利用 Prim 算法求解最小生成树问题，用Python语言描述算法。

Prim算法是一种用于寻找图中连通分量中最短路径的贪心算法，特别适用于求解带权无向图的最小生成树问题。以下是Prim算法的一个基本Python实现：

import heapq

class Node:
    def __init__(self, index, weight=None):
        self.index = index
        self.weight = weight if weight is not None else 0

def prim(graph, start_node):
    # 初始化集合和堆
    visited = set()
    unvisited_nodes = [(node.weight, node) for node in graph]
    heapq.heapify(unvisited_nodes)

    # 创建最小生成树
    mst = []
    while unvisited_nodes:
        current_weight, current_node = heapq.heappop(unvisited_nodes)
        
        # 如果当前节点已访问，则跳过
        if current_node.index in visited:
            continue
        
        # 将当前节点添加到已访问集合，并加入最小生成树
        visited.add(current_node.index)
        mst.append((current_node.index, current_node.weight))

        # 更新未访问节点集，考虑所有与当前节点相连且尚未访问的节点
        for neighbor, weight in graph[current_node.index].items():
            if neighbor not in visited:
                heapq.heappush(unvisited_nodes, (weight, Node(neighbor, weight)))

    return mst

# 示例：一个邻接字典表示的图，键是节点，值是字典，键是邻居节点，值是边的权重
graph = {
    'A': {'B': 5, 'D': 1},
    'B': {'A': 5, 'C': 2},
    'C': {'B': 2, 'E': 4},
    'D': {'A': 1, 'E': 8},
    'E': {'C': 4, 'D': 8}
}

start_node = 'A'
min_spanning_tree = prim(graph, start_node)
print(f"最小生成树：{min_spanning_tree}")