<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[105][105];
    int INF = 1e5;

    int count(string s) {
        int change = 0;
        int i = 0, j = s.size()-1;

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

        cout<<s<<" "<<change<<endl;

        return change;
    }

    int go(int pos, string& s, int k) {
        if (pos == s.size() && k >= 1) return INF;

        if (k == 1) {
            //Need to make complete partition palindrome.
            return count(s.substr(pos, s.size()));
        } 

        int& ans = dp[pos][k];
        if (ans != -1) return ans;

        ans = INF;

        for (int i = pos; i < s.size(); i++) {
            string tmp = s.substr(pos, i-pos+1);
            ans = min(ans, count(tmp) + go(i+1, s, k-1));
        }   

        return ans;
    }

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