結果
問題 | No.1392 Don't be together |
ユーザー |
|
提出日時 | 2021-02-12 21:55:10 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,862 ms / 2,000 ms |
コード長 | 20,274 bytes |
コンパイル時間 | 15,933 ms |
コンパイル使用メモリ | 307,008 KB |
最終ジャッジ日時 | 2025-01-18 18:26:06 |
ジャッジサーバーID (参考情報) |
judge2 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 27 |
ソースコード
#pragma region Macros// #pragma GCC target("avx2")#pragma GCC optimize("O3")// #pragma GCC optimize("unroll-loops")#include <bits/stdc++.h>#define ll long long#define ld long double#define rep2(i, a, b) for(ll i = a; i <= b; ++i)#define rep(i, n) for(ll i = 0; i < n; ++i)#define rep3(i, a, b) for(ll i = a; i >= b; --i)#define pii pair<int, int>#define pll pair<ll, ll>#define pb push_back#define eb emplace_back#define vi vector<int>#define vll vector<ll>#define vpi vector<pii>#define vpll vector<pll>#define overload2(_1, _2, name, ...) name#define vec(type, name, ...) vector<type> name(__VA_ARGS__)#define VEC(type, name, size)\vector<type> name(size);\IN(name)#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define VV(type, name, h, w)\vector<vector<type>> name(h, vector<type>(w));\IN(name)#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__))))#define mt make_tuple#define fi first#define se second#define all(c) begin(c), end(c)#define SUM(v) accumulate(all(v), 0LL)#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)))using namespace std;constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};const string YESNO[2] = {"NO", "YES"};const string YesNo[2] = {"No", "Yes"};const string yesno[2] = {"no", "yes"};void YES(bool t = 1) { cout << YESNO[t] << endl; }void Yes(bool t = 1) { cout << YesNo[t] << endl; }void yes(bool t = 1) { cout << yesno[t] << endl; }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 pq = priority_queue<T>;template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;#define si(c) (int)(c).size()#define INT(...)\int __VA_ARGS__;\IN(__VA_ARGS__)#define LL(...)\ll __VA_ARGS__;\IN(__VA_ARGS__)#define STR(...)\string __VA_ARGS__;\IN(__VA_ARGS__)#define CHR(...)\char __VA_ARGS__;\IN(__VA_ARGS__)#define DBL(...)\double __VA_ARGS__;\IN(__VA_ARGS__)int scan() { return getchar(); }void scan(int &a) { cin >> a; }void scan(long long &a) { cin >> a; }void scan(char &a) { cin >> a; }void scan(double &a) { cin >> a; }void scan(string &a) { cin >> a; }template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }template <class T> void scan(vector<T> &);template <class T> void scan(vector<T> &a) {for(auto &i : a) scan(i);}template <class T> void scan(T &a) { cin >> a; }void IN() {}template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {scan(head);IN(tail...);}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); }vi iota(int n) {vi a(n);iota(all(a), 0);return a;}template <typename T> vi iota(vector<T> &a, bool greater = false) {vi res(a.size());iota(all(res), 0);sort(all(res), [&](int i, int j) {if(greater) return a[i] > a[j];return a[i] < a[j];});return res;}#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())template <class T> T POW(T x, int n) {T res = 1;for(; n; n >>= 1, x *= x)if(n & 1) res *= x;return res;}vector<pll> factor(ll x) {vector<pll> ans;for(ll i = 2; i * i <= x; i++)if(x % i == 0) {ans.push_back({i, 1});while((x /= i) % i == 0) ans.back().second++;}if(x != 1) ans.push_back({x, 1});return ans;}template <class T> vector<T> divisor(T x) {vector<T> ans;for(T i = 1; i * i <= x; i++)if(x % i == 0) {ans.pb(i);if(i * i != x) ans.pb(x / i);}return ans;}template <typename T> void