<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:
    long long calculate(string s, int start, int end, int k, int dp[101][101][101]) {
        if(start>end) return INT_MAX;
        if(k<1) return INT_MAX;
        if(end-start+1 < k) return INT_MAX;
        if(dp[start][end][k]!=-1) return dp[start][end][k];
        if(k==1) {
            int st = start;
            int en = end;
            //cout<<st<<en<<endl;
            long long ans =0;
            while(st<=en) {
                if(s[st]!=s[en]) ans++;
                st++; en--;
            }
            //cout<<ans<<endl;
            return dp[start][end][k]=ans;
        }
        else {
            long long ans = INT_MAX;
            for(int i=start+1;i<=end;i++) {
                ans = min(ans, calculate(s,start,i-1,1,dp) + calculate(s,i,end,k-1,dp));
            }
            //cout<<start<<" "<<end<<" "<<ans<<endl;
            return dp[start][end][k]=ans;
        }
        return 0;
    }
    int palindromePartition(string s, int k) {
        long long ans = INT_MAX;
        int dp[101][101][101];
        memset(dp,-1,sizeof(dp));
        return calculate(s,0,s.length()-1,k,dp);
        return ans;
    }
};
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