Artifact 19f42a31025a41f778ec26e9277c557f48db7659
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
using namespace std;
vector<double> solve_linear_eq( int n, vector< vector<double> > M, const vector<double>& V )
{
vector<double> A(V);
for(int i=0; i<n; ++i)
{
// pivot
if( M[i][i] == 0 )
for(int j=i+1; j<n; ++j)
if( M[j][i] != 0 )
{swap(M[i], M[j]); swap(A[i], A[j]); break;}
if( M[i][i] == 0 )
throw "no anser";
// M[i][i] <-- 1
double p = M[i][i];
for(int j=i; j<n; ++j)
M[i][j] /= p;
A[i] /= p;
// M[*][i] <-- 0
for(int j=0; j<n; ++j) if(j!=i)
{
double r = M[j][i];
for(int k=i; k<n; ++k)
M[j][k] -= M[i][k] * r;
A[j] -= A[i] * r;
}
}
return A;
}
//-------------------------------------------------------------
// Check the given list can be a degree list of some graph
// O(n^2 log n)
//
// Verified by
// - SRM 398 Div1 LV3
//
//((
// Havel-Hakimi
// If G[0], ..., G[n] (decreasing) is graphical,
// then G[1]-1, G[2]-1, ..., G[G[0]]-1, G[G[0]+1], .., G[n]
// is also graphical.
//))
//-------------------------------------------------------------
bool isGraphical( vector<int> G )
{
sort( G.begin(), G.end() );
vector<int>::iterator b = lower_bound( G.begin(), G.end(), 1 );
vector<int>::iterator e = G.end();
while( b < e )
{
int n = *(--e);
if( e-b < n )
return false;
for(vector<int>::iterator i=e-n; i!=e; ++i)
--*i;
inplace_merge( b, e-n, e );
b = lower_bound( G.begin(), G.end(), 1 );
}
return true;
}
struct MyFriends
{
string calcFriends(vector <int> sumFriends, int k)
{
int n = sumFriends.size();
vector< vector<double> > M(n, vector<double>(n));
for(int i=0; i<n; ++i)
for(int j=0; j<n; ++j)
M[i][j] = (i==j || (i+k)%n==j ? 0 : 1);
// calc #friends of each kid
vector<double> V( sumFriends.begin(), sumFriends.end() );
vector<double> Ad = solve_linear_eq( n, M, V );
vector<int> A;
for(int i=0; i<n; ++i)
A.push_back( (int)floor(Ad[i]+0.5) );
// verify
for(int i=0; i<n; ++i)
{
int sum = 0;
for(int j=0; j<n; ++j)
sum += (i==j || (i+k)%n==j ? 0 : A[j]);
if( sum != sumFriends[i] )
return "IMPOSSIBLE";
}
return isGraphical(A) ? "POSSIBLE" : "IMPOSSIBLE";
}
};