zip(vector<T> &x) {vector<T> y = x;sort(all(y));for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }}int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }// int allbit(int n) { return (1 << n) - 1; }ll allbit(ll n) { return (1LL << n) - 1; }int popcount(signed t) { return __builtin_popcount(t); }int popcount(ll t) { return __builtin_popcountll(t); }bool ispow2(int i) { return i && (i & -i) == i; }int in() {int x;cin >> x;return x;}ll lin() {unsigned long long x;cin >> x;return x;}template <class T> pair<T, T> operator-(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi - y.fi, x.se - y.se); }template <class T> pair<T, T> operator+(const pair<T, T> &x, const pair<T, T> &y) { return pair<T, T>(x.fi + y.fi, x.se + y.se); }// template <class T> pair<T, T> &operator+=(pair<T, T> x, const pair<T, T> &y) {// x = x + y;// return &x;// }// template <class T> pair<T, T> &operator-=(pair<T, T> x, const pair<T, T> &y) {// x = x - y;// return &x;// }template <class T> ll operator*(const pair<T, T> &x, const pair<T, T> &y) { return (ll)x.fi * y.fi + (ll)x.se * y.se; }template <typename T> struct edge {int from, to;T cost;int id;edge(int to, T cost) : from(-1), to(to), cost(cost) {}edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}edge &operator=(const int &x) {to = x;return *this;}operator int() const { return to; }};template <typename T> using Edges = vector<edge<T>>;using Tree = vector<vector<int>>;using Graph = vector<vector<int>>;template <class T> using Wgraph = vector<vector<edge<T>>>;Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {Tree res(n);if(m == -1) m = n - 1;while(m--) {int a, b;cin >> a >> b;a -= margin, b -= margin;res[a].emplace_back(b);if(!directed) res[b].emplace_back(a);}return move(res);}template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {Wgraph<T> res(n);if(m == -1) m = n - 1;while(m--) {int a, b;T c;cin >> a >> b >> c;a -= margin, b -= margin;res[a].emplace_back(b, c);if(!directed) res[b].emplace_back(a, c);}return move(res);}#define i128 __int128_t#define ull unsigned long long int#define TEST\INT(testcases);\while(testcases--)template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {for(auto it = begin(v); it != end(v); ++it) {if(it == begin(v))os << *it;elseos << " " << *it;}return os;}template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {os << p.first << " " << p.second;return os;}template <class S, class T> string to_string(pair<S, T> p) { return "(" + to_string(p.first) + "," + to_string(p.second) + ")"; }template <class A> string to_string(A v) {if(v.empty()) return "{}";string ret = "{";for(auto &x : v) ret += to_string(x) + ",";ret.back() = '}';return ret;}string to_string(string s) { return "\"" + s + "\""; }void dump() { cerr << endl; }template <class Head, class... Tail> void dump(Head head, Tail... tail) {cerr << to_string(head) << " ";dump(tail...);}#define endl '\n'#ifdef _LOCAL#undef endl#define debug(x)\cout << #x << ": ";\dump(x)#else#define debug(x)#endiftemplate <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;struct Setup_io {Setup_io() {ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);cout << fixed << setprecision(15);}} setup_io;#define drop(s) cout << #s << endl, exit(0)#pragma endregionstruct UnionFind {vector<int> data;int num;UnionFind(int n) : num(n) { data.assign(n, -1); }bool unite(int x, int y) {x = find(x), y = find(y);if(x == y) return false;num--;if(data[x] > data[y]) swap(x, y);data[x] += data[y];data[y] = x;return true;}bool same(int x, int y) { return find(x) == find(y); }int