<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 functools import cache
from itertools import accumulate
class Solution:
    def splitArray(self, nums: List[int], k: int) -> int:
        cumsum = list(accumulate(nums))
        @cache
        def compute(start, k):
            # print(start, k)
            if k == 1:
                return cumsum[-1] - (cumsum[start-1] if start > 0 else 0)
            l = start; r = len(nums)-k+1
            res = 10**9
            while l < r:
                i = (l+r) // 2
                s1 = cumsum[i] - (cumsum[start-1] if start > 0 else 0)
                s2 = compute(i+1, k-1)
                res = min(res, max(s1, s2))
                if s1 <= s2:
                    l = i + 1
                else:
                    r = i
                # print(l, i, r)
                # break
            return res
        # def compute(start, k):
        #     if k == 1:
        #         return sum(nums[start:])
        #     s = 0
        #     r = 10**9
        #     for i in range(start, len(nums)-k+1):
        #         s += nums[i]
        #         s2 = compute(i+1, k-1)
        #         r = min(r, max(s, s2))
        #         if s >= s2: break
        #     return r
        return compute(0, k)
19200