<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 dp1(string&s,int start,int end,int k,vector<vector<vector<int>>>&dp){
        if(k==1){
            int cnt=0;
            while(start<end){
                if(s[start]!=s[end]){
                    cnt++;
                }
                start++;
                end--;
            }
            return cnt;
        }
        if(k==(end-start+1)){
            return 0;
        }
        if(dp[start][end][k]!=-1){
            return dp[start][end][k];
        }
        int min1=s.size();
        // int u1=k-1;
        for(int j=start;j<end;j++){
            int len1=(j-start+1);
            int len2=(end-(j+1)+1);
            for(int u=1;u<k;u++){
                if(u<=len1 && (k-u)<=len2){
                    min1=min(min1,dp1(s,start,j,u,dp)+dp1(s,j+1,end,k-u,dp));
                }
            }
        }
        dp[start][end][k]=min1;
        return min1;
    }
    int palindromePartition(string s, int k) {
        vector<vector<vector<int>>>dp(s.size(),vector<vector<int>>(s.size(),vector<int>(k+1,-1)));
        return dp1(s,0,s.size()-1,k,dp);
        
    }
};
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