LeetCode 题解工作台
逐步求和得到正数的最小值
给你一个整数数组 nums 。你可以选定任意的 正数 startValue 作为初始值。 你需要从左到右遍历 nums 数组，并将 startValue 依次累加上 nums 数组中的值。 请你在确保累加和始终大于等于 1 的前提下，选出一个最小的 正数 作为 startValue 。 示例 1： …
2
题型
6
代码语言
3
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答案摘要
class Solution: def minStartValue(self, nums: List[int]) -> int:
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题目描述
给你一个整数数组 nums 。你可以选定任意的 正数 startValue 作为初始值。
你需要从左到右遍历 nums 数组，并将 startValue 依次累加上 nums 数组中的值。
请你在确保累加和始终大于等于 1 的前提下，选出一个最小的 正数 作为 startValue 。
示例 1：
输入：nums = [-3,2,-3,4,2]
输出：5
解释：如果你选择 startValue = 4，在第三次累加时，和小于 1 。
累加求和
startValue = 4 | startValue = 5 | nums
(4 -3 ) = 1 | (5 -3 ) = 2 | -3
(1 +2 ) = 3 | (2 +2 ) = 4 | 2
(3 -3 ) = 0 | (4 -3 ) = 1 | -3
(0 +4 ) = 4 | (1 +4 ) = 5 | 4
(4 +2 ) = 6 | (5 +2 ) = 7 | 2
示例 2：
输入：nums = [1,2] 输出：1 解释：最小的 startValue 需要是正数。
示例 3：
输入：nums = [1,-2,-3] 输出：5
提示：
1 <= nums.length <= 100-100 <= nums[i] <= 100
解题思路
方法一
class Solution:
def minStartValue(self, nums: List[int]) -> int:
s, t = 0, inf
for num in nums:
s += num
t = min(t, s)
return max(1, 1 - t)
复杂度分析
| 指标 | 值 |
|---|---|
| 时间 | Depends on the final approach |
| 空间 | Depends on the final approach |
面试官常问的追问
外企场景- question_mark
Understanding of prefix sums and cumulative calculations is required.
- question_mark
The candidate should be able to relate the concept of array adjustments and prefix sum manipulation to real-world scenarios.
- question_mark
The candidate may need to demonstrate efficiency in solving this problem with respect to both time and space.
常见陷阱
外企场景- error
Forgetting to consider the negative values in the array, which can reduce the cumulative sum below 1.
- error
Confusing the minimum prefix sum with the overall cumulative sum, leading to incorrect start values.
- error
Not optimizing the approach to handle larger arrays efficiently, which may result in time limit exceed errors.
进阶变体
外企场景- arrow_right_alt
Modify the problem to allow negative start values and analyze how the solution adapts.
- arrow_right_alt
Introduce more complex arrays, such as those with very large or very small numbers, and observe performance changes.
- arrow_right_alt
Add constraints to the problem, like limiting the number of positive or negative values, to test the robustness of the solution.