<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 helper(vector<int>& arr, int k, int currk, int index, int currMax,vector<vector<int>>& dp) {

        if (index >= arr.size() - 1) {
            currMax = max(currMax,arr[index]);
            return (currMax * currk);
        }
        if(dp[currk][index] != -1) return dp[currk][index];
        int breakHere = 0;
        int dontBreak = 0;
        currMax = max(currMax, arr[index]);
        if (currk >= k) {
            breakHere = (currMax * k) + helper(arr, k, 1, index + 1, 0,dp);
        } else {
            breakHere = (currMax * currk) + helper(arr, k, 1, index + 1, 0,dp);
            dontBreak = helper(arr, k, currk + 1, index + 1, currMax,dp);
        }

        return dp[currk][index] = max(breakHere, dontBreak);
    }

    int maxSumAfterPartitioning(vector<int>& arr, int k) {
        vector<vector<int>> dp(k + 1,vector<int>(arr.size() + 1,-1));
        return helper(arr, k, 1, 0, arr[0],dp);
    }
};
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