結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
提出日時 | 2020-09-20 01:58:04 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 63 ms / 2,000 ms |
コード長 | 4,672 bytes |
コンパイル時間 | 928 ms |
コンパイル使用メモリ | 91,080 KB |
実行使用メモリ | 12,436 KB |
最終ジャッジ日時 | 2024-06-24 00:29:06 |
合計ジャッジ時間 | 3,195 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#include <iostream> #include <algorithm> #include <iomanip> #include <vector> #include <queue> #include <set> #include <map> #define N_MAX 200002 using namespace std; typedef long long ll; #define MOD 998244353 #define root 3 unsigned int add(const unsigned int x, const unsigned int y){ return (x + y < MOD) ? x + y : x + y - MOD; } unsigned int sub(const unsigned int x, const unsigned int y){ return (x >= y) ? (x - y) : (MOD - y + x); } unsigned int mul(const unsigned int x, const unsigned int y){ return (unsigned long long)x * y % MOD; } unsigned int mod_pow(unsigned int x, unsigned int n){ unsigned int res = 1; while(n > 0){ if(n & 1){ res = mul(res, x); } x = mul(x, x); n >>= 1; } return res; } unsigned int inverse(const unsigned int x){ return mod_pow(x, MOD - 2); } void ntt(vector<int>& a, const bool rev = false){ unsigned int i, j, k, l, p, q, r, s; const unsigned int size = a.size(); if(size == 1) return; vector<int> b(size); r = rev ? (MOD - 1 - (MOD - 1) / size) : (MOD - 1) / size; s = mod_pow(root, r); vector<unsigned int> kp(size / 2 + 1, 1); for(i = 0; i < size / 2; ++i) kp[i + 1] = mul(kp[i], s); for(i = 1, l = size / 2; i < size; i <<= 1, l >>= 1){ for(j = 0, r = 0; j < l; ++j, r += i){ for(k = 0, s = kp[i * j]; k < i; ++k){ p = a[k + r], q = a[k + r + size / 2]; b[k + 2 * r] = add(p, q); b[k + 2 * r + i] = mul(sub(p, q), s); } } swap(a, b); } if(rev){ s = inverse(size); for(i = 0; i < size; i++){ a[i] = mul(a[i], s); } } } vector<int> convolute(const vector<int>& a, const vector<int>& b){ const int size = (int)a.size() + (int)b.size() - 1; int t = 1; while(t < size){ t <<= 1; } vector<int> A(t, 0), B(t, 0); for(int i = 0; i < (int)a.size(); i++){ A[i] = a[i]; } for(int i = 0; i < (int)b.size(); i++){ B[i] = b[i]; } ntt(A), ntt(B); for (int i = 0; i < t; i++){ A[i] = mul(A[i], B[i]); } ntt(A, true); A.resize(size); return A; } class ModInt{ public: ll v; ModInt(ll _v = 0){ v = _v; } ModInt operator+(ll n){ return ModInt((v+n)%MOD); } ModInt operator-(ll n){ return ModInt((v-n+MOD)%MOD); } ModInt operator*(ll n){ return ModInt((v*n)%MOD); } ModInt operator/(ll n){ return ModInt((ModInt(n).inv()*v).v%MOD); } void operator+=(ll n){ v = (v+n)%MOD; } void operator-=(ll n){ v = (v-n+MOD)%MOD; } void operator*=(ll n){ v = (v*n)%MOD; } ModInt operator+(ModInt n){ return ModInt((v+n.v)%MOD); } ModInt operator-(ModInt n){ return ModInt((v-n.v+MOD)%MOD); } ModInt operator*(ModInt n){ return ModInt((v*n.v)%MOD); } ModInt operator/(ModInt n){ return ModInt((n.inv()*v).v%MOD); } void operator+=(ModInt n){ v = (v+n.v)%MOD; } void operator-=(ModInt n){ v = (v-n.v+MOD)%MOD; } void operator*=(ModInt n){ v = (v*n.v)%MOD; } void operator=(ModInt n){ v = n.v; } void operator=(ll n){ v = n; } ModInt inv(){ if(v == 1) return ModInt(1); else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD); } }; ostream& operator<<(ostream& os, const ModInt& m){ os << m.v; return os; } istream & operator >> (istream &in, ModInt &m){ in >> m.v; return in; } ModInt pow(ModInt a, ll n) { ModInt ans = 1; ModInt tmp = a; for (int i = 0; i <= 60; i++) { ll m = (ll)1 << i; if (m & n) { ans *= tmp; } tmp *= tmp; } return ans; } ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX]; void init(){ fac[0]=1;fac[1]=1; finv[0]=1;finv[1]=1; inv[1]=1; for(int i=2;i<N_MAX;i++){ inv[i]=(ModInt)MOD-inv[MOD%i]*(MOD/i); fac[i]=fac[i-1]*(ll) i; finv[i]=finv[i-1]*inv[i]; } } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; init(); ll N, K; cin >> N >> K; vector<int> a(K+1), b(K+1); for(int i = 0; i <= K; i++){ int sgn = (i%2 == 0 ? 1 : -1); a[i] = (finv[i]*sgn).v; a[i] += MOD; a[i] %= MOD; if(i%2 == 1) b[i] = finv[i].v; // a[i] = 1; b[i] = 1; } auto c = convolute(a, b); ModInt ans = 0; for(int i = 0; i <= K; i++){ ModInt tmp = ModInt(c[i])*fac[K]*pow(K-i, N)*finv[K-i]; ans += tmp; } cout << ans << endl; }