<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 arr[101][101], dp[101][101];
    int solve(string s, int k, int i){
        if(i >= s.size()){
            return k == 0 ? 0 : 1e9;
        }
        if(k < 0)return 1e9;
        if(dp[i][k] != -1)return dp[i][k];
        int ans = 1e9;
        for(int j = i; j < s.size(); j++){
            ans = min(ans,arr[i][j] + solve(s,k-1,j+1));
        }
        return dp[i][k] = ans;
    }
public:
    int palindromePartition(string s, int k) {
        memset(arr,0,sizeof(arr));
        memset(dp,-1,sizeof(dp));
        for(int i = 0; i < s.size(); i++){
            for(int j = i; j < s.size(); j++){
                int k = i, l = j, cnt = 0;
                while(k < l){
                    if(s[k] != s[l])cnt++;
                    k++;
                    l--;
                }
                arr[i][j] = cnt;
            }
        }
        return solve(s,k,0);
    }
};
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