Split Array Largest Sum

def splitArray(nums, k):
    n = len(nums)
    # prefix[j] is the sum of the first j values
    prefix = [0] * (n + 1)
    for i, x in enumerate(nums):
        prefix[i + 1] = prefix[i] + x
    # best[j]: the smallest largest part when the first j values form one part
    best = prefix[:]
    for parts in range(2, k + 1):
        nxt = [0] * (n + 1)
        for j in range(parts, n + 1):
            lowest = prefix[j]  # never worse than one part holding everything
            for i in range(parts - 1, j):
                # the first i values form parts-1 parts, nums[i..j-1] is the last part
                worst = max(best[i], prefix[j] - prefix[i])
                if worst < lowest:
                    lowest = worst
            nxt[j] = lowest
        best = nxt
    return best[n]

def splitArray(nums, k):
    def parts_needed(cap):
        # Fill each part left to right and start a new one only when the next value would pass cap.
        parts, current = 1, 0
        for x in nums:
            if current + x > cap:
                parts += 1
                current = x
            else:
                current += x
        return parts

    lo, hi = max(nums), sum(nums)  # one value per part at best, everything in one part at worst
    while lo < hi:
        mid = (lo + hi) // 2
        if parts_needed(mid) <= k:
            hi = mid  # mid works, so the answer is mid or smaller
        else:
            lo = mid + 1  # mid needs more than k parts, so the answer is larger
    return lo