<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 {
    int PartitionArrayForMaximumSum(vector<int>& Arr, const int& K, const int& CurIdx, vector<int>& Memo)
    {
        if (int(Arr.size()) <= CurIdx)
        {
            return 0;
        }

        int& Result = Memo[CurIdx];
        if (Result != -1)
        {
            return Result;
        }

        int MaxSum = 0, MaxValue = 0, Cnt = 1;
        for(int i = CurIdx ; i < int(Arr.size()) && i < CurIdx + K ; ++i, ++Cnt)
        {
            MaxValue = max(MaxValue, Arr[i]);
            int Option = (Cnt * MaxValue) + PartitionArrayForMaximumSum(Arr, K, CurIdx + Cnt, Memo);
        
            MaxSum = max(MaxSum, Option);
        }

        return Result = MaxSum;
    }


public:
    int maxSumAfterPartitioning(vector<int>& arr, int k) 
    {
        vector<int> Memo(arr.size(), -1);
        return PartitionArrayForMaximumSum(arr, k, 0, Memo);
    }
};
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