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A.cpp
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A.cpp
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/*
A - 最大流问题
reference:
https://oi-wiki.org/graph/flow/max-flow/
*/
#include <bits/stdc++.h>
using namespace std;
namespace dicnic {
const int maxn = 250;
const int INF = 0x3f3f3f3f;
struct Edge {
int from, to, cap, flow;
Edge( int u, int v, int c, int f )
: from( u )
, to( v )
, cap( c )
, flow( f ) {}
};
struct Dinic {
// n:点数,m:边数,s:源,t:汇
int n, m, s, t;
// edges:所有边的集合
vector<Edge> edges;
// G:点 x -> x 的所有边在 edges 中的下标
vector<int> G[ maxn ];
int d[ maxn ], cur[ maxn ];
bool vis[ maxn ];
Dinic( int _n, int _m, int _s, int _t )
: n( _n )
, m( _m )
, s( _s )
, t( _t ) {
init( n );
}
void init( int n ) {
for ( int i = 0; i < n; i++ )
G[ i ].clear();
edges.clear();
}
void AddEdge( int from, int to, int cap ) {
edges.push_back( Edge( from, to, cap, 0 ) );
edges.push_back( Edge( to, from, 0, 0 ) );
m = edges.size();
G[ from ].push_back( m - 2 );
G[ to ].push_back( m - 1 );
}
bool BFS() {
memset( vis, false, sizeof( vis ) );
queue<int> Q;
Q.push( s );
d[ s ] = 0;
vis[ s ] = true;
while ( !Q.empty() ) {
int x = Q.front();
Q.pop();
for ( int i = 0; i < G[ x ].size(); i++ ) {
Edge &e = edges[ G[ x ][ i ] ];
if ( !vis[ e.to ] && e.cap > e.flow ) {
vis[ e.to ] = true;
d[ e.to ] = d[ x ] + 1;
Q.push( e.to );
}
}
}
return vis[ t ];
}
int DFS( int x, int a ) {
if ( x == t || a == 0 ) return a;
int flow = 0, f;
for ( int &i = cur[ x ]; i < G[ x ].size(); i++ ) {
Edge &e = edges[ G[ x ][ i ] ];
if ( d[ x ] + 1 == d[ e.to ] &&
( f = DFS( e.to, min( a, e.cap - e.flow ) ) ) > 0 ) {
e.flow += f;
edges[ G[ x ][ i ] ^ 1 ].flow -= f;
flow += f;
a -= f;
if ( a == 0 ) break;
}
}
return flow;
}
// s:源,t:汇
int Maxflow( int s, int t ) {
this->s = s;
this->t = t;
int flow = 0;
while ( BFS() ) {
memset( cur, 0, sizeof( cur ) );
flow += DFS( s, INF );
}
return flow;
}
int Maxflow() { return Maxflow( s, t ); }
};
} // namespace dicnic
int main() {
using namespace dicnic;
int N, M, S, T;
cin >> N >> M >> S >> T;
Dinic dc( N, M, S, T );
for ( int i = 0; i < M; ++i ) {
int u, v, w;
cin >> u >> v >> w;
dc.AddEdge( u, v, w );
}
cout << dc.Maxflow() << endl;
return 0;
}
/*
input:
6 9 4 2
1 3 10
2 1 20
2 3 20
4 3 10
4 5 30
5 2 20
4 6 20
5 6 10
6 2 30
output:
50
*/