phase 5 part 5: cs algorithms, network-os, web-security topics with tested examples; all 43 stacks pass --strict
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"""面试高频算法模式（只用标准库）。每个函数注明时间 / 空间复杂度；`python patterns.py` 运行自检，test_patterns.py 是测试。"""
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from __future__ import annotations
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import heapq
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from collections import Counter, OrderedDict, deque
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from typing import Hashable, Iterable
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# 1. 哈希表：两数之和 O(n) / O(n)
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def two_sum(nums: list[int], target: int) -> tuple[int, int] | None:
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seen: dict[int, int] = {}
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for i, x in enumerate(nums):
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if target - x in seen:
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return seen[target - x], i
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seen[x] = i
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return None
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# 2. 滑动窗口：无重复字符的最长子串 O(n) / O(字符集)
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def longest_unique_substring(s: str) -> int:
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last: dict[str, int] = {}
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left = best = 0
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for right, ch in enumerate(s):
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if last.get(ch, -1) >= left:
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left = last[ch] + 1 # 窗口左边界跳到重复字符的下一位
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last[ch] = right
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best = max(best, right - left + 1)
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return best
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# 3. 二分查找：第一个 >= target 的位置（lower_bound） O(log n) / O(1)
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def lower_bound(arr: list[int], target: int) -> int:
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lo, hi = 0, len(arr) # 左闭右开区间 [lo, hi)
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while lo < hi:
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mid = (lo + hi) // 2
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if arr[mid] < target:
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lo = mid + 1
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else:
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hi = mid
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return lo
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# 4. 堆：出现次数最多的 K 个（例如热门问题） O(n log k) / O(n)
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def top_k_frequent(items: Iterable[Hashable], k: int) -> list[Hashable]:
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counts = Counter(items)
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return [x for _, x in heapq.nlargest(k, ((c, x) for x, c in counts.items()))]
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# 5. BFS：网格最短路径（0 可走，1 障碍） O(行×列) / O(行×列)
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def shortest_path(grid: list[list[int]], start: tuple[int, int], end: tuple[int, int]) -> int:
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rows, cols = len(grid), len(grid[0])
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q = deque([(start, 0)])
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seen = {start}
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while q:
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(r, c), d = q.popleft()
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if (r, c) == end:
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return d
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for dr, dc in ((1, 0), (-1, 0), (0, 1), (0, -1)):
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nr, nc = r + dr, c + dc
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if 0 <= nr < rows and 0 <= nc < cols and grid[nr][nc] == 0 and (nr, nc) not in seen:
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seen.add((nr, nc))
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q.append(((nr, nc), d + 1))
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return -1
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# 6. DFS + 拓扑排序：任务依赖的执行顺序（有环返回 None） O(V+E)
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def topo_order(deps: dict[str, list[str]]) -> list[str] | None:
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"""deps[a] = [b, c] 表示 a 依赖 b 和 c（b、c 要先执行）。"""
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state: dict[str, int] = {} # 0/缺省 未访问，1 访问中，2 已完成
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order: list[str] = []
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def visit(n: str) -> bool:
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if state.get(n) == 1:
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return False # 回到“访问中”的节点：有环
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if state.get(n) == 2:
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return True
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state[n] = 1
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for m in deps.get(n, []):
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if not visit(m):
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return False
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state[n] = 2
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order.append(n)
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return True
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nodes = set(deps) | {m for ms in deps.values() for m in ms}
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for n in sorted(nodes):
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if not visit(n):
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return None
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return order
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# 7. 动态规划：编辑距离（文本相似度、纠错） O(mn) / O(n)
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def edit_distance(a: str, b: str) -> int:
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prev = list(range(len(b) + 1))
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for i in range(1, len(a) + 1):
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cur = [i] + [0] * len(b)
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for j in range(1, len(b) + 1):
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cur[j] = prev[j - 1] if a[i - 1] == b[j - 1] else 1 + min(prev[j - 1], prev[j], cur[j - 1])
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prev = cur
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return prev[-1]
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# 8. 设计题：LRU 缓存 get/put 均为 O(1)
