9d33e96a5e 2012-03-31        kinaba: #include <iostream>
9d33e96a5e 2012-03-31        kinaba: #include <sstream>
9d33e96a5e 2012-03-31        kinaba: #include <iomanip>
9d33e96a5e 2012-03-31        kinaba: #include <vector>
9d33e96a5e 2012-03-31        kinaba: #include <string>
9d33e96a5e 2012-03-31        kinaba: #include <map>
9d33e96a5e 2012-03-31        kinaba: #include <set>
9d33e96a5e 2012-03-31        kinaba: #include <algorithm>
9d33e96a5e 2012-03-31        kinaba: #include <numeric>
9d33e96a5e 2012-03-31        kinaba: #include <iterator>
9d33e96a5e 2012-03-31        kinaba: #include <functional>
9d33e96a5e 2012-03-31        kinaba: #include <complex>
9d33e96a5e 2012-03-31        kinaba: #include <queue>
9d33e96a5e 2012-03-31        kinaba: #include <stack>
9d33e96a5e 2012-03-31        kinaba: #include <cmath>
9d33e96a5e 2012-03-31        kinaba: #include <cassert>
9d33e96a5e 2012-03-31        kinaba: #include <cstring>
9d33e96a5e 2012-03-31        kinaba: #ifdef __GNUC__
9d33e96a5e 2012-03-31        kinaba: #include <ext/hash_map>
9d33e96a5e 2012-03-31        kinaba: #define unordered_map __gnu_cxx::hash_map
9d33e96a5e 2012-03-31        kinaba: #else
9d33e96a5e 2012-03-31        kinaba: #include <unordered_map>
9d33e96a5e 2012-03-31        kinaba: #endif
9d33e96a5e 2012-03-31        kinaba: using namespace std;
9d33e96a5e 2012-03-31        kinaba: typedef long long LL;
9d33e96a5e 2012-03-31        kinaba: typedef complex<double> CMP;
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: class KingXMagicSpells { public:
9d33e96a5e 2012-03-31        kinaba: 	double expectedNumber(vector <int> ducks, vector <int> spellOne, vector <int> spellTwo, int K)
9d33e96a5e 2012-03-31        kinaba: 	{
9d33e96a5e 2012-03-31        kinaba: 		const int N = ducks.size();
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: 		vector<int> revSpellTwo(N);
9d33e96a5e 2012-03-31        kinaba: 		for(int i=0; i<N; ++i) revSpellTwo[spellTwo[i]] = i;
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: 		double e = 0;
9d33e96a5e 2012-03-31        kinaba: 		for(int B=30; B>=0; --B) {
9d33e96a5e 2012-03-31        kinaba: 			vector<int> dd(N);
9d33e96a5e 2012-03-31        kinaba: 			for(int i=0; i<N; ++i)
9d33e96a5e 2012-03-31        kinaba: 				dd[i] = (ducks[i] & (1<<B) ? 1 : 0);
9d33e96a5e 2012-03-31        kinaba: 			vector<int> xx(N);
9d33e96a5e 2012-03-31        kinaba: 			for(int i=0; i<N; ++i)
9d33e96a5e 2012-03-31        kinaba: 				xx[i] = (spellOne[i] & (1<<B) ? 1 : 0);
9d33e96a5e 2012-03-31        kinaba: 			e += solve(dd, xx, revSpellTwo, K) * (1<<B);
9d33e96a5e 2012-03-31        kinaba: 		}
9d33e96a5e 2012-03-31        kinaba: 		return e;
9d33e96a5e 2012-03-31        kinaba: 	}
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: 	double solve(const vector <int>& dd, const vector <int>& xx, const vector <int>& moveBack, int K)
9d33e96a5e 2012-03-31        kinaba: 	{
9d33e96a5e 2012-03-31        kinaba: 		memo.clear();
9d33e96a5e 2012-03-31        kinaba: 		return prob(dd, xx, moveBack, K, 0, 1);
9d33e96a5e 2012-03-31        kinaba: 	}
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: 	map<int, double> memo;
9d33e96a5e 2012-03-31        kinaba: 	double prob(
9d33e96a5e 2012-03-31        kinaba: 		const vector <int>& dd, const vector <int>& xx, const vector <int>& moveBack,
