<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 {
public:
    int changes(string s) {
        int res = 0;
        int low = 0;
        int high = s.size() - 1;
        while(low < high) {
            if(s[low] != s[high])
                res++;
            low++;
            high--;
        }
        return res;
    }
    int func(vector<vector<int>>& dp, int start, int k, string s) {
        if(s.size() - start < k)
            return INT_MAX;
        if(k==1) {
            return dp[start][k] = changes(s.substr(start));
        }
        if(dp[start][k] != -1)
            return dp[start][k];
        int result = INT_MAX;
        string curr = "";
        for(int i = start; i < s.size(); i++) {
            curr += s[i];
            if(func(dp,i+1,k-1,s) != INT_MAX) {
                result = min(result, changes(curr) + func(dp,i+1,k-1,s));
            }
                
        }
        return dp[start][k] = result;

    }
    int palindromePartition(string s, int k) {
        vector<vector<int>> dp(s.size(), vector<int>(k+1,-1));
        return func(dp,0,k,s);
    }
};
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