Artifact 18e652cfb8226cd8700c11531c56d2b24fc5d81e
#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;
int gcd(int a, int b)
{
while(a)
swap(a, b%=a);
return b;
}
class FindPolygons { public:
double minimumPolygon(int L)
{
if(L<=2)
return -1;
if(L%2==1) // euclid%2 == manhattan%2. tour is always even.
return -1;
map<int, vector<pair<int,int>>> pyt;
for(int k=1; k<=L; ++k) {
auto& pk = pyt[k];
pk.emplace_back(0, k);
pk.emplace_back(k, 0);
pk.emplace_back(0, -k);
pk.emplace_back(-k, 0);
}
for(int m=1; m*m<=L/2; ++m)
for(int n=1; n<m && m*m+n*n<=L/2; ++n)
if(((m^n)&1) && gcd(m,n)==1) {
int a = m*m-n*n, b = 2*m*n, c = m*m+n*n;
for(int k=1; k*c<=L; ++k) {
auto& pk = pyt[k*c];
pk.emplace_back(k*a, k*b);
pk.emplace_back(k*a, -k*b);
pk.emplace_back(-k*a, k*b);
pk.emplace_back(-k*a, -k*b);
pk.emplace_back(k*b, k*a);
pk.emplace_back(k*b, -k*a);
pk.emplace_back(-k*b, k*a);
pk.emplace_back(-k*b, -k*a);
}
}
// Triangle
int best = L;
for(int a=1; a*3<=L; ++a)
for(int b=a; a+b*2<=L; ++b)
{
int c = L-a-b;
for(auto& av : pyt[a])
{
int ax=av.first;
int ay=av.second;
if(ax>=0 && ay>=0)
for(auto& bv : pyt[b])
{
int bx=bv.first;
int by=bv.second;
int cx=-ax-bx;
int cy=-ay-by;
if(ax*by!=ay*bx && cx*cx+cy*cy == c*c) {
best = min(best, c-a);
break;
}
}
}
}
if(best < L)
return best;
// Rectangle
if(L%4==0)
return 0;
return 1;
}
};
// 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 double& Expected, const double& Received) {
bool ok = (abs(Expected - Received) < 1e-9);
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(_, FindPolygons().minimumPolygon(L));}
int main(){
CASE(0)
int L = 4;
double _ = 0.0;
END
CASE(1)
int L = 5;
double _ = -1.0;
END
CASE(2)
int L = 12;
double _ = 2.0;
END
CASE(3)
int L = 4984;
double _ = 819.0;
END
CASE(4)
int L = 5000;
double _ = -999;
END
CASE(4)
int L = 20;
double _ = -999;
END
/*
CASE(5)
int L = ;
double _ = ;
END
*/
}
// END CUT HERE