<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:

        arr = list(s)
        arr_len = len(s)

        dp = []
        for _ in range(arr_len+1):
            dp.append([-1 for _ in range(K)])

        palinCheck = []
        for _ in range(arr_len+1):
            palinCheck.append([-1 for _ in range(arr_len+1)])

        def getMinimumPalinChange(l, r):
            if l >= r: return 0
            if palinCheck[l][r] != -1: return palinCheck[l][r]
            if arr[l] == arr[r]:
                val = getMinimumPalinChange(l+1, r-1)
            else:
                val = 1 + getMinimumPalinChange(l+1, r-1)
            palinCheck[l][r] = val
            return val


        def palindromePartition(index, k):

            if k == 0:
                return getMinimumPalinChange(index, arr_len - 1)

            if index == arr_len:
                return 0

            if dp[index][k] != -1:
                return dp[index][k]

            count = arr_len
            for i in range(index, arr_len):
                if i != arr_len - 1:
                    count = min(count, getMinimumPalinChange(index, i) + palindromePartition(i + 1, k - 1))

            dp[index][k] = count

            return count

        return palindromePartition(0, K - 1)
        
17100