最大网络流算法 push-relabel 的 python实现

#!/user/bin/python
#PUSH-RELABEL ALGORITHM
#Author Dan Liu
h=[]
e=[]
f=[]
#V=[0,1,2,3]
#E=[(0,1),(1,2),(1,3),(0,2),(2,3)]
#G=(V,E)
#C={(0,1):3,(1,2):3,(1,3):1,(0,2):4,(2,3):5}
#s=0
#t=3
V=[0,1,2,3,4,5]
E=[(0,1),(1,2),(1,3),(1,4),(0,2),(2,4),(3,5),(4,5)]
G=(V,E)
C={(0,1):3,(1,2):1,(1,3):3,(1,4):4,(0,2):2,(2,4):2,(3,5):2,(4,5):3}
s=0
t=5
Ef=[]
cf={}
def init_preflow(G,s):
    for i in G[1]:
        if i[0] ==s:
            i=(i[1],i[0])            
        Ef.append(i)
        
    for i in C.items():
        key=i[0]
        if i[0][0] == s:
            key=(i[0][1],i[0][0])
        cf[key]=i[1]
    for u in G[0]:
        h.append(0)
        e.append(0)
    for u in G[0]:
        l=[]
        for v in G[0]:            
            l.append(0)
        f.append(l)
    for edge in G[1]:
        f[edge[0]][edge[1]]=0
        f[edge[0]][edge[1]]=0
    h[s]=len(G[0])
    for edge in G[1]:
        if edge[0] == s:
            u=edge[1]
            tmp=C.get(edge)
            f[s][u]=tmp
            f[u][s]=-tmp
            e[u]=tmp
            e[s]-=tmp
            
            
    print "h=",h
    print "f=",f
    print "e=",e

def push_flow(u,v):    
    df=min(e[u],cf.get((u,v)))
    f[u][v]+=df
    f[v][u]=-f[u][v]
    e[u]-=df
    e[v]+=df
    cf[(u,v)]-=df    
    if cf[(u,v)]==0:
        Ef.remove((u,v))
    
def relabel(u):            
    Eh=[]
    for item in Ef:
        if item[0]==u:
            Eh.append(h[item[1]])
    h[u]=1+min(Eh)
    
def check_e(e):
    for i in range(len(V)):
        if i != s and i != t:
            if e[i] > 0:
                return i
    return -1

def check_push(u):
    for item in cf.items():        
        if (item[0][0]) == u and item[1] >0 and (h[u]==(h[item[0][1]]+1)):
            return item[0][1]
    return -1

def check_relabel(u):
    for item in Ef:
        if item[0]==u:
            if h[u]>h[item[1]]:
                return 1
    return -1

def generic_push_relabel(G):
    init_preflow(G,s)
    active_node=check_e(e)
    while active_node > 0:
        v=check_push(active_node)
        is_high=check_relabel(active_node)
        if v != -1:
            print active_node, v
            push_flow(active_node, v)
        elif is_high == -1:
        #else:
            relabel(active_node)
        print e    
        active_node=check_e(e)

generic_push_relabel(G)
print "h=",h
print "f=",f
print "e=",e