<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 {
    int palin(string s){
        int ans=0;
        int start=0;
        int end=s.size()-1;
        while(start<end){
            if(s[start]!=s[end]){
                ans++;
            }
            start++;
            end--;
        }
        return ans;
    }
    int f(int ind,int par,string s,int n,int k,vector<vector<int>>&dp){
        if(ind==n){
            if(par==k){
                return 0;
            }
            else{
                return INT_MAX;
            }
        }
        if(dp[ind][par]!=-1){
            return dp[ind][par];
        }
        int min_val=INT_MAX;
        for(int start=ind;start<n;start++){
            int solve=INT_MAX;
            if(f(start+1,par+1,s,n,k,dp)!=INT_MAX){
            solve=palin(s.substr(ind,start-ind+1))+f(start+1,par+1,s,n,k,dp);
            }
            min_val=min(solve,min_val);
        }
        return dp[ind][par]=min_val;
    }
public:
    int palindromePartition(string s, int k) {
        int n=s.size();
        vector<vector<int>> dp(n+1,vector<int>(n+1,-1));

        return f(0,0,s,n,k,dp);
    }
};
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