Maximum Difference Between Even and Odd Frequency II
<p>You are given a string <code>s</code> and an integer <code>k</code>. Your task is to find the <strong>maximum</strong> difference between the frequency of <strong>two</strong> characters, <code>freq[a] - freq[b]</code>, in a <span data-keyword="substring">substring</span> <code>subs</code> of <code>s</code>, such that:</p>

<ul>
	<li><code>subs</code> has a size of <strong>at least</strong> <code>k</code>.</li>
	<li>Character <code>a</code> has an <em>odd frequency</em> in <code>subs</code>.</li>
	<li>Character <code>b</code> has a <strong>non-zero</strong> <em>even frequency</em> in <code>subs</code>.</li>
</ul>

<p>Return the <strong>maximum</strong> difference.</p>

<p><strong>Note</strong> that <code>subs</code> can contain more than 2 <strong>distinct</strong> characters.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;12233&quot;, k = 4</span></p>

<p><strong>Output:</strong> <span class="example-io">-1</span></p>

<p><strong>Explanation:</strong></p>

<p>For the substring <code>&quot;12233&quot;</code>, the frequency of <code>&#39;1&#39;</code> is 1 and the frequency of <code>&#39;3&#39;</code> is 2. The difference is <code>1 - 2 = -1</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;1122211&quot;, k = 3</span></p>

<p><strong>Output:</strong> <span class="example-io">1</span></p>

<p><strong>Explanation:</strong></p>

<p>For the substring <code>&quot;11222&quot;</code>, the frequency of <code>&#39;2&#39;</code> is 3 and the frequency of <code>&#39;1&#39;</code> is 2. The difference is <code>3 - 2 = 1</code>.</p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;110&quot;, k = 3</span></p>

<p><strong>Output:</strong> <span class="example-io">-1</span></p>
</div>

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

<ul>
	<li><code>3 &lt;= s.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>s</code> consists only of digits <code>&#39;0&#39;</code> to <code>&#39;4&#39;</code>.</li>
	<li>The input is generated that at least one substring has a character with an even frequency and a character with an odd frequency.</li>
	<li><code>1 &lt;= k &lt;= s.length</code></li>
</ul>
String; Enumeration; Prefix Sum; Sliding Window
function maxDifference(S: string, k: number): number {
    const s = S.split('').map(Number);
    let ans = -Infinity;
    for (let a = 0; a < 5; a++) {
        for (let b = 0; b < 5; b++) {
            if (a === b) {
                continue;
            }
            let [curA, curB, preA, preB] = [0, 0, 0, 0];
            const t: number[][] = [
                [Infinity, Infinity],
                [Infinity, Infinity],
            ];
            let l = -1;
            for (let r = 0; r < s.length; r++) {
                const x = s[r];
                curA += x === a ? 1 : 0;
                curB += x === b ? 1 : 0;
                while (r - l >= k && curB - preB >= 2) {
                    t[preA & 1][preB & 1] = Math.min(t[preA & 1][preB & 1], preA - preB);
                    l++;
                    preA += s[l] === a ? 1 : 0;
                    preB += s[l] === b ? 1 : 0;
                }
                ans = Math.max(ans, curA - curB - t[(curA & 1) ^ 1][curB & 1]);
            }
        }
    }
    return ans;
}
