<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 costCal(string s) {
        int lo=0, hi=s.size()-1, ans=0;
        while(lo<hi) {
            if(s[lo++] != s[hi--]) ans++;
        }
        return ans;
    }
    int f(int ind, int n, string &s, int k, vector<vector<int>> &dp) {
        if(ind==n) {
            if(k==0) return 0;
            return 1e9;
        }
        if(dp[ind][k] != -1) return dp[ind][k];
        int ans=1e9;
        for(int i=ind;i<n;i++) {
            if(k>0) {
                int cost=costCal(s.substr(ind, i-ind+1)) + f(i+1, n, s, k-1, dp);
                ans=min(ans, cost);
            }
        }
        return dp[ind][k] = ans;
    }
    int palindromePartition(string &s, int k) {
        int n=s.size();
        vector<vector<int>> dp(n+1, vector<int> (k+1, -1));
        return f(0, n, s, k, dp);
    }
};
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