<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 fn(string s,int i,int j){
    int cnt=0;
    while(i<j){
        if(s[i]!=s[j]){
            cnt++;
        }
        i++;
        j--;
    }
    return cnt;
  }
  int fni(string s,int i,int k,vector<vector<int>>&dp){
    if(i==s.size()){
        return 1e9;
       }
       if(k==1){
        return fn(s,i,s.size()-1);
       }
       
       if(dp[i][k]!=-1) return dp[i][k];
       int ans=1e9;
       for(int j=i;j<s.size();j++){
           int p=fn(s,i,j)+fni(s,j+1,k-1,dp);
           ans=min(ans,p);
       }
       return dp[i][k]=ans;
  }
    int palindromePartition(string s, int k) {
        vector<vector<int>>dp(s.size(),vector<int>(k+1,-1));
        return fni(s,0,k,dp);
    }
};
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