<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>

#include<bits/stdc++.h>

class Solution {
public:

    int min(int a, int b){
        if(a<=b){
            return a;
        }
        return b;
    }

    unordered_map<int, int> hash;

    int recur(vector<int> &arr, int index, int &k){

        if(index == arr.size()){
            return 0;
        }

        if(hash.find(index) !=hash.end()){
            return hash[index];
        }

        int ans = 0;
        int mx = 0;
        int mn = min(index+k, arr.size());

        for(int i=index;i<mn;i++){
            mx = max(mx, arr[i]);
            ans = max(ans, mx*(i-index+1)+recur(arr, i+1, k));
        }

        return hash[index] = ans;

    }

    int maxSumAfterPartitioning(vector<int>& arr, int k) {


        return recur(arr, 0, k);        



    }
};
13400