# CFR 362 E. Petya and Pipes ( MCMF, Binary Search )

Problem - 362E - Codeforces

2 ≤ N ≤ 50
0 ≤ K ≤ 1000
0 ≤ C[ i ][ j ] ≤ 1e6
C[ i ][ i ] = 0
if C[ i ][ j ] = 0, then C[ j ][ i ] = 0

O( N ** 2 * lg MAXC )

```#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 = 50;

int N, K;
int C[ MAXN ][ MAXN ];

signed main() {
ios::sync_with_stdio( 0 );
cin >> N >> K;
for( int i = 0; i < N; ++i ) {
for( int j = 0; j < N; ++j ) {
cin >> C[ i ][ j ];
}
}
int lb = 0, ub = 1e9;
while( lb + 1 != ub ) {
int mid = lb + ub >> 1;
CostFlow< int, long long > mcmf( N + 1, N, N - 1 );
mcmf.add_edge( N, 0, mid, 0 );
for( int i = 0; i < N; ++i ) {
for( int j = 0; j < N; ++j ) if( C[ i ][ j ] ) {
mcmf.add_edge( i, j, C[ i ][ j ], 0 );
mcmf.add_edge( i, j, mcmf.INF, 1 );
}
}
long long flow, cost;
tie( flow, cost ) = mcmf.flow();
( flow == mid and cost <= K ? lb : ub ) = mid;
}
cout << lb << endl;
return 0;
}
```