Python常用算法解析，从优雅简洁到高效实战
目录
一、Python算法哲学：优雅与效率的平衡
1.1 Python算法的核心优势
1.2 Python的内置算法工具
二、列表与字典算法
2.1 列表推导式的艺术
2.2 字典的高级用法
三、排序与搜索算法
3.1 内置排序的灵活运用
3.2 二分查找与二等分模块
四、图形算法与网络分析
4.1 使用networkx进行图分析
4.2 自定义图算法实现
五、数值计算与科学计算
5.1 使用NumPy进行数值计算
5.2 使用pandas进行数据分析
六、机器学习算法
6.1 使用 scikit-learn
6.2 自定义机器学习算法
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一、Python算法哲学：优雅与效率的平衡
1.1 Python算法的核心优势
Python算法设计融合了概率编程范式：
函数式编程：map、filter、reduce、列表推导式
面向对象：自定义数据结构、操作重载
元编程：装饰器、元类、外汇
动态特性：鸭子类型、运行时类型检查
1.2 Python的内置算法工具
# 1. 内置函数（BIFs）中的算法
numbers = [3, 1, 4, 1, 5, 9, 2, 6]
# 排序相关
sorted_nums = sorted(numbers) # 返回新列表
numbers.sort() # 原地排序
reversed_nums = list(reversed(numbers)) # 反转
# 极值查找
max_val = max(numbers)
min_val = min(numbers)
sum_val = sum(numbers)
# 2. 使用key参数进行复杂排序
words = ["apple", "banana", "cherry", "date"]
sorted_words = sorted(words, key=len) # 按长度排序
sorted_words = sorted(words, key=str.lower) # 不区分大小写
# 3. 使用lambda表达式
students = [("Alice", 85), ("Bob", 92), ("Charlie", 78)]
sorted_students = sorted(students, key=lambda x: x[1], reverse=True)
二、列表与字典算法
2.1 列表推导式的艺术
# 1. 基本列表推导式
squares = [x**2 for x in range(10)] # [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
# 2. 带条件的列表推导式
even_squares = [x**2 for x in range(10) if x % 2 == 0] # 偶数的平方
# 3. 嵌套列表推导式
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
flattened = [num for row in matrix for num in row] # 展平二维列表
# 4. 字典推导式
squares_dict = {x: x**2 for x in range(5)} # {0: 0, 1: 1, 2: 4, 3: 9, 4: 16}
# 5. 集合推导式
unique_chars = {char for char in "hello world" if char != ' '} # {'h', 'e', 'l', 'o', 'w', 'r', 'd'}
# 6. 生成器表达式（惰性求值）
large_squares = (x**2 for x in range(1000000)) # 不立即生成所有值
sum_of_squares = sum(x**2 for x in range(1000)) # 内存高效
2.2 字典的高级用法
# 1. defaultdict：自动初始化字典
from collections import defaultdict
# 统计单词出现次数
word_counts = defaultdict(int)
for word in text.split():
word_counts[word] += 1
# 按首字母分组
words_by_letter = defaultdict(list)
for word in words:
words_by_letter[word[0]].append(word)
# 2. Counter：计数专用字典
from collections import Counter
# 统计元素出现次数
colors = ['red', 'blue', 'red', 'green', 'blue', 'blue']
color_counts = Counter(colors) # Counter({'blue': 3, 'red': 2, 'green': 1})
# 最常见的n个元素
most_common = color_counts.most_common(2) # [('blue', 3), ('red', 2)]
# 3. OrderedDict：保持插入顺序（Python 3.7+普通dict已有序）
from collections import OrderedDict
# LRU缓存实现
class LRUCache:
def __init__(self, capacity: int):
self.cache = OrderedDict()
self.capacity = capacity
def get(self, key):
if key not in self.cache:
return -1
self.cache.move_to_end(key) # 移动到末尾表示最近使用
return self.cache[key]
def put(self, key, value):
if key in self.cache:
self.cache.move_to_end(key)
self.cache[key] = value
if len(self.cache) > self.capacity:
self.cache.popitem(last=False) # 移除最旧的项
三、排序与搜索算法
3.1 内置排序的灵活运用
# 1. 复杂对象的排序
class Student:
def __init__(self, name, grade, age):
self.name = name
self.grade = grade
self.age = age
def __repr__(self):
return f"Student({self.name}, {self.grade}, {self.age})"
students = [
Student('Alice', 'A', 20),
Student('Bob', 'B', 19),
Student('Charlie', 'A', 21),
Student('David', 'C', 20)
]
# 按多个字段排序
sorted_students = sorted(students, key=lambda s: (s.grade, s.age))
# 2. 使用attrgetter和itemgetter
from operator import attrgetter, itemgetter
# attrgetter用于对象属性
sorted_by_age = sorted(students, key=attrgetter('age'))
# itemgetter用于元组或字典
data = [{'name': 'Alice', 'score': 85},
{'name': 'Bob', 'score': 92},
{'name': 'Charlie', 'score': 78}]
sorted_data = sorted(data, key=itemgetter('score'), reverse=True)
# 3. 稳定排序的特性
# Python的sorted()是稳定排序，相等元素的相对顺序保持不变
items = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)]
