Python实现经典算法拓扑排序、字符串匹配算法和最小生成树实例

from collections import defaultdict, deque
def topological_sort(num_courses, prerequisites):
    # 构建邻接表和入度数组
    graph = defaultdict(list)
    indegree = [0] * num_courses
    for course, prereq in prerequisites:
        graph[prereq].append(course)
        indegree[course] += 1
    # 使用队列进行拓扑排序
    queue = deque()
    for course in range(num_courses):
        if indegree[course] == 0:
            queue.append(course)
    result = []
    while queue:
        course = queue.popleft()
        result.append(course)
        for neighbor in graph[course]:
            indegree[neighbor] -= 1
            if indegree[neighbor] == 0:
                queue.append(neighbor)
    if len(result) != num_courses:
        return []
    return result
# 示例用法
num_courses = 4
prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2]]
result = topological_sort(num_courses, prerequisites)
print("课程学习顺序:", result)

def string_match(text, pattern):
    m, n = len(text), len(pattern)
    for i in range(m - n + 1):
        j = 0
        while j < n:
            if text[i + j] != pattern[j]:
                break
            j += 1
        if j
 == n:
            return i
    return -1
# 示例用法
text = "Hello, World!"
pattern = "World"
result = string_match(text, pattern)
if result != -1:
    print("模式串在文本串中的位置:", result)
else:
    print("模式串不存在于文本串中")

from heapq import heapify, heappop, heappush
def minimum_spanning_tree(graph):
    visited = set()
    start_vertex = list(graph.keys())[0]
    visited.add(start_vertex)
    edges = [(cost, start_vertex, next_vertex) for next_vertex, cost in graph[start_vertex]]
    heapify(edges)
    while edges:
        cost, u, v = heappop(edges)
        if v not in visited:
            visited.add(v)
            for next_vertex, next_cost in graph[v]:
                if next_vertex not in visited:
                    heappush(edges, (next_cost, v, next_vertex))
    return visited
# 示例用法
graph = {
    'A': [('B', 5), ('C', 1)],
    'B': [('A', 5), ('C', 2), ('D', 1)],
    'C': [('A', 1), ('B', 2), ('D', 4)],
    'D': [('B', 1), ('C', 4)]
}
result = minimum_spanning_tree(graph)
print("最小生成树的顶点集合:", result)