhs / rhs).val, mdl); } + friend bool operator==(const MLL& lhs, const MLL& rhs) { return lhs.val == rhs.val; } + friend bool operator!=(const MLL& lhs, const MLL& rhs) { return lhs.val != rhs.val; } + void operator+=(const MLL& rhs) { val = (*this + rhs).val; } + void operator-=(const MLL& rhs) { val = (*this - rhs).val; } + void operator*=(const MLL& rhs) { val = (*this * rhs).val; } + void operator/=(const MLL& rhs) { val = (*this / rhs).val; } + void operator%=(const MLL& rhs) { val = (*this % rhs).val; } }; -struct Tag { - int val = 0; - void apply(const Tag& rhs) { - val += rhs.val; - } -}; +template +ostream& operator<<(ostream& out, const MLL& num) { + return out << num.val; +} -struct Info { - int val = INT_MAX; - void apply(const Tag& rhs, size_t len) { - val += rhs.val; - } -}; +template +istream& operator>>(istream& in, MLL& num) { + return in >> num.val; +} -Info operator+(const Info &a, const Info &b) { - return {min(a.val, b.val)}; +constexpr int MAXN = 6e5 + 10; +MLL fact[MAXN], pw[MAXN]; +void prep() { + fact[0] = 1, pw[0] = 1; + for (int i = 1; i < MAXN; ++i) { + fact[i] = fact[i - 1] * i; + pw[i] = pw[i - 1] * 2; + } } void solve() { - unordered_map mp = {{'(', 1}, {')', -1}}; - read(int, n, q); - read(string, s); - int curr = 0; - segtree ps(n); + read(int, k); + int n = 1 << k; + vector a(n, -1); for (int i = 0; i < n; ++i) { - curr += mp[s[i]]; - ps.set(i, { curr }); - } - set st1, st2; - for (int i = 0; i < n - 1; ++i) { - if (s[i] == '(' && s[i + 1] == '(') { - st1.emplace(i); - } - if (s[i] == ')' and s[i + 1] == ')') { - st2.emplace(i); - } - } - while (q--) { - read(int, i), --i; - if (s[i] == '(') { - if (i && st1.count(i - 1)) st1.erase(i - 1); - if (i + 1 < n && st1.count(i)) st1.erase(i); - if (i and s[i - 1] == ')') st2.emplace(i - 1); - if (i + 1 < n and s[i + 1] == ')') st2.emplace(i); - s[i] = ')'; - ps.range_apply(i, n - 1, {-2}); + read(int, x); + if (x == -1) { + ;; } else { - if (i && s[i - 1] == '(') st1.emplace(i - 1); - if (i + 1 < n && s[i + 1] == '(') st1.emplace(i); - if (i and st2.count(i - 1)) st2.erase(i - 1); - if (i + 1 < n and st2.count(i)) st2.erase(i); - s[i] = '('; - ps.range_apply(i, n - 1, {2}); + a[x - 1] = i; } - // debug(s); - int f = ps.query(n - 1).val % 2 == 0; - int j = st1.size() ? *st1.begin() - 1 : n - 1; - if (j >= 0 and ps.range_query(0, j).val < 0) { - f = 0; - } - j = st2.size() ? *st2.rbegin() + 2 : 0; - if (j <= n - 1 and ps.query(n - 1).val - (j ? ps.query(j - 1).val : 0) > 0) { - f = 0; - } - if (f) { - cout << "YES\n"; - } else { - cout << "NO\n"; - } - // if (st.size()) { - // int j = *st.begin(); - // if (j == 0 or ps.range_query(0, j - 1).val >= 0) { - // cout << "YES\n"; - // } else { - // cout << "NO\n"; - // } - // } else { - // if (ps.range_query(0, n - 1).val >= 0) { - // cout << "YES\n"; - // } else { - // cout << "NO\n"; - // } - // } } + MLL res = 1; + for (int i = 0; i < k; ++i) { + int tot = 1 << k - i; + unordered_set left, right; + int cnt = 0; + for (int j = 0; j < tot / 2; ++j) { + if (a[j] == -1) continue; + if (left.count(a[j] >> i) or left.count((a[j] >> i) ^ 1)) { + cout << 0 << '\n'; + return; + } + left.emplace(a[j] >> i); + } + for (int j = tot / 2; j < tot; ++j) { + if (a[j] == -1) continue; + if (left.count(a[j] >> i) or right.count(a[j] >> i) or right.count((a[j] >> i) ^ 1)) { + cout << 0 << '\n'; + return; + } + right.emplace(a[j] >> i); + cnt += 1; + } + int to_swap = tot / 2; + for (int j = 0; j < tot / 2; ++j) { + if (left.count(j << 1) or left.count((j << 1) + 1) or right.count(j << 1) or right.count((j << 1) + 1)) { + to_swap -= 1; + } + } + res = (res * fact[tot / 2 - cnt]) * pw[to_swap]; + } + cout << res << '\n'; } int main() { diff --git a/src/bin/std.in b/src/bin/std.in index 86ab9b5..f7cfd38 100644 --- a/src/bin/std.in +++ b/src/bin/std.in @@ -1,4 +1,2 @@ -3 2 -(() -2 3 +-1 7 -1 8 2 -1 -1 5

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