<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];
    bool isPalindrome(string& s,int i,int j){ 
        while(i <= j){ 
            if(s[i] != s[j]){ 
                return false;
            }
            i++;
            j --;
        }

        return true;
    }
    int cost(string &s){ 
        int i = 0, j = s.size() - 1;
        int cst = 0;
        while(i <= j){ 
            if(s[i] != s[j]){ 
                cst += 1;
            }
            i++;
            j --;
        }

        return cst;
    }
    int solve(string s,int k,int idx,int cuts) { 
        if(idx >= s.size() && cuts == k) return 0;
        if(dp[idx][cuts] != -1) return dp[idx][cuts];
        
        int splits = 10000;
        
        for(int i = idx ; i < s.size() ; i ++ ) { 
            string temp = s.substr(idx,i - idx + 1);
            if(isPalindrome(temp,0,temp.size() - 1)) { 
                splits = min(splits,solve(s,k,i + 1,cuts + 1));
            }else { 
                int vals  = cost(temp);
                splits = min(splits,vals + solve(s,k,i + 1,cuts + 1));
            }
        }

        return dp[idx][cuts] = splits;
    }
    int palindromePartition(string s, int k) {
        memset(dp,-1,sizeof(dp));
        return solve(s,k,0,0);
    }
};
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