背景和问题描述：

我有一些代码可以解决图形着色问题（广义地定义为将“颜色”分配给无向图的问题，请确保没有两个通过边连接的顶点具有相同的颜色）。我正在尝试使用约束传播来实现一种解决方案，以提高标准递归回溯算法的效率，但是却遇到以下错误：

  File "C:\Users\danisg\Desktop\coloring\Solver.py", 
  line 99, in solve
  for color in self.domains[var]:
  RuntimeError: Set changed size during iteration

在这里，对于每个顶点，我都会保留set该特定顶点可能的特定值：

  self.domains = { var: set(self.colors) for var in self.vars }

进行分配后，我将此约束传播到相邻域，以限制搜索空间：

  for key in node.neighbors:          # list of keys corresponding to adjacent vertices
      if color in self.domains[key]:  # remove now to prune possible choices
          self.domains[key].remove(color)

这不是引发实际错误的地方（在我的代码中，我指出了问题在哪里try-except），但可能是问题的根源。

我的问题：

如果没有正确的实施方法，我是否有正确的想法？更重要的是，我该如何解决？另外，是否有必要保留单独的domains词典？还是可以domain为图中的每个节点设置一个属性？

我的代码：

这solve是调用此代码的函数：

def solve(self):

    uncolored = [var for var in self.vars if self.map[var].color == None]
    if len(uncolored) == 0:
        return True

    var  = min(uncolored, key = lambda x: len(self.domains[var]))
    node = self.map[var]
    old  = { var: set(self.domains[var]) for var in self.vars }

    for color in self.domains[var]:

        if not self._valid(var, color):
            continue


        self.map[var].color = color
        for key in node.neighbors:

            if color in self.domains[key]:
                self.domains[key].remove(color)

        try:
            if self.solve():
                return True
        except:
            print('happening now')


        self.map[var].color = None
        self.domains = old


    return False

我的实现使用一个Node对象：

class Solver:

    class Node:

        def __init__(self, var, neighbors, color = None, domain = set()):

            self.var       = var
            self.neighbors = neighbors
            self.color     = color
            self.domain    = domain

        def __str__(self):
            return str((self.var, self.color))



    def __init__(self, graph, K):

        self.vars    = sorted( graph.keys(), key = lambda x: len(graph[x]), reverse = True )  # sort by number of links; start with most constrained
        self.colors  = range(K)
        self.map     = { var: self.Node(var, graph[var]) for var in self.vars }
        self.domains = { var: set(self.colors)           for var in self.vars }

这是另外两个有用/有用的功能：

def validate(self):

    for var in self.vars:
        node = self.map[var]

        for key in node.neighbors:
            if node.color == self.map[key].color:
                return False

    return True

def _valid(self, var, color):

    node = self.map[var]

    for key in node.neighbors:

        if self.map[key].color == None:
            continue

        if self.map[key].color == color:
            return False

    return True

代码失败的数据和示例：

我正在使用的示例图可以在这里找到。

读取数据的功能：

def read_and_make_graph(input_data):

    lines = input_data.split('\n')

    first_line = lines[0].split()
    node_count = int(first_line[0])
    edge_count = int(first_line[1])

    graph = {}
    for i in range(1, edge_count + 1):
        line  = lines[i]
        parts = line.split()
        node, edge = int(parts[0]), int(parts[1])

        if node in graph:
            graph[node].add(edge)

        if edge in graph:
            graph[edge].add(node)

        if node not in graph:
            graph[node] = {edge}

        if edge not in graph:
            graph[edge] = {node}

    return graph

应该这样称呼：

file_location = 'C:\\Users\\danisg\\Desktop\\coloring\\data\\gc_50_3'
input_data_file = open(file_location, 'r')
input_data = ''.join(input_data_file.readlines())
input_data_file.close()

graph  = read_and_make_graph(input_data)
solver = Solver(graph, 6)  # a 6 coloring IS possible

print(solver.solve())      # True if we solved; False if we didn't