<p>You are given a <strong>0-indexed</strong> string <code>s</code> and an integer <code>k</code>.</p> <p>You are to perform the following partitioning operations until <code>s</code> is <strong>empty</strong>:</p> <ul> <li>Choose the <strong>longest</strong> <strong>prefix</strong> of <code>s</code> containing at most <code>k</code> <strong>distinct</strong> characters.</li> <li><strong>Delete</strong> the prefix from <code>s</code> and increase the number of partitions by one. The remaining characters (if any) in <code>s</code> maintain their initial order.</li> </ul> <p><strong>Before</strong> the operations, you are allowed to change <strong>at most</strong> <strong>one</strong> index in <code>s</code> to another lowercase English letter.</p> <p>Return <em>an integer denoting the <strong>maximum</strong> number of resulting partitions after the operations by optimally choosing at most one index to change.</em></p> <p> </p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> s = "accca", k = 2 <strong>Output:</strong> 3 <strong>Explanation: </strong>In this example, to maximize the number of resulting partitions, s[2] can be changed to 'b'. s becomes "acbca". The operations can now be performed as follows until s becomes empty: - Choose the longest prefix containing at most 2 distinct characters, "<u>ac</u>bca". - Delete the prefix, and s becomes "bca". The number of partitions is now 1. - Choose the longest prefix containing at most 2 distinct characters, "<u>bc</u>a". - Delete the prefix, and s becomes "a". The number of partitions is now 2. - Choose the longest prefix containing at most 2 distinct characters, "<u>a</u>". - Delete the prefix, and s becomes empty. The number of partitions is now 3. Hence, the answer is 3. It can be shown that it is not possible to obtain more than 3 partitions.</pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> s = "aabaab", k = 3 <strong>Output:</strong> 1 <strong>Explanation: </strong>In this example, to maximize the number of resulting partitions we can leave s as it is. The operations can now be performed as follows until s becomes empty: - Choose the longest prefix containing at most 3 distinct characters, "<u>aabaab</u>". - Delete the prefix, and s becomes empty. The number of partitions becomes 1. Hence, the answer is 1. It can be shown that it is not possible to obtain more than 1 partition. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> s = "xxyz", k = 1 <strong>Output:</strong> 4 <strong>Explanation:</strong> In this example, to maximize the number of resulting partitions, s[1] can be changed to 'a'. s becomes "xayz". The operations can now be performed as follows until s becomes empty: - Choose the longest prefix containing at most 1 distinct character, "<u>x</u>ayz". - Delete the prefix, and s becomes "ayz". The number of partitions is now 1. - Choose the longest prefix containing at most 1 distinct character, "<u>a</u>yz". - Delete the prefix, and s becomes "yz". The number of partitions is now 2. - Choose the longest prefix containing at most 1 distinct character, "<u>y</u>z". - Delete the prefix, and s becomes "z". The number of partitions is now 3. - Choose the longest prefix containing at most 1 distinct character, "<u>z</u>". - Delete the prefix, and s becomes empty. The number of partitions is now 4. Hence, the answer is 4. It can be shown that it is not possible to obtain more than 4 partitions. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= s.length <= 10<sup>4</sup></code></li> <li><code>s</code> consists only of lowercase English letters.</li> <li><code>1 <= k <= 26</code></li> </ul>