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
class Solution:
    def maxDifference(self, S: str, k: int) -> int:
        s = list(map(int, S))
        ans = -inf
        for a in range(5):
            for b in range(5):
                if a == b:
                    continue
                curA = curB = 0
                preA = preB = 0
                t = [[inf, inf], [inf, inf]]
                l = -1
                for r, x in enumerate(s):
                    curA += x == a
                    curB += x == b
                    while r - l >= k and curB - preB >= 2:
                        t[preA & 1][preB & 1] = min(t[preA & 1][preB & 1], preA - preB)
                        l += 1
                        preA += s[l] == a
                        preB += s[l] == b
                    ans = max(ans, curA - curB - t[curA & 1 ^ 1][curB & 1])
        return ans
