<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 palindromePartition(string s, int k) {
        int n = s.length();
        vector<vector<vector<int>>> memo(n, vector<vector<int>>(n, vector<int>(k+1,-1)));
        return solve(0,n-1,k,s,memo);
    }

private:
    int solve(int i, int j, int k, const string& s, vector<vector<vector<int>>>& memo) {
        if (memo[i][j][k]>=0) return memo[i][j][k];
        if (j-i+1==1 || j-i+1==k) return memo[i][j][k] = 0;
        if (k==1) {
            int halfLen = (j-i+1)/2;
            string firstHalf = s.substr(i,halfLen);
            string secondHalf = s.substr(ceil((j+i+1)/2.0), halfLen);
            int ans = 0;
            for (int p=0; p<halfLen; ++p) {
                if (firstHalf[p]!=secondHalf[halfLen-p-1]) ans++;
            }
            return memo[i][j][k] = ans;
        }
        int minChanges = INT_MAX, temp;
        for (int r=i; r<=(j-k+1);++r) {
            temp = solve(i,r,1,s,memo) + solve(r+1,j,k-1,s,memo);
            minChanges = min(minChanges, temp);
        }
        return memo[i][j][k] = minChanges;
    }
};
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