<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 dp[101][101];
    int dpx[101][101];

    int cost(int i,int j,string &s){
        if(i>=j) return 0;
        if(dpx[i][j]!=-1) return dpx[i][j];
        int ans=cost(i+1,j-1,s);
        if(s[i]!=s[j]) ans++;
        return dpx[i][j]=ans;
    }

    int rec(int i,int j,string s){
        if(i!=-1 && j==0){
            return 1e9;
        }
        if(i==-1){
            if(j==0){
                return 0;
            }else{
                return 1e9;
            }
        }
        if(dp[i][j]!=-1) return dp[i][j];
        int ans=1e9;
        for(int x=i;x>=0;x--){
            int costy=rec(x-1,j-1,s)+cost(x,i,s);
            ans=min(costy,ans);
        }
        return dp[i][j]=ans;

    }

    int palindromePartition(string s, int k) {
        memset(dp,-1,sizeof(dp));
        memset(dpx,-1,sizeof(dp));
        return rec(s.size()-1,k,s);
    }
};
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