Artifact e145c5181a2633a04247058705b2879f1bea3bc9
#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>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const unsigned MODVAL = 1000000007;
struct mint
{
unsigned val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(unsigned x):val(x%MODVAL) {}
mint(LL x):val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x+=y; }
mint operator-(mint x, mint y) { return x-=y; }
mint operator*(mint x, mint y) { return x*=y; }
mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
mint operator/(mint x, mint y) { return x/=y; }
vector<mint> FAC_(1,1);
mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*LL(FAC_.size()) ); return FAC_[n]; }
// nCk :: O(1) time, O(n^2) space.
vector< vector<mint> > CP_;
mint C(int n, int k) {
while( CP_.size() <= n ) {
int nn = CP_.size();
CP_.push_back(vector<mint>(nn+1,1));
for(int kk=1; kk<nn; ++kk)
CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
}
return k<0 || n<k ? 0 : CP_[n][k];
}
class AlmostEulerianGraph { public:
int calculateGraphs(int n)
{
memo.assign(n+1, -1);
return (calcExactEulerian(n) * (LL(n)*(n-1)/2+1)).val;
}
vector<int> memo;
mint calcExactEulerian(int n)
{
if(n == 1)
return 1;
if(memo[n] != -1)
return memo[n];
mint sum = 0;
for(int k=1; k<n; ++k)
sum += k * C(n, k) * POW(2, C(n-k-1, 2).val) * calcExactEulerian(k);
return memo[n] = (POW(2, C(n-1, 2).val) - sum/n).val;
}
};
// 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 int& Expected, const int& 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(_, AlmostEulerianGraph().calculateGraphs(n));}
int main(){
CASE(0)
int n = 3;
int _ = 4;
END
CASE(1)
int n = 2;
int _ = 0;
END
CASE(2)
int n = 42;
int _ = 29010676;
END
CASE(3)
int n = 2000;
int _ = -1;
END
/*
CASE(4)
int n = ;
int _ = ;
END
*/
}
// END CUT HERE