Change Minimum Characters to Satisfy One of Three Conditions
<p>You are given two strings <code>a</code> and <code>b</code> that consist of lowercase letters. In one operation, you can change any character in <code>a</code> or <code>b</code> to <strong>any lowercase letter</strong>.</p>

<p>Your goal is to satisfy <strong>one</strong> of the following three conditions:</p>

<ul>
	<li><strong>Every</strong> letter in <code>a</code> is <strong>strictly less</strong> than <strong>every</strong> letter in <code>b</code> in the alphabet.</li>
	<li><strong>Every</strong> letter in <code>b</code> is <strong>strictly less</strong> than <strong>every</strong> letter in <code>a</code> in the alphabet.</li>
	<li><strong>Both</strong> <code>a</code> and <code>b</code> consist of <strong>only one</strong> distinct letter.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> number of operations needed to achieve your goal.</em></p>

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

<pre>
<strong>Input:</strong> a = &quot;aba&quot;, b = &quot;caa&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> Consider the best way to make each condition true:
1) Change b to &quot;ccc&quot; in 2 operations, then every letter in a is less than every letter in b.
2) Change a to &quot;bbb&quot; and b to &quot;aaa&quot; in 3 operations, then every letter in b is less than every letter in a.
3) Change a to &quot;aaa&quot; and b to &quot;aaa&quot; in 2 operations, then a and b consist of one distinct letter.
The best way was done in 2 operations (either condition 1 or condition 3).
</pre>

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

<pre>
<strong>Input:</strong> a = &quot;dabadd&quot;, b = &quot;cda&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The best way is to make condition 1 true by changing b to &quot;eee&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= a.length, b.length &lt;= 10<sup>5</sup></code></li>
	<li><code>a</code> and <code>b</code> consist only of lowercase letters.</li>
</ul>
Hash Table; String; Counting; Prefix Sum
class Solution {
    private int ans;

    public int minCharacters(String a, String b) {
        int m = a.length(), n = b.length();
        int[] cnt1 = new int[26];
        int[] cnt2 = new int[26];
        for (int i = 0; i < m; ++i) {
            ++cnt1[a.charAt(i) - 'a'];
        }
        for (int i = 0; i < n; ++i) {
            ++cnt2[b.charAt(i) - 'a'];
        }
        ans = m + n;
        for (int i = 0; i < 26; ++i) {
            ans = Math.min(ans, m + n - cnt1[i] - cnt2[i]);
        }
        f(cnt1, cnt2);
        f(cnt2, cnt1);
        return ans;
    }

    private void f(int[] cnt1, int[] cnt2) {
        for (int i = 1; i < 26; ++i) {
            int t = 0;
            for (int j = i; j < 26; ++j) {
                t += cnt1[j];
            }
            for (int j = 0; j < i; ++j) {
                t += cnt2[j];
            }
            ans = Math.min(ans, t);
        }
    }
}