<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 {
    int dp1[100][100];
    int dp[100][100];
    int cost(int i, int j, string &s) {
        if(i >= j) return 0;
        if(dp1[i][j] != -1) return dp1[i][j];
        dp1[i][j] = cost(i+1, j-1, s);
        if(s[i] != s[j]) dp1[i][j]++;
        return dp1[i][j];
    }
    int f(int i, int k, string &s) {
        if(k == 0 && i != -1) {
            return 1e9;
        }
        if(i == -1) {
            return k == 0 ? 0 : 1e9;
        }

        if(dp[i][k] != -1)
            return dp[i][k];
        
        dp[i][k] =  1e9;
        for(int j = i; j >= 0; j--) {
            dp[i][k] = min(dp[i][k], f(j-1, k-1, s) + cost(j, i, s));
        }
        return dp[i][k];
    }
public:
    int palindromePartition(string s, int k) {
        memset(dp, -1, sizeof(dp));
        memset(dp1, -1, sizeof(dp1));

        return f(s.size()-1, k, s);
    }
};
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