9d33e96a5e 2012-03-31        kinaba: 		int K, int room, int bit) {
9d33e96a5e 2012-03-31        kinaba: 		if( K == 0 ) {
9d33e96a5e 2012-03-31        kinaba: 			return dd[room]==bit ? 1.0 : 0.0;
9d33e96a5e 2012-03-31        kinaba: 		}
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: 		int key = (K * 100 + room) * 2 + bit;
9d33e96a5e 2012-03-31        kinaba: 		if( memo.count(key) )
9d33e96a5e 2012-03-31        kinaba: 			return memo[key];
9d33e96a5e 2012-03-31        kinaba: 		double e = 0.5 * prob(dd,xx,moveBack,K-1,moveBack[room],bit)
9d33e96a5e 2012-03-31        kinaba: 		         + 0.5 * prob(dd,xx,moveBack,K-1,room,bit^xx[room]);
9d33e96a5e 2012-03-31        kinaba: 		return memo[key] = e;
9d33e96a5e 2012-03-31        kinaba: 	}
9d33e96a5e 2012-03-31        kinaba: };
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: // BEGIN CUT HERE
9d33e96a5e 2012-03-31        kinaba: #include <ctime>
9d33e96a5e 2012-03-31        kinaba: double start_time; string timer()
9d33e96a5e 2012-03-31        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
9d33e96a5e 2012-03-31        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
9d33e96a5e 2012-03-31        kinaba:  { os << "{ ";
9d33e96a5e 2012-03-31        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
9d33e96a5e 2012-03-31        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
9d33e96a5e 2012-03-31        kinaba: void verify_case(const double& Expected, const double& Received) {
9d33e96a5e 2012-03-31        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
9d33e96a5e 2012-03-31        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
9d33e96a5e 2012-03-31        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
9d33e96a5e 2012-03-31        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
9d33e96a5e 2012-03-31        kinaba: #define END	 verify_case(_, KingXMagicSpells().expectedNumber(ducks, spellOne, spellTwo, K));}
9d33e96a5e 2012-03-31        kinaba: int main(){
9d33e96a5e 2012-03-31        kinaba: 
9d33e96a5e 2012-03-31        kinaba: CASE(0)
9d33e96a5e 2012-03-31        kinaba: 	int ducks_[] = {5, 3, 7};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> ducks(ducks_, ducks_+sizeof(ducks_)/sizeof(*ducks_));
9d33e96a5e 2012-03-31        kinaba: 	int spellOne_[] = {1, 7, 4};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellOne(spellOne_, spellOne_+sizeof(spellOne_)/sizeof(*spellOne_));
9d33e96a5e 2012-03-31        kinaba: 	int spellTwo_[] = {1, 0, 2};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellTwo(spellTwo_, spellTwo_+sizeof(spellTwo_)/sizeof(*spellTwo_));
9d33e96a5e 2012-03-31        kinaba: 	int K = 1;
9d33e96a5e 2012-03-31        kinaba: 	double _ = 3.5;
9d33e96a5e 2012-03-31        kinaba: END
9d33e96a5e 2012-03-31        kinaba: CASE(1)
9d33e96a5e 2012-03-31        kinaba: 	int ducks_[] = {5, 8};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> ducks(ducks_, ducks_+sizeof(ducks_)/sizeof(*ducks_));
9d33e96a5e 2012-03-31        kinaba: 	int spellOne_[] = {53, 7};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellOne(spellOne_, spellOne_+sizeof(spellOne_)/sizeof(*spellOne_));
9d33e96a5e 2012-03-31        kinaba: 	int spellTwo_[] = {1, 0};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellTwo(spellTwo_, spellTwo_+sizeof(spellTwo_)/sizeof(*spellTwo_));