sorted_items = sorted(items, key=lambda x: x[0])
# 结果：[('blue', 1), ('blue', 2), ('red', 1), ('red', 2)]
# 相同颜色的元素保持了原始顺序
3.2 二分查找与二等分模块
import bisect
# 1. 基本二分查找
sorted_list = [1, 3, 5, 7, 9, 11, 13]
# 查找元素位置（返回插入位置）
position = bisect.bisect_left(sorted_list, 7) # 3
position = bisect.bisect_right(sorted_list, 7) # 4（重复元素时有用）
# 2. 插入元素保持有序
bisect.insort_left(sorted_list, 6) # 在适当位置插入6
bisect.insort_right(sorted_list, 8) # 插入8
# 3. 自定义比较函数的二分查找
def binary_search_custom(arr, target, key_func):
"""使用自定义key函数的二分查找"""
lo, hi = 0, len(arr)
while lo < hi:
mid = (lo + hi) // 2
if key_func(arr[mid]) < target:
lo = mid + 1
else:
hi = mid
return lo if lo < len(arr) and key_func(arr[lo]) == target else -1
# 4. 查找范围
def find_range(arr, target):
"""在有序数组中查找目标值的起始和结束位置"""
left = bisect.bisect_left(arr, target)
right = bisect.bisect_right(arr, target)
return (left, right) if left < right else (-1, -1)
# 示例
nums = [5, 7, 7, 8, 8, 8, 10]
start, end = find_range(nums, 8) # (3, 6)
四、图形算法与网络分析
4.1 使用networkx进行图分析
import networkx as nx
import matplotlib.pyplot as plt
# 1. 创建图
G = nx.Graph() # 无向图
# G = nx.DiGraph() # 有向图
# 添加节点和边
G.add_nodes_from([1, 2, 3, 4, 5])
G.add_edges_from([(1, 2), (1, 3), (2, 3), (3, 4), (4, 5)])
# 2. 基本图算法
# 最短路径
shortest_path = nx.shortest_path(G, source=1, target=5) # [1, 3, 4, 5]
# 连通分量
connected_components = list(nx.connected_components(G))
# 度中心性
degree_centrality = nx.degree_centrality(G)
# 3. PageRank算法
pagerank_scores = nx.pagerank(G, alpha=0.85)
# 4. 社区检测
from networkx.algorithms import community
# Louvain方法
communities = community.greedy_modularity_communities(G)
# 5. 可视化
pos = nx.spring_layout(G) # 布局算法
nx.draw(G, pos, with_labels=True, node_color='lightblue',
node_size=500, font_size=10)
plt.show()
4.2 自定义图算法实现
from collections import deque, defaultdict
# 1. BFS（广度优先搜索）
def bfs(graph, start):
"""图的广度优先遍历"""
visited = set()
queue = deque([start])
result = []
while queue:
vertex = queue.popleft()
if vertex not in visited:
visited.add(vertex)
result.append(vertex)
queue.extend(graph[vertex] - visited)
return result
# 2. DFS（深度优先搜索）- 递归版本
def dfs_recursive(graph, vertex, visited=None):
if visited is None:
visited = set()
visited.add(vertex)
for neighbor in graph[vertex]:
if neighbor not in visited:
dfs_recursive(graph, neighbor, visited)
return visited
# 3. Dijkstra算法
import heapq
def dijkstra(graph, start):
"""单源最短路径 - Dijkstra算法"""
distances = {vertex: float('infinity') for vertex in graph}
distances[start] = 0
pq = [(0, start)] # 优先队列
while pq:
current_distance, current_vertex = heapq.heappop(pq)
if current_distance > distances[current_vertex]:
continue
for neighbor, weight in graph[current_vertex].items():
distance = current_distance + weight
if distance < distances[neighbor]:
distances[neighbor] = distance
heapq.heappush(pq, (distance, neighbor))
return distances
# 4. 拓扑排序
def topological_sort(graph):
"""有向无环图的拓扑排序"""
in_degree = {u: 0 for u in graph}
# 计算入度
for u in graph:
for v in graph[u]:
in_degree[v] += 1
# 收集入度为0的节点
queue = deque([u for u in graph if in_degree[u] == 0])
result = []
while queue:
u = queue.popleft()
result.append(u)
for v in graph[u]:
in_degree[v] -= 1
if in_degree[v] == 0:
queue.append(v)
if len(result) != len(graph):
raise ValueError("图中存在环")
return result
五、数值计算与科学计算
5.1 使用NumPy进行数值计算
import numpy as np
# 1. 数组创建和操作
arr = np.array([1, 2, 3, 4, 5])
matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
# 2. 向量化操作（避免Python循环）
# 传统Python方式
squares = [x**2 for x in range(1000000)] # 慢
# NumPy向量化方式
squares_np = np.arange(1000000) ** 2 # 快
# 3. 广播机制
a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([10, 20, 30])
