410. 分割数组的最大值(二分贪心)

不断二分尝试分段的最大值为mx时能不能划分为k段

class Solution:
    def splitArray(self, nums: List[int], k: int) -> int:
        def check(mx: int) -> bool:
            cnt = 1
            s = 0
            for x in nums:
                if s + x <= mx:
                    s += x
                else:
                    if cnt==k or x>mx:
                        return False
                    cnt += 1
                    s = x
            return cnt<=k
        right = sum(nums)
        left = max(max(nums) - 1, (right-1) // k)
        while left < right:
            mid = (left + right) // 2
            if check(mid):
                right = mid
            else:
                left = mid+1
        return left

划分dp的做法（ dp[i][j]即nums[:i+1]划分为j段的最小最大值）

class Solution:
    def splitArray(self, nums: List[int], k: int) -> int:
        pre = [0] * (len(nums)+1) # 前缀和
        dp = [[float('inf')] * k for _ in range(len(nums))]
        for i in range(len(nums)):
            pre[i+1] = pre[i] + nums[i]
            dp[i][0] = pre[i+1]
        for i in range(len(nums)):
            for j in range(1,k):
                for t in range(j-1,i):
                    dp[i][j] = min(dp[i][j],max(dp[t][j-1], pre[i+1]-pre[t+1]))
        return int(dp[-1][-1])