<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 change(int i, int j, string &s){
        int ans=0;
        while(i<j){
            if(s[i] != s[j]){
                ans++;
            }
            i++, j--;
        }
        return ans;
    }
    int solve(int i, int j, string s, int k, vector<vector<int>> &dp){
        int n = s.length();
        if(i>=n){
            if(j==k){
                return 0;
            }
            return 1e9;
        }

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

        int ans = 1e9;

        for(int l=i; l<n; l++){
            if(j+1 <=k){
                ans = min(ans, change(i, l, s)+solve(l+1, j+1, s, k, dp));
            }
        }
        return dp[i][j]=ans;
    }
    int palindromePartition(string s, int k) {
        int n = s.length();
        vector<vector<int>> dp(n+1, vector<int>(n+1, -1));
        return solve(0, 0, s, k, dp);
    }
};
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