Python实现图算法、堆操作和并查集代码实例

from collections import defaultdict
class Graph:
    def __init__(self):
        self.graph = defaultdict(list)
    def add_edge(self, u, v):
        self.graph[u].append(v)
        self.graph[v].append(u)
    def dfs(self, v, visited):
        visited.add(v)
        for neighbor in self.graph[v]:
            if neighbor not in visited:
                self.dfs(neighbor, visited)
    def count_connected_components(self):
        visited = set()
        count = 0
        for vertex in self.graph:
            if vertex not in visited:
                self.dfs(vertex, visited)
                count += 1
        return count
# 示例用法
g = Graph()
g.add_edge(0, 1)
g.add_edge(0, 2)
g.add_edge(3, 4)
result = g.count_connected_components()
print("连通分量个数:", result)

import heapq
def find_kth_largest(nums, k):
    heap = []
    for num in nums:
        if len(heap) < k:
            heapq.heappush(heap, num)
        else:
            heapq.heappushpop(heap, num)
    return heap[0]
# 示例用法
nums = [3, 2, 1, 5, 6, 4]
k = 2
result = find_kth_largest(nums, k)
print("第k大的元素:", result)

class UnionFind:
    def __init__(self, n):
        self.parent = list(range(n))
        self.rank = [0] * n
    def find(self, x):
        if self.parent[x] != x:
            self.parent[x] = self.find(self.parent[x])
        return self.parent[x]
    def union(self, x, y):
        root_x = self.find(x)
        root_y = self.find(y)
        if root_x != root_y:
            if self.rank[root_x] < self.rank[root_y]:
                self.parent[root_x] = root_y
            elif self.rank[root_x] > self.rank[root_y]:
                self.parent[root_y] = root_x
            else:
                self.parent[root_y] = root_x
                self.rank[root_x] += 1
    def is_cyclic(self, edges):
        for edge in edges:
            x, y = edge
            if self.find(x) == self.find(y):
                return True
            self.union(x, y)
        return False
# 示例用法
edges = [(0, 1), (1, 2), (2, 0)]
n = 3
uf = UnionFind(n)
result = uf.is_cyclic(edges)
print("图中是否存在环路:", result)