Artifact efa7784af0c0c5301f3005579d53d4fae24ec439

• File SRM/565-U/1B.cpp
  • 2012-12-21 10:45:08 - part of checkin [42f877f59c] on branch trunk - 565 (user: kinaba) [annotate]

#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;

class TheDivisionGame { public:
	long long countWinningIntervals(int L, int R)
	{
		// eratos ---------------------------------
		vector<int> ps;
		{
			static const int N = 50000;
			vector<bool> isp(N+1, true);
			for(int p=2; p<=N; ++p)
				if( isp[p] ) {
					ps.push_back(p);
					for(int q=p+p; q<=N; q+=p)
						isp[q] = false;
				}
		}

		// prime decomposition --------------------
		vector< vector<int> > pd(R-L+1);
		vector<int> rm(R-L+1);
		for(int v=L; v<=R; ++v)
			rm[v-L] = v;

		for(int i=0; i<ps.size(); ++i)
		{
			int p = ps[i];
			for(int q=(L+p-1)/p*p; q<=R; q+=p)
			{
				int& r = rm[q-L];
				int qn = 0;
				while(r%p==0) qn++, r/=p;
				pd[q-L].push_back(qn);
			}
		}

		for(int v=L; v<=R; ++v)
			if(rm[v-L] > 1)
				pd[v-L].push_back(1);

		// grundy ------------------------------------
		vector<int> nim;
		for(int i=0; i<pd.size(); ++i) {
			nim.push_back(nim_calc(pd[i]));
		}

		// xorsum ------------------------------------
		vector<int> sum;
		map<int, LL> hist;
		sum.push_back(0);
		hist[sum.back()] ++;
		for(int i=0; i<nim.size(); ++i) {
			sum.push_back(sum.back() ^ nim[i]);
			hist[sum.back()] ++;
		}

		LL lose = 0;
		for(map<int,LL>::iterator it=hist.begin(); it!=hist.end(); ++it)
			lose += it->second * (it->second-1) / 2;
		LL w = R-L+2;
		LL total = w*(w-1)/2;
		return total - lose;
	}

	int nim_calc(vector<int> sig)
	{
		if( sig.empty() )
			return 0;
		int v = sig[0];
		for(int i=1; i<sig.size(); ++i)
			v = merge(v, sig[i]);
		return v;
	}

	map<pair<int,int>, int> memo;
	int merge(int a, int b)
	{
		if(a>b) swap(a,b);
		if(a==0)
			return b;
		pair<int,int> key(a,b);
		if(memo.count(key))
			return memo[key];

		vector<bool> used;
		for(int x=0; x<=a; ++x)
		for(int y=0; y<=b; ++y)
		if(x!=a || y!=b)
		{
			int k = merge(x, y);
			if(used.size()<=k) used.resize(k+1);
			used[k] = true;
		}

		used.push_back(false);
		return memo[key] = find(used.begin(), used.end(), false) - used.begin();
	}
};

// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
 { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
 { os << "{ ";
   for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
   os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const long long& Expected, const long long& Received) {
 bool ok = (Expected == Received);
 if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
 cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END	 verify_case(_, TheDivisionGame().countWinningIntervals(L, R));}
int main(){
CASE(0)
	int L = 9; 
	int R = 10; 
	long long _ = 2LL; 
END
CASE(1)
	int L = 2; 
	int R = 5; 
	long long _ = 9LL; 
END
CASE(2)
	int L = 2; 
	int R = 6; 
	long long _ = 13LL; 
END
CASE(3)
	int L = 2; 
	int R = 100; 
	long long _ = 4345LL; 
END
CASE(4)
	int L = 12566125; 
	int R = 12567777; 
	long long _ = 1313432LL; 
END
CASE(5)
	int L = 1000000000; 
	int R = 1001000000; 
	long long _ = -1LL; 
END
CASE(6)
	int L = 2; 
	int R = 2; 
	long long _ = 0LL; 
END
CASE(6)
	int L = 2; 
	int R = 3; 
	long long _ = 0LL; 
END
CASE(6)
	int L = 2; 
	int R = 4; 
	long long _ = 3LL; 
END
CASE(6)
	int L = 4; 
	int R = 4; 
	long long _ = 1LL; 
END

}
// END CUT HERE