<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:
    map<pair<int, int>, int>mp;

    int countChanges(int low, int high, string str){
        int res = 0;
        while(low < high){
            if(str[low]!=str[high])
                ++res;
            ++low;
            --high;
        }

        return res;
    }

    int dp[101][101];

    int solve(string str, int k, int index, int n){
        if(n <= index){
            if(k == 0)
                return 0;
            return 1e9;
        }

        if(k == 1){
            return mp[{index, n-1}];
        }

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

        int res = 1e9;

        for(int i=index;i<n;i++){
            int val = mp[{index, i}];
            res = min(res, val + solve(str, k-1, i+1, n));
        }

        return dp[k][index] = res;
    }

    int palindromePartition(string s, int k) {
        int n = s.length();

        for(int i=0;i<n;i++){
            for(int j=i;j<n;j++){
                int val = countChanges(i, j, s);
                mp.insert({{i, j}, val});
            }
        }

        memset(dp, -1, sizeof(dp));

        return solve(s, k, 0, n);
    }
};
101803