python实现prim 最小生成树算法

1.按照Prim 方法，从顶点1 出发，该网的最小生成树的产生过程如图:

2.代码:

'''#file:py_prim.py#最小生成树 prim算法的python实现普里姆（Prim）算法：由线到点，适合边稠密。时间复杂度O(N^2)href=http://blog.csdn.net/hguisu/article/details/7719428'''debug=0MAX_NUM=10000v_num=6grapharr=[[0,6,1,5,MAX_NUM,MAX_NUM],          [6,0,5,MAX_NUM,3,MAX_NUM],          [1,5,0,5,5,4],          [5,MAX_NUM,5,0,MAX_NUM,2],          [MAX_NUM,3,6,MAX_NUM,0,6],          [MAX_NUM,MAX_NUM,4,2,6,0],          ]#######################################U放已经匹配好的顶点:U=[]#V初始化为所有顶点的集合:V=[]#T放各个边:T=[]def init():    if(debug):        print("grapharr=",end="")        print(grapharr)        i=0    while i<v_num:        V.append(i+1)        i=i+1    if(graph_check()=="合法"):        print("合法")    else:        print("非法")        exit(1)def graph_check():    print("检查图表数组是否合法")    return "合法"def prim_start_vertex(start):    if(start<1):        print("ERROR:start=",start)        print("ERROR:change start to 1 by default!")        start=1            U.append(start)    del V[start-1]def list_sort(l):    if(len(l)<1):        print("ERROR:len of l =",len(l))        exit(1)         index=0    i=0    min_val=l[0]    while i < len(l):        if min_val > l[i]:            min_val=l[i]            index=i        i=i+1    if(debug):        print("[list_sort]:l=",l,";index=",index)    return indexdef min_wui():    m=MAX_NUM    close_edge={'u':-1,'v':-1}    edge_list=[]    vertex_list=[]    i=0    j=0    #算出U和V之间所有边的长度:    lu=len(U)    lv=len(V)    if(debug):        print("##############entry min_wui###########")        print("lu=",lu,";lv=",lv)    while i < len(U):        while j < len(V):            if(debug):                print("i=",i,";j=",j)                print("U[i]=",U[i],";V[j]=",V[j])            temp=grapharr[U[i]-1][V[j]-1]            if(temp>0):                if(temp<MAX_NUM):                    close_edge={'u':U[i],'v':V[j]}                if(debug):                                        print("close_edge=",close_edge)                vertex_list.append(close_edge)                edge_list.append(temp)                        j=j+1        #for i:        i=i+1        j=0    #end of :for while i    if(debug):                print("vertex_list=",vertex_list)        print("edge_list=",edge_list)         min_index=list_sort(edge_list)    close_edge=vertex_list[min_index]    U.append(close_edge['v'])    del V[V.index(close_edge['v'])]    if(debug):        print("U=",U)        print("V=",V)            return close_edgedef py_prim(start):    init()    prim_start_vertex(start)    print("init values:")    print("U=",U)    print("V=",V)    print("T=",T)    while(len(U)!=v_num):        if(debug):                            print("len(U)=",len(U))        our_edge=min_wui()        T.append(our_edge)    print("========RESULT============")    print("U=",U)    print("V=",V)    print("T=",T)    ######################################if(__name__=="__main__"):#开始主程序:    debug=0    py_prim(1)      

3.结果:

>>> 检查图表数组是否合法合法init values:U= [1]V= [2, 3, 4, 5, 6]T= []========RESULT============U= [1, 3, 6, 4, 2, 5]V= []T= [{'u': 1, 'v': 3}, {'u': 3, 'v': 6}, {'u': 6, 'v': 4}, {'u': 3, 'v': 2}, {'u': 2, 'v': 5}]>>> 

4.说明:

代码可以到“我的资源” 下载 http://download.csdn.net/detail/playboyno/4475898