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

<p>Given a string <code>s</code> consisting of lowercase English letters only, return <em>the <strong>largest variance</strong> possible among all <strong>substrings</strong> of</em> <code>s</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;abcde&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong>
No letter occurs more than once in s, so the variance of every substring is 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>4</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

#include <string>
using namespace std;

class Solution {
public:
    int largestVariance(string s) {
        int ans = 0;
        int len = s.size();
        vector<int> dp(len + 1, 0);
        for (int i = 0; i < 26; i++) {
            for (int j = i + 1; j < 26; j++) {
                char x = i + 'a';
                char y = j + 'a';
                int minimum = 0, maximum = 0;
                int curans = 0;
                int cur = 0;
                dp[0] = 0;
                int index = -1;
                int xindex = -1;
                int yindex = -1;
                for (int k = 0; k < len; k++) {
                    if (s[k] == x) {
                        xindex = k + 1;
                        cur++;
                    } else if (s[k] == y) {
                        yindex = k + 1;
                        cur--;
                    }
                    dp[k + 1] = cur;
                    int maxindex = min(xindex, yindex);
                    while (index + 1 < maxindex) {
                        index++;
                        minimum = min(minimum, dp[index]);
                        maximum = max(maximum, dp[index]);
                    }
                    if (index >= 0) {
                        curans = max(curans, abs(cur - minimum));
                        curans = max(curans, abs(cur - maximum));
                    }
                }
                ans = max(ans, curans);
            }
        }
        return ans;
    }
};
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