python实现最短路径的实例方法

#-*- coding:utf-8 -*-
 #python实现Floyd算法
 
N = 4 
_=float('inf')   #无穷大 
 graph = [[ 0, 2, 6, 4],[ _, 0, 3, _],[ 7, _, 0, 1],[ 5, _,12, 0]] 
 path = [[-1,-1,-1,-1],[-1,-1,-1,-1],[-1,-1,-1,-1],[-1,-1,-1,-1]]    #记录路径，最后一次经过的点
def back_path(path,i,j):      #递归回溯
while(-1 != path[i][j]):
   back_path(path,i,path[i][j])
    back_path(path,path[i][j],j)
   print path[i][j],14    
 return;
  return;
print "Graph:\n",graph
for k in range(N):
 for i in range(N):
   for j in range(N):
      if graph[i][j] > graph[i][k] + graph[k][j]:
       graph[i][j] = graph[i][k] + graph[k][j]
      path[i][j] = k
 print "Shortest distance:\n",graph
 print "Path:\n",path
 print "Points pass-by:"
 for i in range(N):
 for j in range(N):
   print "%d -> %d:" % (i,j),
    back_path(path,i,j)
    print "\n",

#!usr/bin/env python#encoding:utf-8
'''
功能：使用floyd算法求最短路径距离
'''
import random
import time
def random_matrix_genetor(vex_num=10):  
  '''
  随机图顶点矩阵生成器
  输入：顶点个数，即矩阵维数  
  '''
  data_matrix=[]  
  for i in range(vex_num):
    one_list=[]    
    for j in range(vex_num):
      one_list.append(random.randint(1, 100))
    data_matrix.append(one_list)  
    return data_matrixdef floyd(data_matrix):  
    '''
  输入：原数据矩阵，即：一个二维数组
  输出：顶点间距离  '''
  dist_matrix=[]
  path_matrix=[]
  vex_num=len(data_matrix) 
  for h in range(vex_num):
    one_list=['N']*vex_num
    path_matrix.append(one_list)
    dist_matrix.append(one_list)  
  for i in range(vex_num):    
    for j in range(vex_num):
      dist_matrix=data_matrix
      path_matrix[i][j]=j  
  for k in range(vex_num):    
    for i in range(vex_num):      
      for j in range(vex_num):        
        if dist_matrix[i][k]=='N' or dist_matrix[k][j]=='N':
          temp='N'
        else:
          temp=dist_matrix[i][k]+dist_matrix[k][j]        
        if dist_matrix[i][j]>temp:
          dist_matrix[i][j]=temp
          path_matrix[i][j]=path_matrix[i][k]  
  return dist_matrix, path_matrixdef main_test_func(vex_num=10):  
   '''
   主测试函数
   '''
  data_matrix=random_matrix_genetor(vex_num)
  dist_matrix, path_matrix=floyd(data_matrix)  
  for i in range(vex_num):    
  for j in range(vex_num):      
  print '顶点'+str(i)+'----->'+'顶点'+str(j)+'最小距离为:', dist_matrix[i][j]
if __name__ == '__main__':
  data_matrix=[['N',1,'N',4],[1,'N',2,'N'],['N',2,'N',3],[4,'N',3,'N']]
  dist_matrix, path_matrix=floyd(data_matrix)  
  print dist_matrix  
  print path_matrix
 
  time_list=[] 
  print '------------------------------节点数为10测试情况------------------------------------'
  start_time0=time.time()
  main_test_func(10)
  end_time0=time.time()
  t1=end_time0-start_time0
  time_list.append(t1)  
  print '节点数为10时耗时为：', t1 
  print '------------------------------节点数为100测试情况------------------------------------'
  start_time1=time.time()
  main_test_func(100)
  end_time1=time.time()
  t2=end_time1-start_time1
  time_list.append(t2)  
  print '节点数为100时耗时为：', t2 
  print '------------------------------节点数为1000测试情况------------------------------------'
  start_time1=time.time()
  main_test_func(1000)
  end_time1=time.time()
  t3=end_time1-start_time1
  time_list.append(t3)  
  print '节点数为100时耗时为：', t3 
  print '--------------------------------------时间消耗情况为：--------------------------------'
  for one_time in time_list:    
  print one_time

import numpy as np
Max   = 100
v_len  = 4
edge  = np.mat([[0,1,Max,4],[Max,0,9,2],[3,5,0,8],[Max,Max,6,0]])
A    = edge[:]
path  = np.zeros((v_len,v_len)) 
 
def Folyd():  
  for i in range(v_len):    
    for j in range(v_len):      
      if(edge[i,j] != Max and edge[i,j] != 0):
        path[i][j] = i 
  print 'init:'
  print A,'\n',path  
  for a in range(v_len):    
    for b in range(v_len):      
      for c in range(v_len):        
        if(A[b,a]+A[a,c]<A[b,c]):
          A[b,c] = A[b,a]+A[a,c]
          path[b][c] = path[a][c]  
  print 'result:'      
  print A,'\n',path        
 
if __name__ == "__main__":
  Folyd()