<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>>pl;
    void pal (string s){
        //setting up identity
        int n = s.length(); 
        for(int i = 0;i < s.length();i++){
            pl[i][i] = 0;
        }
        for(int i = 0; i < n-1; i++){
            if(s[i] == s[i+1]){
                pl[i][i+1] = pl[i+1][i]= 0;
            }else{
                pl[i][i+1] = 1;
            }
        }
        for(int j = 0; j < n; j++){
            for(int i  = 0; i < j-1;i++){
                if(s[i] == s[j]){
                    pl[i][j] = 0;
                }else{
                    pl[i][j] = 1;
                }
                pl[i][j] += pl[i+1][j-1];
            }
        }
    }
    vector<vector<int>>dp;
    int solve(int i,int k,string s){
        //base
        int n = s.length();
        if(i == n){
            if(k == 0){
                return 0;
            }else{
                return 200;
            }
        }
        if(k <= 0)return 200;
        if(dp[i][k] != -1){
            return dp[i][k];
        }
        int ans = 200;
        for(int j = i; j < n; j++){
            ans = min(ans,pl[i][j] + solve(j+1,k-1,s));
        }
        return dp[i][k] = ans;
    }
    int palindromePartition(string s, int k) {
        int n = s.length();
        pl.resize(n,vector<int>(n,0));
        dp.resize(n,vector<int>(k+1,-1));
        pal(s);
        return solve(0,k,s);
    }
};
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