bellman-ford算法_python+实例

文章目录

• the python code:
• • the result:
• overview
• understand the process:
• a long example:
• Correctness:

the python code:

the code base the vertex(nodes) set and edge set seperately

import math
import logging as l
 
l.basicConfig(level=l.INFO)
 
class Edge():
    def __init__(self, start, end, weight):
        self.start = start
        self.end = end
        self.weight = weight
 
 
class Node():
    def __init__(self, sign):
        # self.number = number
        self.sign = sign
        # for initial nodes(vertex) of the graph
        self.distance = math.inf
        # set the node's precursor:
        self.precursor = None
 
    def initalize_source_node(self):
        self.distance = 0
        return self
 
 
class G():
    s_node=None
    def __init__(self, edges, nodes):
        self.edges = edges
        self.nodes = nodes
    # def generate_nodes(self):
    #     # get the nodes number(you can custom the number regularity,there use the default simple number system)
    #     self.nodes = [Node(chr(sign)) for sign in range(ord('A'), ord('E')+1)]
    def log_print_nodes(self):
        for node in self.nodes:
            l.debug(f'{node.sign,node.distance}')
    
    def weight(self, u, v):
        for edge in self.edges:
            if edge.start == u and edge.end == v:
                return edge.weight
        
        return math.inf
 
    def relax(self, edge):
        u=edge.start
        v=edge.end
        l.debug(f'self.weight(u, v):{self.weight(u, v)}')
        new_distance= u.distance+self.weight(u, v)
        #debug
        l.debug(f'{edge.start.sign,edge.end.sign}')
        l.debug(f'new_distance:{new_distance}')
        if v.distance >new_distance:
            v.distance=new_distance
            v.precursor=u
 
    # def initialize_single_source(G, source_node):
        #     # for node in G.nodes:
        #     #     node.distance=0
        #     #     node.precursor=None
        #     source_node.distance = 0
    
    def  bellman_ford(self, s):
        G.s_node=s.initalize_source_node()
        l.info(f'G.s_node:{G.s_node.sign}')
        for i in range(len(self.nodes)-1):
            for edge in self.edges:
                self.relax(edge)
                l.debug(f'{edge.end.distance}')
            #debug
            self.log_print_nodes()
        return self
    
    def print_ford_result(self):
        # self.bellman_ford(s)
        if not self.is_exist_shortest():
            print("there is a nagetive circle.")
        else:
            for node in self.nodes:
                # print()'''  '''
                print(f'to node:{node.sign},the distance is:{node.distance}')
    def is_exist_shortest(self):
        for edge in self.edges:
            if edge.end.distance>edge.start.distance+edge.weight:
                return False
        return True
    def print_precursor(self,node):
        if node.sign==G.s_node.sign:
            print(G.s_node.sign,end=" ")
            # return
        else:
            if node.precursor==None:
                print(G.s_node.sign,"->",node.sign,"(the node is not accessible)",end=" ")
            else:
                self.print_precursor(node.precursor)
                print(node.sign,end=" ")
    def print_path(self):
        for node in self.nodes:
            # print(node.sign)
            
            self.print_precursor(node)
            print()
 
def generate_nodes():
    # get the nodes number(you can custom the number regularity,there use the default simple number system)
    nodes = [Node(chr(sign)) for sign in range(ord('A'), ord('E')+1)]
    return nodes
 
#debug:print nodes:
def print_nodes():
    for node in nodes:
        print(node.sign,node.distance)
# print_nodes()
    
def get_node_instance(sign):
    for node in nodes:
        if node.sign==sign:
            return node
    
    #throw exception
    return None
    
# get the edges parameters to instantiate the edge nodes ,put the edges to the list edges;
 
def generate_edges():
    while(True):
        line = input("input node:")
        if line == "0":
            break
        edge_param = line.split(",")
        start, end, weight = edge_param[0], edge_param[1], int(edge_param[2])
        start_node=get_node_instance(start)
        end_node=get_node_instance(end)
        # print(end_node.sign)
        edges.append(Edge(start_node,end_node , weight))
    return edges
 
 
'''debug the edges is right: '''
def print_edges():
    for edge in edges:
        # print(edge.start.sign,edge.end.sign,edge.weight)
        l.info((edge.start.sign,edge.end.sign,edge.weight))
# print_edges()
nodes=[]
nodes=generate_nodes() 
edges = []
edges=generate_edges()
G=G(edges,nodes)
# G.print_nodes()
source_node=input("input the source node you want:(from 'A'~'E')\n")
G.bellman_ford(get_node_instance(source_node))
G.print_ford_result()
G.print_path()
''' 
test data:
 
A,B,-1
A,C,4
B,C,3
D,C,5
D,B,1
B,D,2
B,E,2
E,D,-3
0
 
 
'''
 

the result:

source A:

source D:

overview

understand the process:

a long example:

Correctness: