<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:
    void populate(string s, vector<vector<int>>&dp){
        int n = s.size();
        for(int gap=0; gap<n; gap++){
            for(int i=0, j=gap; i<n&&j<n; i++,j++){
                if(gap == 0){
                    dp[i][j] = 0;
                }
                else if(gap == 1){
                    if(s[i] != s[j]){
                        dp[i][j] = 1;
                    }
                    else dp[i][j] = 0;
                }
                else{
                    dp[i][j] = dp[i+1][j-1];
                    if(s[i] != s[j]){
                        dp[i][j] += 1;
                    }
                }
            }

        }
    }
    int helper(int ind, string s, int k, vector<vector<int>>&dp, vector<vector<int>>&memo){
        if(ind == s.size()){
            if(k == 0)return 0;
            else return 1e9;
        }
        if(k < 0)return 1e9;
        if(memo[ind][k] != -1)return memo[ind][k];
        int ans = INT_MAX;
        for(int i=ind; i<s.size(); i++){
            int cost = dp[ind][i];
            ans = min(ans,helper(i+1,s,k-1,dp,memo)+cost);
        }
        return memo[ind][k] = ans;
    }
    int palindromePartition(string s, int k) {
        int n = s.size();
        vector<vector<int>>dp(n,vector<int>(n,0));
        populate(s,dp);
        vector<vector<int>>memo(n,vector<int>(k+1,-1));
        return helper(0,s,k,dp,memo);
    }
};
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