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class LRUCache:
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def __init__(self, capacity: int):
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self.capacity = capacity
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self.data: OrderedDict[Hashable, object] = OrderedDict()
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def get(self, key: Hashable) -> object | None:
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if key not in self.data:
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return None
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self.data.move_to_end(key) # 最近使用的移到末尾
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return self.data[key]
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def put(self, key: Hashable, value: object) -> None:
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self.data[key] = value
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self.data.move_to_end(key)
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if len(self.data) > self.capacity:
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self.data.popitem(last=False) # 淘汰最久未使用的（头部）
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# 9. 区间合并：合并重叠的时间段（排班、会议室） O(n log n)
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def merge_intervals(intervals: list[tuple[int, int]]) -> list[tuple[int, int]]:
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out: list[tuple[int, int]] = []
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for s, e in sorted(intervals):
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if out and s <= out[-1][1]:
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out[-1] = (out[-1][0], max(out[-1][1], e))
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else:
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out.append((s, e))
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return out
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if __name__ == "__main__":
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assert two_sum([2, 7, 11, 15], 9) == (0, 1)
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assert longest_unique_substring("abcabcbb") == 3
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assert lower_bound([1, 3, 3, 5], 3) == 1
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assert top_k_frequent(["退货", "发票", "退货", "物流", "退货", "物流"], 2) == ["退货", "物流"]
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assert shortest_path([[0, 0, 0], [1, 1, 0], [0, 0, 0]], (0, 0), (2, 0)) == 6
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assert topo_order({"deploy": ["test"], "test": ["build"]}) == ["build", "test", "deploy"]
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assert edit_distance("kitten", "sitting") == 3
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assert merge_intervals([(1, 3), (2, 6), (8, 10)]) == [(1, 6), (8, 10)]
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print("全部自检通过")
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@@ -0,0 +1,63 @@
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import random
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import pytest
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from patterns import (LRUCache, edit_distance, longest_unique_substring, lower_bound, merge_intervals,
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shortest_path, top_k_frequent, topo_order, two_sum)
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def test_two_sum():
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assert two_sum([3, 3], 6) == (0, 1)
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assert two_sum([1, 2], 10) is None
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@pytest.mark.parametrize("s,n", [("", 0), ("bbbb", 1), ("pwwkew", 3), ("abba", 2), ("你好你们好", 3)])
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def test_longest_unique(s, n):
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assert longest_unique_substring(s) == n
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def test_lower_bound_matches_bisect():
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import bisect
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rng = random.Random(0)
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for _ in range(200): # 与标准库对拍
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arr = sorted(rng.randint(0, 20) for _ in range(rng.randint(0, 15)))
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t = rng.randint(-1, 21)
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assert lower_bound(arr, t) == bisect.bisect_left(arr, t)
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def test_top_k():
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assert top_k_frequent([], 3) == []
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assert top_k_frequent(list("aaabbc"), 1) == ["a"]
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def test_shortest_path_blocked():
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assert shortest_path([[0, 1], [1, 0]], (0, 0), (1, 1)) == -1
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assert shortest_path([[0]], (0, 0), (0, 0)) == 0
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def test_topo_cycle_and_order():
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assert topo_order({"a": ["b"], "b": ["a"]}) is None
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order = topo_order({"app": ["db", "cache"], "cache": ["net"], "db": ["net"]})
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assert order is not None
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pos = {n: i for i, n in enumerate(order)}
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assert pos["net"] < pos["db"] < pos["app"] and pos["net"] < pos["cache"] < pos["app"]
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def test_edit_distance():
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assert edit_distance("", "abc") == 3
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assert edit_distance("退货申请", "退款申请") == 1
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def test_lru():
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c = LRUCache(2)
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c.put("a", 1)
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c.put("b", 2)
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assert c.get("a") == 1 # a 变成最近使用
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c.put("c", 3) # 淘汰 b
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assert c.get("b") is None and c.get("a") == 1 and c.get("c") == 3
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def test_merge_intervals():
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assert merge_intervals([]) == []
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assert merge_intervals([(1, 4), (4, 5)]) == [(1, 5)]
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assert merge_intervals([(5, 6), (1, 2)]) == [(1, 2), (5, 6)]
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