<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 n;
    vector<vector<int>> dp;

    int countForPalindrome(string &s) {
        int n = s.length();
        int ans = 0;
        int si = 0;
        int ei = n-1;

        while(si < ei)
        {
            if(s[si] != s[ei])
            ans++;

            si++;
            ei--;
        }

        return ans;
    }

    int memoPalindromePartition(string &s, int cur, int k) {
        if(cur >= n)
        return 0;

        if(dp[cur][k] == -1)
        {
            if(k == 0)
            {
                string tstr = s.substr(cur,n-cur);
                dp[cur][k] = countForPalindrome(tstr);
            }
            else
            {
                int tmp = INT_MAX;
                for(int i = cur; i < n-k; i++)
                {
                    string tstr = s.substr(cur,i-cur+1);
                    tmp = min(tmp, countForPalindrome(tstr) + memoPalindromePartition(s,i+1,k-1));
                }
                dp[cur][k] = tmp;
            }
        }

        return dp[cur][k];
    }


    int palindromePartition(string s, int k) {
        n = s.length();
        dp.resize(n, vector<int>(k,-1));
        return memoPalindromePartition(s,0,k-1);
    }
};
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