<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>

// Instead of modifying each character
// Count the number of unmatched characters

class Solution {
public:
    int countUnmatched(string s) {
        int l = 0, r = s.size() - 1, res = 0;
        while(l < r) {
            if(s[l++] != s[r--]) {
                res++;
            }
        }
        return res;
    }

    int dp[101][101][101];

    int helper(int j, int i, string& s, int k) {
        if(i == s.size() || k == 0) {
            if(i == s.size() && k == 0) {
                return 0;
            }
            return 1e9;
        }
        if(dp[j][i][k] != -1) {
            return dp[j][i][k];
        }

        int cnt = countUnmatched(s.substr(j, i - j + 1));
        int take = cnt + helper(i + 1, i + 1, s, k - 1);
        int notTake1 = cnt + helper(j, i + 1, s, k);
        int notTake2 = helper(j, i + 1, s, k);
        return dp[j][i][k] = min({take, notTake1, notTake2});
    }

    int palindromePartition(string s, int k) {
        memset(dp, -1, sizeof(dp));
        return helper(0, 0, s, k);
    }
};
38801