<p>You are given a string <code>s</code> containing lowercase letters and an integer <code>k</code>. You need to :</p>

<ul>
	<li>First, change some characters of <code>s</code> to other lowercase English letters.</li>
	<li>Then divide <code>s</code> into <code>k</code> non-empty disjoint substrings such that each substring is a palindrome.</li>
</ul>

<p>Return <em>the minimal number of characters that you need to change to divide the string</em>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;abc&quot;, k = 2
<strong>Output:</strong> 1
<strong>Explanation:</strong>&nbsp;You can split the string into &quot;ab&quot; and &quot;c&quot;, and change 1 character in &quot;ab&quot; to make it palindrome.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aabbc&quot;, k = 3
<strong>Output:</strong> 0
<strong>Explanation:</strong>&nbsp;You can split the string into &quot;aa&quot;, &quot;bb&quot; and &quot;c&quot;, all of them are palindrome.</pre>

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

<pre>
<strong>Input:</strong> s = &quot;leetcode&quot;, k = 8
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= s.length &lt;= 100</code>.</li>
	<li><code>s</code> only contains lowercase English letters.</li>
</ul>

class Solution:
    def palindromePartition(self, s: str, k: int) -> int:
        # Utility function to calculate the minimum changes required to make any substring a palindrome
        def min_changes_palindrome(l: int, r: int) -> int:
            changes = 0
            while l < r:
                if s[l] != s[r]:
                    changes += 1
                l += 1
                r -= 1
            return changes
        n = len(s)
        # dp[i][j] will store the minimum number of changes required to make the first i characters of s into j palindromic substrings
        dp = [[float('inf')] * (k + 1) for _ in range(n + 1)]
        dp[0][0] = 0
        for i in range(1, n + 1):
            for j in range(1, min(i, k) + 1):
                for m in range(i):
                    dp[i][j] = min(dp[i][j], dp[m][j - 1] + min_changes_palindrome(m, i - 1))
        return dp[n][k]
16700