find(int x) {if(data[x] < 0) return x;return (data[x] = find(data[x]));}int size(int x) { return -data[find(x)]; }const int operator[](const int k) { return find(k); }vector<vi> belong() {vector<vi> res(data.size());rep(i, data.size()) res[find(i)].eb(i);return res;}void reset() {num = data.size();data.assign(num, -1);}};namespace modular {constexpr ll MOD = 998244353;const int MAXN = 11000000;template <ll Modulus> class modint;#define mint modint<MOD>#define vmint vector<mint>vector<mint> Inv;mint inv(int x);template <ll Modulus> class modint {public:static constexpr int mod() { return Modulus; }ll a;constexpr modint(const ll x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {}constexpr ll &value() noexcept { return a; }constexpr const ll &value() const noexcept { return a; }constexpr modint operator-() const noexcept { return modint() - *this; }constexpr modint operator+() const noexcept { return *this; }constexpr modint &operator++() noexcept {if(++a == MOD) a = 0;return *this;}constexpr modint &operator--() noexcept {if(!a) a = MOD;a--;return *this;}constexpr modint operator++(int) {modint res = *this;++*this;return res;}constexpr modint operator--(int) {mint res = *this;--*this;return res;}constexpr modint &operator+=(const modint rhs) noexcept {a += rhs.a;if(a >= Modulus) { a -= Modulus; }return *this;}constexpr modint &operator-=(const modint rhs) noexcept {if(a < rhs.a) { a += Modulus; }a -= rhs.a;return *this;}constexpr modint &operator*=(const modint rhs) noexcept {a = a * rhs.a % Modulus;return *this;}constexpr modint &operator/=(const modint rhs) noexcept {a = a * (modular::inv(rhs.a)).a % Modulus;return *this;}constexpr modint pow(long long n) const noexcept {if(n < 0) {n %= Modulus - 1;n = (Modulus - 1) + n;}modint x = *this, r = 1;while(n) {if(n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr modint inv() const noexcept { return pow(Modulus - 2); }constexpr friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += modint(rhs); }constexpr friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= modint(rhs); }constexpr friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= modint(rhs); }constexpr friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= modint(rhs); }constexpr friend modint operator==(const modint &lhs, const modint &rhs) { return lhs.a == rhs.a; }constexpr friend modint operator!=(const modint &lhs, const modint &rhs) { return lhs.a != rhs.a; }// constexpr friend modint operator^=(const modint &lhs, const modint &rhs) { return modint(lhs) ^= modint(rhs); }};vmint Fact{1, 1}, Ifact{1, 1};mint inv(int n) {if(n > MAXN) return (mint(n)).pow(MOD - 2);if(Inv.empty()) Inv.emplace_back(0), Inv.emplace_back(1);if(Inv.size() > n)return Inv[n];else {for(int i = Inv.size(); i <= n; ++i) {auto [y, x] = div(int(MOD), i);Inv.emplace_back(Inv[x] * (-y));}return Inv[n];}}mint fact(int n) {if(Fact.size() > n)return Fact[n];elsefor(int i = Fact.size(); i <= n; ++i) Fact.emplace_back(Fact[i - 1] * i);return Fact[n];}mint ifact(int n) {if(Ifact.size() > n)return Ifact[n];elsefor(int i = Ifact.size(); i <= n; ++i) Ifact.emplace_back(Ifact[i - 1] * inv(i));return Ifact[n];}mint modpow(ll a, ll n) { return mint(a).pow(n); }mint inv(mint a) { return inv(a.a); }mint ifact(mint a) { return ifact(a.a); }mint fact(mint a) { return fact(a.a); }mint modpow(mint a, ll n) { return modpow(a.a, n); }mint C(int a, int b) {if(a < 0 || b < 0) return 0;if(a < b) return 0;if(a > MAXN) {mint res = 1;rep(i, b) res *= a - i, res /= i + 1;return