Python中常用的算法包括但不限于：排序算法、搜索算法、图算法、动态规划、数据结构操作等。以下是几个常见算法的简单示例：
排序算法：
# 快速排序示例
def quicksort(arr):
if len(arr) <= 1:
return arr
pivot = arr[len(arr) // 2]
left = [x for x in arr if x < pivot]
middle = [x for x in arr if x == pivot]
right = [x for x in arr if x > pivot]
return quicksort(left) + middle + quicksort(right)
arr = [3,6,8,10,1,2,1]
print(quicksort(arr)) # 输出: [1, 1, 2, 3, 6, 8, 10]
搜索算法：
# 二分搜索示例
def binary_search(arr, x):
left = 0
right = len(arr) - 1
while left <= right:
mid = (left + right) // 2
if arr[mid] == x:
return True
elif arr[mid] > x:
right = mid - 1
else:
left = mid + 1
return False
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
x = 6
print(binary_search(arr, x)) # 输出: True
图算法：
- 深度优先搜索（DFS）
- 广度优先搜索（BFS）
- Dijkstra算法（单源最短路径）
- 最小生成树算法（Prim/Kruskal）
# 深度优先搜索示例（DFS）
from collections import deque
def dfs(graph, start):
visited = set()
stack = [start]
while stack:
vertex = stack.pop()
if vertex not in visited:
visited.add(vertex)
stack.extend(set(graph[vertex]) - visited)
return visited
# 使用DFS的图示例
graph = {'A': ['B', 'C'],
'B': ['A', 'D', 'E'],
'C': ['A', 'F'],
'D': ['B'],
'E': ['B', 'F'],
'F': ['C', 'E']}
print(dfs(graph, 'A')) # 输出: {'A', 'C', 'B', 'E', 'F', 'D'}
动态规划：
# 0-1背包问题示例
def knapsack(weight, value, n, W):
K = [[0 for w in range(W+1)] for i in range(n+1)]
for i in range(n+1):
for w in range(W+1):
if i == 0 or w == 0:
K[i][w] = 0
elif weight[i-1] <= w:
K[i][w] = max(K[i-1][w], K[i-1][w-weight[i-1]] + value[i-1])
else:
K[i][w] = K[i-1][w]
return K[n][W]
# 使用动态规划解决0-1背包问题的示例
weights = [2, 1, 3]
values = [4,