<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:
    vector<vector<int>> dp;
    int requiredCharacters(string s,int i,int j) {
        int count = 0;
        while(i < j) {
            if(s[i] != s[j]) {
                count++;
            }
            i++;
            j--;
        }
        return count;
    }
    int solve(int i,int k,string s) {
        if(k == 1) return requiredCharacters(s,i,s.size()-1);
        if(i == s.size()) {
            return INT_MAX;
        }
        if(dp[i][k] != -1) return dp[i][k];
        int ans = INT_MAX;
        for(int j = i;j<=s.size()-k;j++) {
            int cost = requiredCharacters(s,i,j);
            ans = min(ans,cost + solve(j+1,k-1,s));
        }
        return dp[i][k] = ans;
    }
    int palindromePartition(string s, int k) {
        int size = s.size();
        dp.resize(size, vector<int>(k + 1, -1));
        return solve(0,k,s);
    }
};
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