用Python解决最大团问题；

最大团问题是图论中的一个经典问题，它要求在一个无向图中找到一个完全子图，使得这个子图中的任意两个顶点都有边相连，并且这个子图的顶点数最大。下面是两种用Python解决最大团问题的方法：

1. 回溯法：

def backtrack(graph, clique):
    global max_clique
    if not graph:
        if len(clique) > len(max_clique):
            max_clique = clique
        return
    for node in graph:
        if all(node in graph[neighbor] for neighbor in clique):
            new_graph = {n: graph[n] & graph[node] for n in graph if n != node}
            backtrack(new_graph, clique + [node])

def find_max_clique(graph):
    global max_clique
    max_clique = []
    backtrack(graph, [])
    return max_clique

2. 分支限界法：

def branch_and_bound(graph):
    global max_clique
    max_clique = []
    nodes = list(graph.keys())
    nodes.sort(key=lambda x: len(graph[x]), reverse=True)
    def dfs(clique, candidates):
        global max_clique
        if not candidates:
            if len(clique) > len(max_clique):
                max_clique = clique
            return
        if len(clique) + len(candidates) <= len(max_clique):
            return
        pivot = candidates.pop(0)
        new_candidates = [node for node in candidates if node in graph[pivot]]
        dfs(clique + [pivot], new_candidates)
        dfs(clique, candidates)
    dfs([], nodes)
    return max_clique