結果

問題 No.2514 Twelvefold Way Returns
ユーザー chineristAC
提出日時 2023-10-20 22:32:29
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 671 ms / 3,000 ms
コード長 3,324 bytes
コンパイル時間 6,487 ms
コンパイル使用メモリ 177,336 KB
最終ジャッジ日時 2025-02-17 10:13:58
ジャッジサーバーID
(参考情報)
judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 38
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <random>
#include <stdio.h>
#include <fstream>
#include <functional>
#include <cassert>
#include <atcoder/modint>
using namespace std;
using namespace atcoder;
using mint = modint998244353;
#define rep(i,n) for (int i=0;i<n;i+=1)
#define append push_back
#define all(x) (x).begin(), (x).end()
template<class T>
using vec = vector<T>;
template<class T>
using vvec = vec<vec<T>>;
template<class T>
using vvvec = vec<vvec<T>>;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
template<class T>
bool chmin(T &a, T b){
if (a>b){
a = b;
return true;
}
return false;
}
template<class T>
bool chmax(T &a, T b){
if (a<b){
a = b;
return true;
}
return false;
}
template<class T>
T sum(vec<T> x){
T res=0;
for (auto e:x){
res += e;
}
return res;
}
template<class T>
void printv(vec<T> x){
for (auto e:x){
cout<<e<<" ";
}
cout<<"\n";
}
template<class T>
ostream& operator<<(ostream& os, const vec<T>& A){
os << "{";
rep(i,A.size()){
os << A[i];
if (i!=A.size()-1){
os << ", ";
}
}
os << "}" ;
return os;
}
template<class T>
ostream& operator<<(ostream& os, const deque<T>& A){
os << "deque{[";
rep(i,A.size()){
os << A[i];
if (i!=A.size()-1){
os << ", ";
}
}
os << "]}" ;
return os;
}
template<class T>
ostream& operator<<(ostream& os, const pair<T,T>& A){
os << "(";
os << A.first ;
os << ", ";
os << A.second;
os << ")";
return os;
}
pair<mint,mint> omega_prod(pair<mint,mint> X,pair<mint,mint> Y){
auto [a,b] = X;
auto [c,d] = Y;
return {(a*d+b*c-a*c),b*d-a*c};
};
pair<mint,mint> omega_pow(pair<mint,mint> X,int N){
pair<mint,mint> res = {0,1};
while (N){
if ((N&1)){
res = omega_prod(res,X);
}
X = omega_prod(X,X);
N >>= 1;
}
return res;
}
ostream& operator<<(ostream& os, const mint a){
os << a.val();
return os;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N,M;
cin>>N>>M;
vec<vec<pair<mint,mint>>> dp(2*M+1,vec<pair<mint,mint>>(2*M+1,{0,0}));
pair<mint,mint> zero = {0,0};
dp[M][M] = {0,1};
mint i3 = mint(3).inv();
for (int _=0;_<M;_++){
vec<vec<pair<mint,mint>>> ndp(2*M+1,vec<pair<mint,mint>>(2*M+1,{0,0}));
for (int i=0;i<=2*M;i++){
for (int j=0;j<=2*M;j++){
if (dp[i][j] == zero) continue;
auto e = dp[i][j];
ndp[i][j+1].first += e.first * i3;
ndp[i][j+1].second += e.second * i3;
e = omega_prod(e,{1,0});
ndp[i-1][j-1].first += e.first * i3;
ndp[i-1][j-1].second += e.second * i3;
e = omega_prod(e,{1,0});
ndp[i+1][j].first += e.first * i3;
ndp[i+1][j].second += e.second * i3;
}
}
swap(dp,ndp);
}
mint res = 0;
for (int i=0;i<=2*M;i++){
for (int j=0;j<=2*M;j++){
auto e = omega_pow({i-M,j-M},N);
auto f = omega_prod(dp[i][j],e);
res += f.second;
}
}
cout << res.val() << endl;
}
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