<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 totalChange (string s){
        int cnt = 0;
        int n = s.size();
        int i = 0, j = n-1;

        while (i <= j){
            if (s[i] != s[j]){
                cnt++;
            }
            i++;j--;
        }
        return cnt;
    }

    int helper (int curr, int k, string &s, vector <vector <int>> &sub, vector <vector <int>> &dp){
        int n = s.size();
        if (curr == n){
            if (k == 0) return 0;
            return 1e9;
        }
        if (k == 0) return 1e9;

        if (dp[curr][k] != -1) return dp[curr][k];
        
        int cnt = 1e9;
        for (int i = curr; i < n; i++){
            int a = sub[curr][i];
            cnt = min (cnt, a + helper (i+1, k-1, s, sub, dp));
        }
        return dp[curr][k] = cnt;
    }

public:
    int palindromePartition(string s, int k) {
        int n = s.size();

        vector <vector <int>> sub (n, vector <int> (n, 0));
        for (int i = 0; i < n; i++){
            for (int j = i+1; j < n; j++){
                sub[i][j] = totalChange (s.substr(i, j-i+1));
            }
        }
        vector <vector <int>> dp (n, vector <int> (k+1, -1));
        return helper (0, k, s, sub, dp);
    }
};
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