result = a + b # 广播：[[11, 22, 33], [14, 25, 36]]
# 4. 线性代数运算
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
dot_product = np.dot(A, B) # 矩阵乘法
determinant = np.linalg.det(A) # 行列式
eigenvalues, eigenvectors = np.linalg.eig(A) # 特征值和特征向量
# 5. 统计计算
data = np.random.randn(1000, 10) # 1000行10列的随机数据
mean = np.mean(data, axis=0) # 每列的平均值
std = np.std(data, axis=0) # 每列的标准差
correlation = np.corrcoef(data.T) # 相关系数矩阵
5.2 使用pandas进行数据分析
import pandas as pd
import numpy as np
# 1. 创建DataFrame
data = {
'Name': ['Alice', 'Bob', 'Charlie', 'David'],
'Age': [25, 30, 35, 40],
'Salary': [50000, 60000, 70000, 80000],
'Department': ['HR', 'Engineering', 'Engineering', 'HR']
}
df = pd.DataFrame(data)
# 2. 数据筛选和查询
# 基本筛选
engineering_df = df[df['Department'] == 'Engineering']
high_salary = df[df['Salary'] > 60000]
# 复杂查询
result = df.query('Age > 30 and Salary < 75000')
# 3. 分组聚合
grouped = df.groupby('Department')
summary = grouped.agg({
'Age': ['mean', 'min', 'max'],
'Salary': ['sum', 'mean', 'std']
})
# 4. 数据透视表
pivot = pd.pivot_table(df,
values='Salary',
index='Department',
columns=None,
aggfunc=['mean', 'count', 'sum'])
# 5. 时间序列处理
dates = pd.date_range('2023-01-01', periods=100, freq='D')
time_series = pd.Series(np.random.randn(100), index=dates)
# 重采样
monthly_avg = time_series.resample('M').mean()
rolling_avg = time_series.rolling(window=7).mean() # 7天移动平均
六、机器学习算法
6.1 使用 scikit-learn
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.preprocessing import StandardScaler
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import classification_report, confusion_matrix
import numpy as np
# 1. 加载数据
iris = load_iris()
X, y = iris.data, iris.target
# 2. 数据预处理
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
# 3. 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(
X_scaled, y, test_size=0.2, random_state=42, stratify=y
)
# 4. 训练模型
clf = RandomForestClassifier(n_estimators=100, random_state=42)
clf.fit(X_train, y_train)
# 5. 模型评估
y_pred = clf.predict(X_test)
print(classification_report(y_test, y_pred))
# 6. 交叉验证
cv_scores = cross_val_score(clf, X_scaled, y, cv=5)
print(f"交叉验证平均得分: {cv_scores.mean():.3f}")
# 7. 特征重要性
feature_importances = clf.feature_importances_
for name, importance in zip(iris.feature_names, feature_importances):
print(f"{name}: {importance:.3f}")
6.2 自定义机器学习算法
import numpy as np
from collections import Counter
class KNN:
"""K近邻算法实现"""
def __init__(self, k=3):
self.k = k
def fit(self, X, y):
self.X_train = X
self.y_train = y
def predict(self, X):
predictions = [self._predict(x) for x in X]
return np.array(predictions)
def _predict(self, x):
# 计算距离
distances = [np.linalg.norm(x - x_train) for x_train in self.X_train]
# 获取k个最近邻的索引
k_indices = np.argsort(distances)[:self.k]
# 获取k个最近邻的标签
k_nearest_labels = [self.y_train[i] for i in k_indices]
# 多数投票
most_common = Counter(k_nearest_labels).most_common(1)
return most_common[0][0]
class LinearRegression:
"""线性回归实现（梯度下降）"""
def __init__(self, learning_rate=0.01, n_iterations=1000):
self.learning_rate = learning_rate
self.n_iterations = n_iterations
self.weights = None
self.bias = None
def fit(self, X, y):
n_samples, n_features = X.shape
# 初始化参数
self.weights = np.zeros(n_features)
self.bias = 0
# 梯度下降
for _ in range(self.n_iterations):
# 预测
y_pred = np.dot(X, self.weights) + self.bias
# 计算梯度
dw = (1/n_samples) * np.dot(X.T, (y_pred - y))
db = (1/n_samples) * np.sum(y_pred - y)
# 更新参数
self.weights -= self.learning_rate * dw
self.bias -= self.learning_rate * db
def predict(self, X):
return np.dot(X, self.weights) + self.bias
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