题目要求

Find the length of the longest substring T of a given string (consists of lowercase letters only) such that every character in T appears no less than k times.

Example 1:

Input:
s = "aaabb", k = 3

Output:
3

The longest substring is "aaa", as 'a' is repeated 3 times.
Example 2:

Input:
s = "ababbc", k = 2

Output:
5

The longest substring is "ababb", as 'a' is repeated 2 times and 'b' is repeated 3 times.

找出字符串中的最长子字符串，满足该子字符串中任何字符出现的次数都大于k。

思路和代码

这是一个经典的分治法解决的问题，关键在于我们如何将这个问题分解为更小的子问题。反过来想，这个子字符串一定不包含什么元素呢？当一个元素出现的总次数小于k，那么该元素一定不在子字符串中，只需要将其作为分界点，分别找出左半部分和右半部分的满足条件的最长子字符串。

    public int longestSubstring(String s, int k) {
        return longestSubstring(s, k, 0, s.length()-1);
    }
    
    public int longestSubstring(String s, int k, int left, int right) {
        if(left > right) {
            return 0;
        }

        int[] count = new int[26];
        for(int i = left ; i<=right ; i++) {
            count[s.charAt(i) - 'a']++;
        }
        int result = right - left + 1;
        for(int i = left ; i<=right ; i++) {
            if(count[s.charAt(i)-'a'] < k && count[s.charAt(i)-'a'] > 0) {
                int leftLongest = longestSubstring(s, k, left, i-1);
                int rightLongest = longestSubstring(s, k, i+1, right);
                result = Math.max(leftLongest, rightLongest);
                
                break;
            }
        }
        return result;
    }