最长子串算法中的滑动窗口技术（ Understanding the Sliding Window in Algorithms）

问题描述

Longest Substring Without Repeating Characters

Topic: Hash Table, Two pointer, String, Sliding Windows

给定一个字符串，请找出其中不含有重复字符的 最长子串 的长度。

Given a string s, find the length of the longest substring without repeating characters.

Example 1:

Input: s = "abcabcbb"
Output: 3
Explanation: The answer is "abc", with the length of 3.

Example 2:

Input: s = "bbbbb"
Output: 1
Explanation: The answer is "b", with the length of 1.

Example 3:

Input: s = "pwwkew"
Output: 3
Explanation: The answer is "wke", with the length of 3.
Notice that the answer must be a substring, "pwke" is a subsequence and not a substring.

Example 4:

Input: s = ""
Output: 0

Constraints:

0 <= s.length <= 5 * 104

s consists of English letters, digits, symbols and spaces.

问题分析

一般来说，当您需要跟踪连续的元素序列（例如，对子数组中的值求和、字符串序列等）时，滑动窗口技术很有用。

Generally speaking, the sliding window technique is useful when you need to keep track of a contiguous sequence of elements, such as summing up the values in a subarray.

滑动窗口算法思路

滑动窗口的应用场景有几个特点：

1. 需要输出或比较的结果在原数据结构中是连续排列的；

2. 每次窗口滑动时，只需观察窗口两端元素的变化，无论窗口多长，每次只操作两个头尾元素，当用到的窗口比较长时，可以显著减少操作次数；

3. 窗口内元素的整体性比较强，窗口滑动可以只通过操作头尾两个位置的变化实现，但对比结果时往往要用到窗口中所有元素。

问题答案

滑动窗口实现的源代码（Kotlin 语言）：

class Solution {
    fun lengthOfLongestSubstring(s: String): Int {
        var ans = 0
        var left = 0
        var right = 0
        val n = s.length




        val window = mutableSetOf<Char>()




        while (left < n && right < n) {
            // slide window's right side
            if (!window.contains(s[right])) {
                window.add(s[right++])
                ans = Math.max(ans, right - left)
            } else {
                // slide window's left side
                window.remove(s[left++])
            }
        }




        return ans
    }




}

时间复杂度：O(N)，其中N为字符串长度； 

空间复杂度：O(N)，其中N为字符串长度。

参考资料：

​​https://levelup.gitconnected.com/understanding-the-sliding-window-technique-in-algorithms-c6c3bf8226da​​

​​https://logicfirstcoding.com/subarray-with-a-given-sum-sliding-window-technique/​​

​​https://charon.me/posts/leetcode/day13/​​

​​https://leetcode-cn.com/problems/longest-substring-without-repeating-characters​​

​​https://zhuanlan.zhihu.com/p/129018030​​