<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 {
private:
    int f(int i, int j, string &s, vector<vector<int>>& dp) {
        if (i >= j) return 0;
        if (dp[i][j] != -1) return dp[i][j];
        if (s[i] == s[j]) return dp[i][j] = f(i + 1, j - 1, s, dp);
        return dp[i][j] = 1 + f(i + 1, j - 1, s, dp);
    }

    int partition(int l, int r, int k, string &s, vector<vector<vector<int>>>& dp) {
        if (k == 1) return f(l, r, s, dp[k]);
        if (dp[k][l][r] != -1) return dp[k][l][r];

        int min_cost = INT_MAX;
        for (int i = l; i <= r - k + 1; ++i) {
            int cost = f(l, i, s, dp[k]) + partition(i + 1, r, k - 1, s, dp);
            min_cost = min(min_cost, cost);
        }

        return dp[k][l][r] = min_cost;
    }

public:
    int palindromePartition(string s, int k) {
        int n = s.size();
        vector<vector<vector<int>>> dp(k+1, vector<vector<int>>(n, vector<int>(n, -1)));
        int ans = INT_MAX;
        for(int i=0; i<n; ++i) {
			for(int j=i+1; j<n-1; ++j) {
				int cnt = partition(0, n - 1, k, s, dp);
				ans = min(ans, cnt);
			}
		}
		return ans;
    }
};
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