<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 n;
    int use;
    int rec(int prev_index , int used , string s , vector<vector<int>> & dp){
        if(prev_index == n - 1){
           if(used == use + 1){
                return 0;
           }
           else{
                return 1e5;
           }
        }
        if(prev_index != -1){
            cout << prev_index << " " << used << endl;
            if(dp[prev_index][used] != -1){
                return dp[prev_index][used];
            }
        }
        int ans = INT_MAX;
        for(int i = prev_index + 1 ; i < n ; i++){
            int cnt = 0;
            int len = i - prev_index;
            for(int j = 0 ; j < len ; j++){
                if(s[prev_index + j + 1] != s[prev_index + len - j]){
                    cnt++;
                }
            }
            ans = min(ans , (cnt/2) + rec(i , used + 1 , s , dp));
        }
        if(prev_index != -1){
            dp[prev_index][used] = ans;
        }
        return ans;
    }
    int palindromePartition(string s, int k) {
        n = s.size();
        use = k - 1;
        vector<vector<int>> dp(n  , vector<int>(n + 1 , -1));
        int ans = rec(-1 , 0 , s , dp);
        return ans;
    }
};
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