9d33e96a5e 2012-03-31        kinaba: 	int K = 2;
9d33e96a5e 2012-03-31        kinaba: 	double _ = 21.5;
9d33e96a5e 2012-03-31        kinaba: END
9d33e96a5e 2012-03-31        kinaba: CASE(2)
9d33e96a5e 2012-03-31        kinaba: 	int ducks_[] = {123, 456, 789, 1234, 56789};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> ducks(ducks_, ducks_+sizeof(ducks_)/sizeof(*ducks_));
9d33e96a5e 2012-03-31        kinaba: 	int spellOne_[] = {0, 0, 0, 0, 0};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellOne(spellOne_, spellOne_+sizeof(spellOne_)/sizeof(*spellOne_));
9d33e96a5e 2012-03-31        kinaba: 	int spellTwo_[] = {0, 1, 2, 3, 4};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellTwo(spellTwo_, spellTwo_+sizeof(spellTwo_)/sizeof(*spellTwo_));
9d33e96a5e 2012-03-31        kinaba: 	int K = 50;
9d33e96a5e 2012-03-31        kinaba: 	double _ = 123.0;
9d33e96a5e 2012-03-31        kinaba: END
9d33e96a5e 2012-03-31        kinaba: CASE(3)
9d33e96a5e 2012-03-31        kinaba: 	int ducks_[] = {83291232, 3124231, 192412, 3813249, 629231, 9998989};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> ducks(ducks_, ducks_+sizeof(ducks_)/sizeof(*ducks_));
9d33e96a5e 2012-03-31        kinaba: 	int spellOne_[] = {58, 37, 44, 66, 72, 19};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellOne(spellOne_, spellOne_+sizeof(spellOne_)/sizeof(*spellOne_));
9d33e96a5e 2012-03-31        kinaba: 	int spellTwo_[] = {2, 0, 1, 5, 4, 3};
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellTwo(spellTwo_, spellTwo_+sizeof(spellTwo_)/sizeof(*spellTwo_));
9d33e96a5e 2012-03-31        kinaba: 	int K = 11;
9d33e96a5e 2012-03-31        kinaba: 	double _ = 2.888186784716797E7;
9d33e96a5e 2012-03-31        kinaba: END
9d33e96a5e 2012-03-31        kinaba: /*
9d33e96a5e 2012-03-31        kinaba: CASE(4)
9d33e96a5e 2012-03-31        kinaba: 	int ducks_[] = ;
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> ducks(ducks_, ducks_+sizeof(ducks_)/sizeof(*ducks_));
9d33e96a5e 2012-03-31        kinaba: 	int spellOne_[] = ;
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellOne(spellOne_, spellOne_+sizeof(spellOne_)/sizeof(*spellOne_));
9d33e96a5e 2012-03-31        kinaba: 	int spellTwo_[] = ;
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellTwo(spellTwo_, spellTwo_+sizeof(spellTwo_)/sizeof(*spellTwo_));
9d33e96a5e 2012-03-31        kinaba: 	int K = ;
9d33e96a5e 2012-03-31        kinaba: 	double _ = ;
9d33e96a5e 2012-03-31        kinaba: END
9d33e96a5e 2012-03-31        kinaba: CASE(5)
9d33e96a5e 2012-03-31        kinaba: 	int ducks_[] = ;
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> ducks(ducks_, ducks_+sizeof(ducks_)/sizeof(*ducks_));
9d33e96a5e 2012-03-31        kinaba: 	int spellOne_[] = ;
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellOne(spellOne_, spellOne_+sizeof(spellOne_)/sizeof(*spellOne_));
9d33e96a5e 2012-03-31        kinaba: 	int spellTwo_[] = ;
9d33e96a5e 2012-03-31        kinaba: 	  vector <int> spellTwo(spellTwo_, spellTwo_+sizeof(spellTwo_)/sizeof(*spellTwo_));
9d33e96a5e 2012-03-31        kinaba: 	int K = ;
9d33e96a5e 2012-03-31        kinaba: 	double _ = ;
9d33e96a5e 2012-03-31        kinaba: END
9d33e96a5e 2012-03-31        kinaba: */
9d33e96a5e 2012-03-31        kinaba: }
9d33e96a5e 2012-03-31        kinaba: // END CUT HERE