<p>Given an integer array <code>arr</code>, partition the array into (contiguous) subarrays of length <strong>at most</strong> <code>k</code>. After partitioning, each subarray has their values changed to become the maximum value of that subarray.</p>

<p>Return <em>the largest sum of the given array after partitioning. Test cases are generated so that the answer fits in a <strong>32-bit</strong> integer.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [1,15,7,9,2,5,10], k = 3
<strong>Output:</strong> 84
<strong>Explanation:</strong> arr becomes [15,15,15,9,10,10,10]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [1,4,1,5,7,3,6,1,9,9,3], k = 4
<strong>Output:</strong> 83
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [1], k = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 500</code></li>
	<li><code>0 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= k &lt;= arr.length</code></li>
</ul>

class Solution {
public:
    int dp[505][505];
    int n;
    int k;
    int solve(int index, int taken, int start, int mx, vector<int>& arr){
        if(index == n){
            return mx * (n - start);
        }
        if(dp[index][taken] != -1){
            return dp[index][taken];
        }
        int ans = mx * (index - start) + solve(index + 1, 1, index, arr[index], arr);
        if(taken < k){
            ans = max(ans, solve(index + 1, taken + 1, start, max(mx, arr[index]), arr));
        }
        dp[index][taken] = ans;
        return ans;
    }
    int maxSumAfterPartitioning(vector<int>& arr, int k) {
        ios_base::sync_with_stdio(0);
        cin.tie(0);
        cout.tie(0);
        this -> n = arr.size();
        this -> k = k;
        for(int i = 0; i < n; i++){
            for(int j = 0; j <= k; j++){
                dp[i][j] = -1;
            }
        }
        return solve(0, 0, 0, INT_MIN, arr);
    }
};
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