# 2272. Substring With Largest Variance

## 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.

## Solutions

• class Solution {
public int largestVariance(String s) {
int n = s.length();
int ans = 0;
for (char a = 'a'; a <= 'z'; ++a) {
for (char b = 'a'; b <= 'z'; ++b) {
if (a == b) {
continue;
}
int[] f = new int[] {0, -n};
for (int i = 0; i < n; ++i) {
if (s.charAt(i) == a) {
f[0]++;
f[1]++;
} else if (s.charAt(i) == b) {
f[1] = Math.max(f[0] - 1, f[1] - 1);
f[0] = 0;
}
ans = Math.max(ans, f[1]);
}
}
}
return ans;
}
}

• class Solution {
public:
int largestVariance(string s) {
int n = s.size();
int ans = 0;
for (char a = 'a'; a <= 'z'; ++a) {
for (char b = 'a'; b <= 'z'; ++b) {
if (a == b) continue;
int f[2] = {0, -n};
for (char c : s) {
if (c == a) {
f[0]++;
f[1]++;
} else if (c == b) {
f[1] = max(f[1] - 1, f[0] - 1);
f[0] = 0;
}
ans = max(ans, f[1]);
}
}
}
return ans;
}
};

• class Solution:
def largestVariance(self, s: str) -> int:
ans = 0
for a, b in permutations(ascii_lowercase, 2):
if a == b:
continue
f = [0, -inf]
for c in s:
if c == a:
f[0], f[1] = f[0] + 1, f[1] + 1
elif c == b:
f[1] = max(f[1] - 1, f[0] - 1)
f[0] = 0
if ans < f[1]:
ans = f[1]
return ans


• func largestVariance(s string) int {
ans, n := 0, len(s)
for a := 'a'; a <= 'z'; a++ {
for b := 'a'; b <= 'z'; b++ {
if a == b {
continue
}
f := [2]int{0, -n}
for _, c := range s {
if c == a {
f[0]++
f[1]++
} else if c == b {
f[1] = max(f[1]-1, f[0]-1)
f[0] = 0
}
ans = max(ans, f[1])
}
}
}
return ans
}