<p>Given an integer array <code>nums</code> and an integer <code>k</code>, split <code>nums</code> into <code>k</code> non-empty subarrays such that the largest sum of any subarray is <strong>minimized</strong>.</p>

<p>Return <em>the minimized largest sum of the split</em>.</p>

<p>A <strong>subarray</strong> is a contiguous part of the array.</p>

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

<pre>
<strong>Input:</strong> nums = [7,2,5,10,8], k = 2
<strong>Output:</strong> 18
<strong>Explanation:</strong> There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5], k = 2
<strong>Output:</strong> 9
<strong>Explanation:</strong> There are four ways to split nums into two subarrays.
The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= k &lt;= min(50, nums.length)</code></li>
</ul>

from typing import List, Dict, Tuple

class Solution:
    def splitArray(self, nums: List[int], k: int) -> int:
        presum: List[int] = [0]
        for n in nums:
            presum.append(presum[-1] + n)
        
        memo: Dict[Tuple[int, int], int] = {}
        return self._dfs(0, k, len(nums), presum, memo)
    
    def _dfs(self, i: int, k: int, n: int, presum: List[int], memo: Dict[Tuple[int, int], int]) -> int:
        if (i, k) in memo:
            return memo[(i, k)]
        
        if k == 1:
            memo[(i, k)] = presum[n] - presum[i]
            return memo[(i, k)]
        
        result = presum[n]
        for j in range(i+1, n):
            curr_sum = presum[j] - presum[i]
            result = min(result, max(curr_sum, self._dfs(j, k-1, n, presum, memo)))

            if curr_sum >= result:
                break
        
        memo[(i, k)] = result
        return result
        
24000