<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 totalCost(int i , int j , string s){
        int count = 0 ; 
        while(i<j){
            if(s[i] != s[j]) count++ ;  ; 
            i++ ; 
            j-- ; 
        }
        return count ; 
    }

    int helper(int index , int partitions , string s , vector<vector<int>> &dp, int n){

        if(index >= n){
            return 0 ; 
        }

        if(partitions == 0){
            return totalCost(index , n-1 , s) ; 
        }

        if(dp[index][partitions] != -1) return dp[index][partitions] ;
        int ans = 1e9 ; 

        for(int i = index ; i<n-1 ; i++){
            int cost = totalCost(index , i , s) + helper(i+1 , partitions-1 , s ,dp , n) ; 
                ans = min(ans , cost) ;         
            }
        return dp[index][partitions] = ans ; 
    }

    int palindromePartition(string s, int k) {
        int n = s.size();
        vector<vector<int>> dp(n , vector<int>(k+1 , -1)) ; 
        return helper(0 , k-1 , s , dp , n) ;    
        // final parition ko minus karte   
    }
};
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