結果

問題 No.2872 Depth of the Parentheses
コンテスト
ユーザー torus711
提出日時 2024-09-06 22:21:45
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 113 ms / 2,000 ms
コード長 4,915 bytes
コンパイル時間 1,187 ms
コンパイル使用メモリ 123,348 KB
最終ジャッジ日時 2025-02-24 04:32:39
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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 * 20 RE * 5
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 # 

#include <iostream>
#include <iomanip>
#include <sstream>
#include <vector>
#include <string>
#include <set>
#include <unordered_set>
#include <map>
#include <unordered_map>
#include <stack>
#include <queue>
#include <deque>
#include <algorithm>
#include <functional>
#include <iterator>
#include <ranges>
#include <limits>
#include <numeric>
#include <utility>
#include <type_traits>
#include <cmath>
#include <cassert>
#include <cstdio>

using namespace std;
using namespace placeholders;

using LL = long long;
using ULL = unsigned long long;
using VI = vector< int >;
using VVI = vector< vector< int > >;
using VLL = vector< long long >;
using VVLL = vector< vector< long long > >;
using VS = vector< string >;
using ISS = istringstream;
using OSS = ostringstream;
using PII = pair< int, int >;
using VPII = vector< pair< int, int > >;
template < typename T = int > using LIM = numeric_limits< T >;
template < typename T = int > using OSI = ostream_iterator< T >;

template < typename T > inline istream& operator>>( istream &s, vector< T > &v ){ for ( T &t : v ) { s >> t; } return s; }
template < typename T > inline ostream& operator<<( ostream &s, const vector< T > &v ){ for ( int i = 0; i < int( v.size() ); ++i ){ s << ( " " + !i ) << v[i]; } return s; }

void in_impl(){};
template < typename T, typename... TS > void in_impl( T &head, TS &... tail ){ cin >> head; in_impl( tail ... ); }
#define IN( T, ... ) T __VA_ARGS__; in_impl( __VA_ARGS__ );

template < typename T, typename V >
auto make_vector( const int n, const V &v )
{
 return vector< T >( n, v );
}
template < typename T, typename... TS >
auto make_vector( const int n, TS... ts )
{
 return vector< decltype( make_vector< T >( forward< TS >( ts )...) ) >( n, make_vector< T >( forward< TS >( ts )... ) );
}

template < typename T, typename V >
auto make_vector0()
{
	return vector< T >();
}
template < typename T, typename... TS >
auto make_vector0( const int n, TS... ts )
{
	return vector< decltype( make_vector0< T >( forward< TS >( ts )...) ) >( n, make_vector0< T >( forward< TS >( ts )... ) );
}

template < typename T > inline T fromString( const string &s ) { T res; istringstream iss( s ); iss >> res; return res; }
template < typename T > inline string toString( const T &a ) { ostringstream oss; oss << a; return oss.str(); }

#define NUMBERED( name, number ) NUMBERED2( name, number )
#define NUMBERED2( name, number ) name ## _ ## number
#define REP1( n ) REP2( NUMBERED( REP_COUNTER, __LINE__ ), n )
#define REP2( i, n ) REP3( i, 0, n )
#define REP3( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i )
#define GET_REP( a, b, c, F, ... ) F
#define REP( ... ) GET_REP( __VA_ARGS__, REP3, REP2, REP1 )( __VA_ARGS__ )
#define FOR( e, c ) for ( auto &&e : c )
#define ALL( c ) begin( c ), end( c )
#define AALL( a ) ( remove_all_extents< decltype( a ) >::type * )a, ( remove_all_extents< decltype( a ) >::type * )a + sizeof( a ) / sizeof( remove_all_extents< decltype( a ) >::type )

#define MAP_PRED( c ) transform( begin( c ), end( c ), begin( c ), bind( minus< int >(), _1, 1 ) );

#define SZ( v ) ( (int)( v ).size() )
#define EXISTS( c, e ) ( ( c ).find( e ) != ( c ).end() )

template < typename T > inline bool chmin( T &a, const T &b ){ if ( b < a ) { a = b; return true; } return false; }
template < typename T > inline bool chmax( T &a, const T &b ){ if ( a < b ) { a = b; return true; } return false; }

#define PB push_back
#define EM emplace
#define EB emplace_back
#define BI back_inserter

#define MP make_pair
#define fst first
#define snd second

#define DUMP( x ) cerr << #x << " = " << ( x ) << endl

//     Λ   Λ＿_
//  ／(*ﾟーﾟ)／＼
// ／| ￣U U￣|＼／
//   |      |／

#include <atcoder/modint>
using namespace atcoder;
using MINT = modint998244353;
inline istream& operator>>( istream &s, MINT &t ){ int a; s >> a; t = a; return s; };
inline istream& operator>>( istream &s, vector< MINT > &v ){ for ( MINT &a : v ){ s >> a; } return s; }
inline ostream& operator<<( ostream &s, const MINT &t ){ s << t.val(); return s; }

MINT expected( const MINT &P, const string &S )
{
	int ma = 0, d = 0;
	MINT prob = 1;
	FOR( c, S )
	{
		if ( c == '(' )
		{
			++d;
			prob *= P;
		}
		else
		{
			--d;
			prob *= P.inv();
		}
		if ( d < 0 )
		{
			return 0;
		}
		chmax( ma, d );
	}

	return d ? 0 : ma * prob;
}

int main()
{
	cin.tie( nullptr );
	ios::sync_with_stdio( false );
	cout << setprecision( 12 ) << fixed;

	IN( int, X, K );

	assert( K <= 10 );

	if ( X == 0 || X == 100 )
	{
		cout << 0 << endl;
		return 0;
	}

	const MINT P = X * MINT( 100 ).inv();

	VI is_closing( 2 * K );
	fill( begin( is_closing ) + K, end( is_closing ), 1 );

	MINT res = 0;
	do
	{
		string s;
		REP( i, 2 * K )
		{
			s += "()"[ is_closing[i] ];
		}

		res += P.pow( K ) * ( 1 - P ).pow( K ) * expected( P, s );
	}
	while ( next_permutation( ALL( is_closing ) ) );

	cout << res << endl;

	return 0;
}
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