<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:
    map<pair<string, int>, int> mpp;
    int change(string s){
        int count = 0;
        int start = 0;
        int end = s.size()-1;

        while(start <= end){
            if(s[start++] != s[end--]){
                count++;
            }
        }
        return count;
    }
    int solve(string s, int k){
        if(k == 1){
            return change(s);
        }
        int ans = 1e9;
        if(mpp.find({s, k}) != mpp.end()) return mpp[{s, k}];
        for(int i=0; i<s.size()-1; i++){
            ans = min(ans, change(s.substr(0, i+1)) + solve(s.substr(i+1), k-1));
        }
        return mpp[{s, k}] = ans;
    }
    int palindromePartition(string s, int k) {
        return solve(s, k);
    }
};
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