結果

問題 No.174 カードゲーム(Hard)
ユーザー shimomireshimomire
提出日時 2015-03-27 01:15:41
言語 C++11
(gcc 11.4.0)
結果
AC  
実行時間 458 ms / 2,000 ms
コード長 7,651 bytes
コンパイル時間 1,075 ms
コンパイル使用メモリ 126,072 KB
実行使用メモリ 19,700 KB
最終ジャッジ日時 2024-07-06 21:27:34
合計ジャッジ時間 5,290 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 1 ms
6,940 KB
testcase_02 AC 444 ms
19,644 KB
testcase_03 AC 448 ms
19,632 KB
testcase_04 AC 445 ms
19,632 KB
testcase_05 AC 447 ms
19,608 KB
testcase_06 AC 458 ms
19,576 KB
testcase_07 AC 444 ms
19,700 KB
testcase_08 AC 447 ms
19,660 KB
testcase_09 AC 442 ms
19,692 KB
testcase_10 AC 1 ms
6,940 KB
testcase_11 AC 2 ms
6,940 KB
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 <cassert>// c
#include <iostream>// io
#include <iomanip>
#include <fstream>
#include <sstream>
#include <vector>// container
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <stack>
#include <algorithm>// other
#include <complex>
#include <numeric>
#include <functional>
#include <random>
#include <regex>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

#define ALL(c) (begin(c)),(end(c))
#define REP(i,n) FOR(i,0,n)
#define REPr(i,n) FORr(i,0,n)
#define FOR(i,l,r) for(int i=(int)(l);i<(int)(r);++i)
#define FORr(i,l,r) for(int i=(int)(r)-1;i>=(int)(l);--i)
#define EACH(it,o) for(auto it = (o).begin(); it != (o).end(); ++it)
#define IN(l,v,r) ((l)<=(v) && (v)<(r))
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end())
//debug
#define DUMP(x)  cerr << #x << " = " << (x)
#define LINE()    cerr<< " (L" << __LINE__ << ")"

class range {
private:
	struct Iter{
		int v;
		int operator*(){return v;}
		bool operator!=(Iter& itr) {return v < itr.v;}
		void operator++() {++v;}
	};
	Iter i, n;
public:
	range(int n) : i({0}), n({n}) {}
	range(int i, int n) : i({i}), n({n}) {}
	Iter& begin() {return i;}
	Iter& end() {return n;}
};

//input
template<typename T1,typename T2> istream& operator >> (istream& is,pair<T1,T2>& p){is>>p.first>>p.second;return is;}
template<typename T1> istream& operator >> (istream& is,tuple<T1>& t){is >> get<0>(t);return is;}
template<typename T1,typename T2> istream& operator >> (istream& is,tuple<T1,T2>& t){is >> get<0>(t) >> get<1>(t);return is;}
template<typename T1,typename T2,typename T3> istream& operator >> (istream& is,tuple<T1,T2,T3>& t){is >>get<0>(t)>>get<1>(t)>>get<2>(t);return is;}
template<typename T1,typename T2,typename T3,typename T4> istream& operator >> (istream& is,tuple<T1,T2,T3,T4>& t){is >> get<0>(t)>>get<1>(t)>>get<2>(t)>>get<3>(t);return is;}
template<typename T1,typename T2,typename T3,typename T4,typename T5> istream& operator >> (istream& is, const tuple<T1,T2,T3,T4,T5>& t){is >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t) >> get<4>(t);return is;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6> istream& operator >> (istream& is, const tuple<T1,T2,T3,T4,T5,T6>& t){is >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t) >> get<4>(t) >> get<5>(t);return is;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6,typename T7> istream& operator >> (istream& is, const tuple<T1,T2,T3,T4,T5,T6,T7>& t){is >> get<0>(t) >> get<1>(t) >> get<2>(t) >> get<3>(t) >> get<4>(t) >> get<5>(t) >> get<6>(t);return is;}
template<typename T> istream& operator >> (istream& is,vector<T>& as){REP(i,as.size())is >>as[i];return is;}

//output
template<typename T> ostream& operator << (ostream& os, const set<T>& ss){for(auto a:ss){if(a!=ss.begin())os<<" "; os<<a;}return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const pair<T1,T2>& p){os<<p.first<<" "<<p.second;return os;}
template<typename K,typename V> ostream& operator << (ostream& os, const map<K,V>& m){bool isF=true;for(auto& p:m){if(!isF)os<<endl;os<<p;isF=false;}return os;}
template<typename T1> ostream& operator << (ostream& os, const tuple<T1>& t){os << get<0>(t);return os;}
template<typename T1,typename T2> ostream& operator << (ostream& os, const tuple<T1,T2>& t){os << get<0>(t)<<" "<<get<1>(t);return os;}
template<typename T1,typename T2,typename T3> ostream& operator << (ostream& os, const tuple<T1,T2,T3>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t)<<" "<<get<5>(t);return os;}
template<typename T1,typename T2,typename T3,typename T4,typename T5,typename T6,typename T7> ostream& operator << (ostream& os, const tuple<T1,T2,T3,T4,T5,T6,T7>& t){os << get<0>(t)<<" "<<get<1>(t)<<" "<<get<2>(t)<<" "<<get<3>(t)<<" "<<get<4>(t)<<" "<<get<5>(t)<<" "<<get<6>(t);return os;}
template<typename T> ostream& operator << (ostream& os, const vector<T>& as){REP(i,as.size()){if(i!=0)os<<" "; os<<as[i];}return os;}
template<typename T> ostream& operator << (ostream& os, const vector<vector<T>>& as){REP(i,as.size()){if(i!=0)os<<endl; os<<as[i];}return os;}

