# CFR 277 E. Binary Tree on Plane ( MCMF )

Problem - 277E - Codeforces

2 ≤ N ≤ 400
abs( X[ i ] ), abs( Y[ i ] ) ≤ 1000

O( N**2 )

```#include <bits/stdc++.h>
using namespace std;

template< class TF, class TC >
struct CostFlow {
static const int MAXV = 10000;
static constexpr TC INF = 1e9;
struct Edge {
int v, r;
TF f;
TC c;
Edge( int _v, int _r, TF _f, TC _c ): v( _v ), r( _r ), f( _f ), c( _c ) {}
};
int n, s, t, pre[ MAXV ], pre_E[ MAXV ], inq[ MAXV ];
TF fl;
TC dis[ MAXV ], cost;
vector< Edge > E[ MAXV ];
CostFlow( int _n, int _s, int _t ): n( _n ), s( _s ), t( _t ), fl( 0 ), cost( 0 ) {}
void add_edge( int u, int v, TF f, TC c ) {
E[ u ].emplace_back( v, E[ v ].size(), f, c );
E[ v ].emplace_back( u, E[ u ].size() - 1, 0, -c );
}
pair< TF, TC > flow() {
while( true ) {
for( int i = 0; i < n; ++i ) {
dis[ i ] = INF;
inq[ i ] = 0;
}
dis[ s ] = 0;
queue< int > que;
que.emplace( s );
while( not que.empty() ) {
int u = que.front();
que.pop();
inq[ u ] = 0;
for( int i = 0; i < E[ u ].size(); ++i ) {
int v = E[ u ][ i ].v;
TC w = E[ u ][ i ].c;
if( E[ u ][ i ].f > 0 and dis[ v ] > dis[ u ] + w ) {
pre[ v ] = u;
pre_E[ v ] = i;
dis[ v ] = dis[ u ] + w;
if( not inq[ v ] ) {
inq[ v ] = 1;
que.emplace( v );
}
}
}
}
if( dis[ t ] == INF ) break;
TF tf = INF;
for( int v = t, u, l; v != s; v = u ) {
u = pre[ v ];
l = pre_E[ v ];
tf = min( tf, E[ u ][ l ].f );
}
for( int v = t, u, l; v != s; v = u ) {
u = pre[ v ];
l = pre_E[ v ];
E[ u ][ l ].f -= tf;
E[ v ][ E[ u ][ l ].r ].f += tf;
}
cost += tf * dis[ t ];
fl += tf;
}
return { fl, cost };
}
};

const int MAXN = 400;

int N;
int X[ MAXN ], Y[ MAXN ];

signed main() {
ios::sync_with_stdio( 0 );
cin >> N;
for( int i = 0; i < N; ++i ) {
cin >> X[ i ] >> Y[ i ];
}
CostFlow< int, double > mcmf( N + N + 2, N + N, N + N + 1 );
for( int i = 0; i < N; ++i ) {
mcmf.add_edge( N + N, i, 2, 0.0 );
mcmf.add_edge( N + i, N + N + 1, 1, 0.0 );
for( int j = 0; j < N; ++j ) if( Y[ i ] > Y[ j ] ) {
auto sqr = [ & ]( int x ) { return x * x; };
mcmf.add_edge( i, N + j, 1, sqrt( sqr( X[ i ] - X[ j ] ) + sqr( Y[ i ] - Y[ j ] ) ) );
}
}
int flow;
double cost;
tie( flow, cost ) = mcmf.flow();
if( flow == N - 1 ) cout << fixed << setprecision( 9 ) << cost << endl;
else cout << -1 << endl;
return 0;
}
```