基础算法：滑动窗口_python版本-平芜编程栈

滑动窗口算法简介

滑动窗口是一种用于处理数组或字符串子区间问题的高效算法。通过维护一个动态窗口（通常由左右指针定义），在遍历过程中调整窗口大小或位置，避免重复计算，将时间复杂度从O(n²)优化至O(n)。适用于连续子数组、子串等问题。

滑动窗口的典型应用场景

寻找满足条件的最小/最大子数组长度（如和≥target的最短子数组）。
统计满足特定条件的子串或子数组数量（如包含所有字符的最短覆盖子串）。
处理固定长度窗口的问题（如计算大小为k的子数组平均值）。

Python实现模板

可变窗口大小（通用模板）

def sliding_window(s, target): left = 0 result = 0 # 或其他初始值（如float('inf')） current_value = 0 # 当前窗口的统计值（如和、字符频率等） for right in range(len(s)): current_value += s[right] # 更新右指针带来的影响 while 窗口满足条件（如current_value >= target）: result = min(result, right - left + 1) # 更新结果（根据问题调整） current_value -= s[left] # 移除左指针的影响 left += 1 # 收缩窗口 return result

固定窗口大小（示例：大小为k的子数组平均值）

def fixed_window(nums, k): window_sum = sum(nums[:k]) result = [window_sum / k] for i in range(k, len(nums)): window_sum += nums[i] - nums[i - k] # 滑动窗口：移除左端，加入右端 result.append(window_sum / k) return result

https://www.zhihu.com/zvideo/1992086275700854850/
https://www.zhihu.com/zvideo/1992086274874578007/
https://www.zhihu.com/zvideo/1992086273930835733/
https://www.zhihu.com/zvideo/1992086272345411781/
https://www.zhihu.com/zvideo/1992086268776039137/
https://www.zhihu.com/zvideo/1992086268062999793/
https://www.zhihu.com/zvideo/1992086267031212429/
https://www.zhihu.com/zvideo/1992086266234282270/
https://www.zhihu.com/zvideo/1992086264002933279/
https://www.zhihu.com/zvideo/1992086262732051397/
https://www.zhihu.com/zvideo/1992086262019023358/
https://www.zhihu.com/zvideo/1992086260995610002/
https://www.zhihu.com/zvideo/1992086260819452112/
https://www.zhihu.com/zvideo/1992086260005757376/
https://www.zhihu.com/zvideo/1992086259796047132/
https://www.zhihu.com/zvideo/1992086258877494228/
https://www.zhihu.com/zvideo/1992086257447236496/
https://www.zhihu.com/zvideo/1992086256990057914/
https://www.zhihu.com/zvideo/1992086255610126469/
https://www.zhihu.com/zvideo/1992086254024673022/
https://www.zhihu.com/zvideo/1992086251709415629/
https://www.zhihu.com/zvideo/1992086251445170546/
https://www.zhihu.com/zvideo/1992086249360597354/
https://www.zhihu.com/zvideo/1992086249796813324/
https://www.zhihu.com/zvideo/1992086247460603291/
https://www.zhihu.com/zvideo/1992086247896786890/
https://www.zhihu.com/zvideo/1992086245468303713/
https://www.zhihu.com/zvideo/1992086244939826725/
https://www.zhihu.com/zvideo/1992086241408223124/
https://www.zhihu.com/zvideo/1992086242108658791/
https://www.zhihu.com/zvideo/1992086239504007889/
https://www.zhihu.com/zvideo/1992086238363145467/
https://www.zhihu.com/zvideo/1992086238778369509/
https://www.zhihu.com/zvideo/1992086235288717115/
https://www.zhihu.com/zvideo/1992086236370858977/
https://www.zhihu.com/zvideo/1992086235800434298/
https://www.zhihu.com/zvideo/1992086233799759300/
https://www.zhihu.com/zvideo/1992086233120265991/
https://www.zhihu.com/zvideo/1992086232621131270/
https://www.zhihu.com/zvideo/1992086231664841273/
https://www.zhihu.com/zvideo/1992086231597741830/
https://www.zhihu.com/zvideo/1992086229181818148/
https://www.zhihu.com/zvideo/1992086229106325237/
https://www.zhihu.com/zvideo/1992086227973845402/
https://www.zhihu.com/zvideo/1992086227508298907/
https://www.zhihu.com/zvideo/1992086223934742995/
https://www.zhihu.com/zvideo/1992086222378639453/
https://www.zhihu.com/zvideo/1992086222340891585/
https://www.zhihu.com/zvideo/1992086220050802315/
https://www.zhihu.com/zvideo/1992086218834461645/
https://www.zhihu.com/zvideo/1992086216741515924/
https://www.zhihu.com/zvideo/1992086214795368066/
https://www.zhihu.com/zvideo/1992086211058234131/
https://www.zhihu.com/zvideo/1992086208965264892/
https://www.zhihu.com/zvideo/1992086209279852609/
https://www.zhihu.com/zvideo/1992086209292412677/
https://www.zhihu.com/zvideo/1992086207132345927/
https://www.zhihu.com/zvideo/1992086207816033726/
https://www.zhihu.com/zvideo/1992086206742295474/
https://www.zhihu.com/zvideo/1992086206352205819/
https://www.zhihu.com/zvideo/1992086206402561315/
https://www.zhihu.com/zvideo/1992086203516884357/
https://www.zhihu.com/zvideo/1992086202308894883/
https://www.zhihu.com/zvideo/1992086201180657319/
https://www.zhihu.com/zvideo/1992086200459227255/
https://www.zhihu.com/zvideo/1992086199846846688/
https://www.zhihu.com/zvideo/1992086198773118078/
https://www.zhihu.com/zvideo/1992086198664045259/
https://www.zhihu.com/zvideo/1992086197598697102/
https://www.zhihu.com/zvideo/1992086196722110763/
https://www.zhihu.com/zvideo/1992086197166694427/

实战案例

案例1：和≥target的最短子数组（LeetCode 209）

def minSubArrayLen(target, nums): left = 0 min_len = float('inf') current_sum = 0 for right in range(len(nums)): current_sum += nums[right] while current_sum >= target: min_len = min(min_len, right - left + 1) current_sum -= nums[left] left += 1 return min_len if min_len != float('inf') else 0

案例2：无重复字符的最长子串（LeetCode 3）

def lengthOfLongestSubstring(s): left = 0 max_len = 0 char_index = {} # 记录字符最后出现的位置 for right in range(len(s)): if s[right] in char_index and char_index[s[right]] >= left: left = char_index[s[right]] + 1 # 移动左指针到重复字符的下一位 char_index[s[right]] = right max_len = max(max_len, right - left + 1) return max_len