<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 dp[101][101];
    int func(int start, int end, const string &s) {
        int count = 0;
        while (start < end) {
            if (s[start] != s[end]) count++;
            start++;
            end--;
        }
        return count;
    }
    int helper(int k,string s, int curr) {
        if (curr >= s.size()) {
            return (k == 0) ? 0 : INT_MAX-200;
        }
        if (k == 0) {
            return INT_MAX-200;
        }
        if (dp[curr][k] != -1) return dp[curr][k];
        
        int ans = INT_MAX;
        for (int i = curr; i < s.size(); i++) {
            int replacements = func(curr, i, s); 
            ans = min(ans, replacements + helper(k - 1, s, i + 1));
        }
        
        return dp[curr][k] = ans;
    }
    
    int palindromePartition(string s, int k) {
        memset(dp, -1, sizeof(dp));
        return helper(k, s, 0);
    }
};

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