<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 minChanges(string s, int from, int to, vector<vector<int>>& changeMemo){
        if(changeMemo[from][to] != -1) return changeMemo[from][to];
        int res = 0;
        int curf = from;
        int curt = to;
        while(curf <= curt) if(s[curf++] != s[curt--]) res++;
        changeMemo[from][to] = res;
        return res;
    }
    int goOver(int from, int leftK, string s, vector<vector<int>>& memo, vector<vector<int>>& changeMemo){
        if(memo[from][leftK] != -1) return memo[from][leftK];
        if(leftK == 1){
            memo[from][leftK] = minChanges(s,from,s.length()-1, changeMemo);
            return memo[from][leftK];
        }
        int res = INT_MAX;
        for(int to = from; to <= s.length()-leftK; to++){
            int curRes = minChanges(s,from,to,changeMemo);
            curRes += goOver(to+1,leftK-1,s,memo,changeMemo);
            res = min(res,curRes);
        }
        memo[from][leftK] = res;
        return res;
    }
    int palindromePartition(string s, int k) {
        vector<vector<int>> memo(101,vector<int>(101,-1));
        vector<vector<int>> changeMemo(101,vector<int>(101,-1));
        return goOver(0,k,s,memo,changeMemo);
    }
};
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