2360. Substring With Largest Variance

Hard
Array
Dynamic Programming

Description

The variance of a string is defined as the largest difference between the number of occurrences of any 2 characters present in the string. Note the two characters may or may not be the same.

Given a string s consisting of lowercase English letters only, return the largest variance possible among all substrings of s.

A substring is a contiguous sequence of characters within a string.

 

Example 1:

Input: s = "aababbb"
Output: 3
Explanation:
All possible variances along with their respective substrings are listed below:
- Variance 0 for substrings "a", "aa", "ab", "abab", "aababb", "ba", "b", "bb", and "bbb".
- Variance 1 for substrings "aab", "aba", "abb", "aabab", "ababb", "aababbb", and "bab".
- Variance 2 for substrings "aaba", "ababbb", "abbb", and "babb".
- Variance 3 for substring "babbb".
Since the largest possible variance is 3, we return it.

Example 2:

Input: s = "abcde"
Output: 0
Explanation:
No letter occurs more than once in s, so the variance of every substring is 0.

 

Constraints:

  • 1 <= s.length <= 104
  • s consists of lowercase English letters.

Hints

Hint 1
Think about how to solve the problem if the string had only two distinct characters.
Hint 2
If we replace all occurrences of the first character by +1 and those of the second character by -1, can we efficiently calculate the largest possible variance of a string with only two distinct characters?
Hint 3
Now, try finding the optimal answer by taking all possible pairs of characters into consideration.

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