Submission #323607

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Source Code Expand

#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 <limits>
#include <numeric>
#include <utility>
#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< VI >;
using VS = vector< string >;
using SS = stringstream;
using PII = pair< int, int >;
using VPII = vector< PII >;
template < typename T = int > using VT = vector<T>;
template < typename T = int > using VVT = VT< VT<T> >;
template < typename T = int > using LIM = numeric_limits< 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<v.size(); ++i ){ s << (" "+!i) << v[i]; } return s; }
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 REP( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i )
#define FOR( e, c ) for ( auto &e : c )
#define ALL( c ) ( c ).begin(), ( c ).end()
#define AALL( a, t ) ( t* )a, ( t* )a + sizeof( a ) / sizeof( t )
#define DRANGE( c, p ) ( c ).begin(), ( c ).begin() + p, ( c ).end()

#define SZ( v ) ( (int)( v ).size() )
#define PB push_back
#define EM emplace
#define EB emplace_back
#define BI back_inserter

#define EXIST( c, e ) ( ( c ).find( e ) != ( c ).end() )

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

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

double dp1[ 128 ][ 128 ][ 128 ];
double dp2[ 128 ][ 128 ];

int main()
{
	cin.tie( 0 );
	ios::sync_with_stdio( false );

	int N;
	cin >> N;

	dp1[0][0][0] = 1;
	REP( i, 0, N + 1 )
	{
		REP( j, 0, N + 1 )
		{
			REP( k, 0, N + 1 )
			{
				const double p = dp1[i][j][k] / 3;
				dp1[ i + 1 ][j][k] += p;
				dp1[i][ j + 1 ][k] += p;
				dp1[i][j][ k + 1 ] += p;
			}
		}
	}


	VVT< double > prob( N + 1, VT< double >( N + 1 ) );
	REP( i, 0, N + 1 )
	{
		REP( j, 0, N + 1 )
		{
			REP( k, 0, N + 1 )
			{
				if ( N < i + j + k || i + j + k <= 1 )
				{
					continue;
				}

				const double p = dp1[i][j][k];

				const int n = i + j + k;
				VI as = { i, j, k };
				sort( ALL( as ) );
				as.erase( remove( ALL( as ), 0 ), as.end() );

				if ( as.back() == n || i == j && j == k )
				{
					prob[n][n] += p;
				}
				else if ( as[0] < as[1] )
				{
					prob[n][ as[0] ] += p;
				}
// 				else if ( as[0] == as[1] && as[1] < as[2] )
				else
				{
					prob[n][ as[0] ] += p;
				}
			}
		}
	}

	dp2[0][N] = 1;
	double res = 0;
	REP( i, 0, 127 )
	{
		res += dp2[i][1] * i;

		REP( j, 2, N + 1 )
		{
			REP( k, 1, N + 1 )
			{
				dp2[ i + 1 ][k] += dp2[i][j] * prob[j][k];
			}
		}
	}

	cout << setprecision( 8 ) << fixed << res << endl;

	return 0;
}

Submission Info

Judge Result