//input
char tmp[1000];
#define nextInt(n) scanf("%d",&n)
#define nextLong(n) scanf("%lld",&n) //I64d
#define nextDouble(n) scanf("%lf",&n) 
#define nextChar(n) scanf("%c",&n)
#define nextString(n) scanf("%s",tmp);n=tmp

// values
template<typename T> T INF(){assert(false);};
template<> int INF<int>(){return 1<<28;};
template<> ll INF<ll>(){return 1LL<<58;};
template<> double INF<double>(){return 1e16;};
template<> long double INF<long double>(){return 1e16;};

template<class T> T EPS(){assert(false);};
template<> int EPS<int>(){return 1;};
template<> ll EPS<ll>(){return 1LL;};
template<> double EPS<double>(){return 1e-8;};
template<> long double EPS<long double>(){return 1e-8;};

template<typename T,typename U> T pmod(T v,U M){return (v%M+M)%M;}

class Main{
	public:
	void run(){
		int N;double PA,PB;cin >> N >> PA >> PB;
		vector<ll> as(N),bs(N); cin >> as >> bs;
		sort(ALL(as));sort(ALL(bs));


		// k 回目に i番目を選ぶ確率
		vector<vector<double>> dpA(N+1,vector<double>(N));
		{
			// k 回目に bit 状態
			vector<double> mvdpA(1<<N);
			vector<double> nmvdpA(1<<N);
			mvdpA[(1<<N)-1]=1;
			for(int k=1;k<=N;k++){
				for(int bit=0;bit<(1<<N);bit++){
					if(__builtin_popcount(bit)!=N-k+1)continue;

					int s=0;
					for(int i=0;i<N;i++)if(bit&(1<<i))s++;

					bool isF=true;
					for(int i=0;i<N;i++)if(bit&(1<<i)){
						if(s==1){
							nmvdpA[bit-(1<<i)]+=mvdpA[bit];
							dpA[k][i] += mvdpA[bit];continue;
						}
						if(isF){
							nmvdpA[bit-(1<<i)]+=PA*mvdpA[bit];
							dpA[k][i] +=PA*mvdpA[bit];
							isF=false;
						}else{
							nmvdpA[bit-(1<<i)]+=(1-PA)/(s-1)*mvdpA[bit];
							dpA[k][i] +=(1-PA)/(s-1)*mvdpA[bit];
						}
					}
				}
				mvdpA=nmvdpA;
			}
		}


		// k 回目に i番目を選ぶ確率
		vector<vector<double>> dpB(N+1,vector<double>(N));
		{
			// k 回目に bit 状態
			vector<double> mvdpB(1<<N);
			vector<double> nmvdpB(1<<N);
			mvdpB[(1<<N)-1]=1;
			for(int k=1;k<=N;k++){
				for(int bit=0;bit<(1<<N);bit++){
					if(__builtin_popcount(bit)!=N-k+1)continue;

					int s=0;
					for(int i=0;i<N;i++)if(bit&(1<<i))s++;

					bool isF=true;
					for(int i=0;i<N;i++)if(bit&(1<<i)){
						if(s==1){
							nmvdpB[bit-(1<<i)]+=mvdpB[bit];
							dpB[k][i] += mvdpB[bit];continue;
						}
						if(isF){
							nmvdpB[bit-(1<<i)]+=PB*mvdpB[bit];
							dpB[k][i] +=PB*mvdpB[bit];
							isF=false;
						}else{
							nmvdpB[bit-(1<<i)]+=(1-PB)/(s-1)*mvdpB[bit];
							dpB[k][i] +=(1-PB)/(s-1)*mvdpB[bit];
						}
					}
				}
				mvdpB=nmvdpB;
			}
		}

		double res = 0;
		for(int k=1;k<=N;k++){
			for(int i=0;i<N;i++)for(int j=0;j<N;j++){
				if(as[i]>bs[j])res+=dpA[k][i]*dpB[k][j]*(as[i]+bs[j]);
			}
		}
		cout << res <<endl;
	}
};

int main(){
	cout <<fixed<<setprecision(20);
	cin.tie(0);
	ios::sync_with_stdio(false);
	Main().run();
	return 0;
}
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