I'm implementing a code to find the shortest path between two nodes, but why when I change the first line of the DFS function the output change too . Isn't it true that
path += [start] is equivalent to path = path + [start]?
the output before changing is ::
Current DFS path: 0
Current DFS path: 0->1
Current DFS path: 0->1->2
Current DFS path: 0->1->2->3
Current DFS path: 0->1->2->3->4
Current DFS path: 0->1->2->3->5
Current DFS path: 0->1->2->4
Current DFS path: 0->2
Current DFS path: 0->2->3
Current DFS path: 0->2->3->1
Current DFS path: 0->2->3->4
Current DFS path: 0->2->3->5
Current DFS path: 0->2->4
shortest path is  0->2->3->5
after changing is ::
Current DFS path: 0
Current DFS path: 0->1
Current DFS path: 0->1->2
Current DFS path: 0->1->2->3
Current DFS path: 0->1->2->3->4
Current DFS path: 0->1->2->3->4->5
shortest path is  0->1->2->3->4->5
The code ::
class Node(object):
    def __init__(self, name):
        """Assumes name is a string"""
        self.name = name
    def getName(self):
        return self.name
    def __str__(self):
        return self.name
class Edge(object):
    def __init__(self, src, dest):
        """Assumes src and dest are nodes"""
        self.src = src
        self.dest = dest
    def getSource(self):
        return self.src
    def getDestination(self):
        return self.dest
    def __str__(self):
        return self.src.getName() + '->' + self.dest.getName()
class WeightedEdge(Edge):
    def __init__(self, src, dest, weight = 1.0):
        """Assumes src and dest are nodes, weight a number"""
        self.src = src
        self.dest = dest
        self.weight = weight
    def getWeight(self):
        return self.weight
    def __str__(self):
        return self.src.getName() + '->(' + str(self.weight) + ')'\
               + self.dest.getName()
#Figure 12.8
class Digraph(object):
    #nodes is a list of the nodes in the graph
    #edges is a dict mapping each node to a list of its children
    def __init__(self):
        self.nodes = []
        self.edges = {}
    def addNode(self, node):
        if node in self.nodes:
            raise ValueError('Duplicate node')
        else:
            self.nodes.append(node)
            self.edges[node] = []
    def addEdge(self, edge):
        src = edge.getSource()
        dest = edge.getDestination()
        if not (src in self.nodes and dest in self.nodes):
            raise ValueError('Node not in graph')
        self.edges[src].append(dest)
    def childrenOf(self, node):
        return self.edges[node]
    def hasNode(self, node):
        return node in self.nodes
    def __str__(self):
        result = ''
        for src in self.nodes:
            for dest in self.edges[src]:
                result = result + src.getName() + '->'\
                         + dest.getName() + '\n'
        return result[:-1] #omit final newline
class Graph(Digraph):
    def addEdge(self, edge):
        Digraph.addEdge(self, edge)
        rev = Edge(edge.getDestination(), edge.getSource())
        Digraph.addEdge(self, rev)
#Figure 12.9
def printPath(path):
    """Assumes path is a list of nodes"""
    result = ''
    for i in range(len(path)):
        result = result + str(path[i])
        if i != len(path) - 1:
            result = result + '->'
    return result 
def DFS(graph, start, end, path, shortest, toPrint = False):
    """Assumes graph is a Digraph; start and end are nodes;
          path and shortest are lists of nodes
       Returns a shortest path from start to end in graph"""
    path = path + [start]
    if toPrint:
        print('Current DFS path:', printPath(path))
    if start == end:
        return path
    for node in graph.childrenOf(start):
        if node not in path: #avoid cycles
            if shortest == None or len(path) < len(shortest):
                newPath = DFS(graph, node, end, path, shortest,
                              toPrint)
                if newPath != None:
                    shortest = newPath
    return shortest
def shortestPath(graph, start, end, toPrint = False):
    """Assumes graph is a Digraph; start and end are nodes
       Returns a shortest path from start to end in graph"""
    return DFS(graph, start, end, [], None, toPrint)
#Figure 12.10
def testSP():
    nodes = []
    for name in range(6): #Create 6 nodes
        nodes.append(Node(str(name)))
    g = Digraph()
    for n in nodes:
        g.addNode(n)
    g.addEdge(Edge(nodes[0],nodes[1]))
    g.addEdge(Edge(nodes[1],nodes[2]))
    g.addEdge(Edge(nodes[2],nodes[3]))
    g.addEdge(Edge(nodes[2],nodes[4]))
    g.addEdge(Edge(nodes[3],nodes[4]))
    g.addEdge(Edge(nodes[3],nodes[5]))
    g.addEdge(Edge(nodes[0],nodes[2]))
    g.addEdge(Edge(nodes[1],nodes[0]))
    g.addEdge(Edge(nodes[3],nodes[1]))
    g.addEdge(Edge(nodes[4],nodes[0]))
    sp = shortestPath(g, nodes[0], nodes[5])
    print('Shortest path found by DFS:', printPath(sp))
Note :: this code is from this book enter link description here