<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 rec( string s , int k , int len,vector<vector<int>> &dp)
    {
        if(k==0)
        {
            int val=0;
            for( int i=0 ; i<s.size()/2 ; i++  )
            {
                if(s[i]!=s[s.size()-1-i])
                val++;
            }
            return val;
        }
        if(dp[len][k]!=-1)
        return dp[len][k];
        int ko=1e9;
        for( int i=1 ; i< s.size() ; i++ )
        {
            int val=0;
            for( int in=0 ; in<i/2; in++)
            {
                if(s[in]!=s[i-1-in])
                val++;
            }
            ko=min(ko,val+rec(s.substr(i),k-1,len+i,dp));
        }
        return dp[len][k]=ko;
    }
    int palindromePartition(string s, int k) {
        vector<vector<int>> dp(s.size()+1, vector<int> (s.size()+1,-1));
        return rec( s,k-1 ,1,dp);
    }
};
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