Ford Fulkerson 算法

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#include <iostream>#include <cstring>#include <vector>using namespace std;#define MAX_V 100#define INF 1 << 30struct Edge{    int to;    int cap;    int rec;    Edge( int to, int cap, int rec ){        this->to  = to;        this->cap = cap;        this->rec = rec;    }};vector< Edge > G[MAX_V];bool visited[MAX_V];void add_edge( int from, int to, int cap ){    Edge e  = Edge( to, cap, G[to].size() );    Edge re = Edge( from, cap, G[from].size() );    G[from].push_back( e );    G[to].push_back( re );}int find_flow( int from, int des, int flow ){    if( from == des )        return flow;    visited[from] = true;    for( int i = 0; i < G[from].size(); ++i ){        Edge& e = G[from][i];        if( !visited[e.to] && e.cap > 0 ){            int f = find_flow( e.to, des, min( flow, e.cap ) );            if( f > 0 ){                e.cap -= f;                G[e.to][e.rec].cap += f;                return f;            }        }    }    return 0;}int max_flow( int src, int des ){    int flow = 0;    while( true ){        memset( visited, false, sizeof( visited ) );        int f = find_flow( src, des, INF );        if( f == 0 )            return flow;        flow += f;    }    return flow;}int main(){    add_edge( 1, 2, 3 );    add_edge( 1, 3, 3 );    add_edge( 2, 3, 2 );    add_edge( 2, 4, 3 );    add_edge( 3, 5, 2 );    add_edge( 5, 6, 3 );    add_edge( 4, 5, 4 );    add_edge( 4, 6, 2 );    int flow = max_flow( 1, 6 );    cout << flow << endl;    return 0;}

class Edge( object ):    def __init__( self, u, v, cap ):        self.src = u        self.des = v        self.cap = cap            def __repr__( self ):        return "%s -> %s( %s )"%( self.src, self.des, self.cap )class FlowNetwork( object ):    def __init__( self ):        self.graph = {}        self.flow  = {}            def find_flow( self, src, des, path ):        if src == des:            return path        for e in self.get_edges( src ):            residuals = e.cap - self.flow[e]            if residuals > 0 and e not in path:                res = self.find_flow( e.des, des, path + [e] )                if res != None:                    return res                    def max_flow( self, src, des ):        while True:            path = self.find_flow( src, des, [] )            if path == None:                return sum( self.flow[e] for e in self.get_edges( src ) )            residuals = [e.cap - self.flow[e] for e in path]            flow = min( residuals )            for e in path:                self.flow[e]    += flow                self.flow[e.re] -= flow                    def add_vertex( self, v ):        self.graph[v] = []            def add_edge( self, u, v, cap ):        if u == v:            raise ValueError( "u == v" )        e     = Edge( u, v, cap )        re    = Edge( v, u, cap )        e.re  = re        re.re = e        self.graph[u].append( e )        self.graph[v].append( re )        self.flow[e]  = 0        self.flow[re] = 0    def get_edges( self, v ):        return self.graph[v]if __name__ == "__main__":        g = FlowNetwork()        for v in range( 1, 7 ):        g.add_vertex( v )            g.add_edge( 1, 2, 3 )    g.add_edge( 1, 3, 3 )    g.add_edge( 2, 3, 2 )    g.add_edge( 2, 4, 3 )    g.add_edge( 3, 5, 2 )    g.add_edge( 5, 6, 3 )    g.add_edge( 4, 5, 4 )    g.add_edge( 4, 6, 2 )        print g.max_flow( 1, 6 )

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