<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][101];

    int getCount(string& s) {
        if (s.size() == 0)
            return 0;

        int n = s.size();
        int x = (n + 1) / 2;
        int c = 0;
        for (int i = 0, j = n - 1; i < x; i++, j--) {
            if (s[i] != s[j])
                c++;
        }
        return c;
    }

    int solve(string s, int i, int j, int k) {
        if (i > j) {
            if (k == 0)
                return 0;
            else
                return 1e9;
        }
        if (i == j) {
            if (k == 1)
                return 0;
            else
                return 1e9;
        }

        if (k == 1) {
            string str = s.substr(i, j - i + 1);
            int x1 = getCount(str);
            return dp[i][j][k] = x1;
        }

        if (dp[i][j][k] != -1)
            return dp[i][j][k];

        int ans = 1e9;
        string s1 = "";
        for (int l = i; l <= j; l++) {
            s1 += s[l];
            int x = getCount(s1);
            ans = min(ans, x + solve(s, l + 1, j, k - 1));
        }

        return dp[i][j][k] = ans;
    }

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