LeetCode刷题之旅(中等-1): 3. 无重复字符的最长子串

本文探讨了在给定字符串中寻找最长无重复字符子串的问题,对比了暴力穷举法与滑动窗口法。暴力法虽直观但效率低下,而滑动窗口法则实现了高效查找,通过动态调整窗口大小,避免了不必要的重复检查。

2019年11月22日

目录

题目: 3. 无重复字符的最长子串

解题1:暴力穷举法

执行结果:

复杂度分析

解法2:滑动窗口法

执行结果:

复杂度分析


题目: 3. 无重复字符的最长子串

 

解题1:暴力穷举法

public class TestLongestSubstringWithoutRepeatingCharacters {
    public static void main(String[] args) {
        // 力扣测试用例
        System.out.println("start="+System.currentTimeMillis());
        String s = "\"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ 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abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789!\\\"#$%&'()*+,-./:;<=>?@[\\\\]^_`{|}~ abcdefghijklmnopqrstuvwxyzABCD\"";
//        System.out.println(s + " : " + lengthOfLongestSubstringV1(s));
        System.out.println(s.length());
        System.out.println("end="+System.currentTimeMillis());
    }



    /**
     * 第一种解法:暴力法
     */
    public static int lengthOfLongestSubstringV1(String s) {
        int length = s.length();
        int res = 0;
        for (int i=0; i<length; i++){
            for (int j=i+1; j<=length;j++){
                if(!haveDuplicateCharacter(s, i, j)){
                    res = Math.max(res, j-i);
                }
            }
        }
        return res;
    }

    private static boolean haveDuplicateCharacter(String s, int i, int j) {
        HashSet<Object> set = new HashSet<>();
        for (int start = i; start < j; start++){
            if (set.contains(s.charAt(start))){
                return true;
            }
            set.add(s.charAt(start));
        }
        return false;
    }
}

执行结果:

  • 本地测试OK,放到leetCode上,测试用例输入了一个长度为31654的字符串,导致执行超时。
  • 我也试着本地跑一下,执行开始与结束时间分别是:2019-11-24 17:54:31 (1574589271194)~ 2019-11-24 18:01:38(1574589698235),耗时接近8分钟。
  • 这是要被替代的解法。

复杂度分析

  1. 时间复杂度:O(n^3)。
  2. 空间复杂度:O(min(n,m)),我们需要 O(k)O(k) 的空间来检查子字符串中是否有重复字符,其中 kk 表示 Set 的大小。而 Set 的大小取决于字符串 nn 的大小以及字符集/字母 mm 的大小。

解法2:滑动窗口法

class Solution {
   /**
     * 第二种解法:滑动窗口法
     */
    public static int lengthOfLongestSubstring(String s) {
        int length = s.length();
        Integer res = 0;
        HashMap<Character, Integer> map = new HashMap<>();
        //遍历一次序列,头指针/尾指针都从0开始
        for (int end = 0, start = 0; end < length; end ++){
            char character = s.charAt(end);
            if(map.get(character) != null){
                // map不含有这个key=元素的键值对时,表示不重复;如果已存在key=元素的键值对,则取出下标比较与更新头结点;
                start = Math.max(start, map.get(character));
                // 我这里纳闷,为何不直接赋值呢?因为发生重复的可能是多个元素,只有一个元素发送重复,那直接赋值没问题,但是多个元素可能重复,
                //那就要比较下了,因为新的重复元素也可以存在于另一个不重复序列里面的!
            }
            res = Math.max(res, end - start + 1);
            map.put(character, end+1);
        }
        return res;
    }
    
}

执行结果:

复杂度分析

  • 时间复杂度:O(n),索引 j 将会迭代 n 次。
  • 空间复杂度(HashMap):O(min(m, n)),与之前的方法相同。
  • 空间复杂度(Table):O(m),m 是字符集的大小。

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