<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 countChange(string s, int start, int end){
        int ans = 0;
        int st = start;
        int ed = end;
        while(st < ed){
            if(s[st] != s[ed]){
                ans++;
            }
            st++;
            ed--;
        }
        return ans;
    }

    int solve(string s, int k, int start, int end, vector<vector<vector<int>>> &dp){
        if(start > end){
            if(k == 0) return 0;
            else if(k>0) return 99999;
        }

        if(end-start+1 == k){
            dp[k][start][end] = 0;
            return 0;
        }
        if(end-start+1 < k){
            return dp[k][start][end] = 99999;
        }

        if(k == 1){
            int a = countChange(s, start,end);
            dp[k][start][end] = a;
            return a;
        }

        if(dp[k][start][end] != -1) return dp[k][start][end];

        int ans = 99999;
        for(int i = start; i<= end; i++){
            int a = solve(s, 1, start, i, dp);
            int b = solve(s, k-1, i+1, end, dp);
            ans = min(ans, a+b);
        }
        return dp[k][start][end] = ans;
    }

    int palindromePartition(string s, int k) {
        int n = s.size()-1;
        vector<vector<vector<int>>> dp(k+1, vector<vector<int>> (n+2, vector<int>(n+2, -1)));
        int ans = solve(s, k, 0, n, dp);
        return ans;
    }   
};
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