res;}return fact(a) * ifact(b) * ifact(a - b);}mint P(int a, int b) {if(a < 0 || b < 0) return 0;if(a < b) return 0;if(a > MAXN) {mint res = 1;rep(i, b) res *= a - i;return res;}return fact(a) * ifact(a - b);}ostream &operator<<(ostream &os, mint a) {os << a.a;return os;}istream &operator>>(istream &is, mint &a) {ll x;is >> x;a = x;return is;}mint proot = 3;void FMT(vmint &f, const bool is_inv = false) {const int n = f.size();const mint root = is_inv ? inv(proot) : proot;vmint g(n);for(int b = n >> 1; b > 0; b >>= 1) {mint a = root.pow((MOD - 1) / (n / b)), p = 1;for(int i = 0; i < n; i += b << 1) {rep(j, b) {f[i + j + b] *= p;g[(i >> 1) + j] = f[i + j] + f[i + b + j];g[(n >> 1) + (i >> 1) + j] = f[i + j] - f[i + b + j];}p *= a;}swap(f, g);}if(is_inv) rep(i, n) f[i] *= inv(n);}vmint mul(vmint x, const vmint &y) {int n = x.size() + y.size() - 1;int s = 1;while(s < n) s <<= 1;x.resize(s);FMT(x);vmint z(s);rep(i, y.size()) z[i] = y[i];FMT(z);rep(i, s) x[i] *= z[i];FMT(x, true);x.resize(n);return x;}using Poly = vmint;Poly operator-(Poly f) {for(auto &&e : f) e = -e;return f;}Poly &operator+=(Poly &l, const Poly &r) {l.resize(max(l.size(), r.size()));rep(i, r.size()) l[i] += r[i];return l;}Poly operator+(Poly l, const Poly &r) { return l += r; }Poly &operator-=(Poly &l, const Poly &r) {l.resize(max(l.size(), r.size()));rep(i, r.size()) l[i] -= r[i];return l;}Poly operator-(Poly l, const Poly &r) { return l -= r; }Poly &operator<<=(Poly &f, size_t n) { return f.insert(f.begin(), n, 0), f; }Poly operator<<(Poly f, size_t n) { return f <<= n; }Poly &operator>>=(Poly &f, size_t n) { return f.erase(f.begin(), f.begin() + min(f.size(), n)), f; }Poly operator>>(Poly f, size_t n) { return f >>= n; }Poly operator*(const Poly &l, const Poly &r) { return mul(l, r); }Poly &operator*=(Poly &l, const Poly &r) { return l = l * r; }Poly inv(const Poly &f) {Poly g{1 / f[0]};while(g.size() < f.size()) {Poly x(f.begin(), f.begin() + min(f.size(), g.size() << 1)), y = g;x.resize(g.size() << 1), FMT(x);y.resize(g.size() << 1), FMT(y);rep(i, x.size()) x[i] *= y[i];FMT(x, true);x >>= g.size();x.resize(g.size() << 1), FMT(x);rep(i, x.size()) x[i] *= -y[i];FMT(x, true);g.insert(g.end(), x.begin(), x.begin() + g.size());}return Poly{begin(g), begin(g) + f.size()};}Poly integ(const Poly &f) {Poly res(f.size() + 1);for(int i = 1; i < (int)res.size(); ++i) res[i] = f[i - 1] / i;return res;}Poly deriv(const Poly &f) {if(f.size() == 0) return Poly();Poly res(f.size() - 1);rep(i, res.size()) res[i] = f[i + 1] * (i + 1);return res;}Poly log(const Poly &f) {Poly g = integ(inv(f) * deriv(f));return Poly{g.begin(), g.begin() + f.size()};}Poly exp(const Poly &f) {Poly g{1};while(g.size() < f.size()) {Poly x(f.begin(), f.begin() + min(f.size(), g.size() * 2));x[0] += 1;g.resize(2 * g.size());x -= log(g);x *= {g.begin(), g.begin() + g.size() / 2};rep2(i, g.size() / 2, min<int>(x.size(), g.size()) - 1) g[i] = x[i];}return {g.begin(), g.begin() + f.size()};}} // namespace modularusing namespace modular;int main() {INT(n, m);VEC(int, a, n);if(m == 1) drop(0);rep(i, n) a[i]--;UnionFind uf(n);rep(i, n) uf.unite(i, a[i]);vi v;rep(i, n) if(uf[i] == i) v.eb(uf.size(i));mint ans;vmint DP(m + 1);rep2(e, 1, m) {vv(mint, dp, n + 1, 2);dp[0][1] = e;rep(i, n) {dp[i + 1][0] += dp[i][0] * (e - 2) + dp[i][1] * (e - 1);dp[i + 1][1] += dp[i][0];}// cout << dp << endl;mint tmp = 1;for(auto i : v) { tmp *= dp[i - 1][0]; }DP[e] = tmp;}rep2(i, 2, m) { rep2(j, 1, i - 1) DP[i] -= DP[j] * C(i, j); }cout << DP[m] * ifact(m) << endl;}