<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 memo[501][501];
    int sum[501][501];
    int findSubarraySum(int i, int j, vector<int>& arr){
        if(i>j) return 0;
        if(sum[i][j]!=-1) return sum[i][j];
        int length = j-i+1;
        int maxelement = INT_MIN;
        for(int ind = i; ind<=j; ind++){
            maxelement = max(maxelement, arr[ind]);
        }
        return sum[i][j] = maxelement*length;
    }
    int rec(int i, int j, vector<int>& arr, int maxlength){
        if(j-i+1<=maxlength){
            return findSubarraySum(i, j, arr);
        }
        if(memo[i][j]!=-1) return memo[i][j];
        memo[i][j] = INT_MIN;
        for(int k=i;k<j;k++){
            memo[i][j] = max(memo[i][j], rec(i, k, arr, maxlength) + rec(k+1, j, arr, maxlength));
        }
        return memo[i][j];
    }
    int maxSumAfterPartitioning(vector<int>& arr, int maxlength) {
        memset(memo, -1, sizeof(memo));
        memset(sum, -1, sizeof(sum));
        return rec(0, arr.size()-1,  arr, maxlength);
    }
};
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