Hex.*

LC1413 - Minimum Value to Get Positive Step by Step Sum

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Datastructure and Algorithm: DAY 70. Leetcode: 246/2736

Description

Given an array of integers nums, you start with an initial positive value startValue.
In each iteration, you calculate the step by step sum of startValue plus elements in nums (from left to right).
Return the minimum positive value of startValue such that the step by step sum is never less than 1.

Example 1:

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Input: nums = [-3,2,-3,4,2]
Output: 5
Explanation: If you choose startValue = 4, in the third iteration your step by step sum is less than 1.
step by step sum
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

Example 2:

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Input: nums = [1,2]
Output: 1
Explanation: Minimum start value should be positive.

Example 3:

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Input: nums = [1,-2,-3]
Output: 5

Constraints:

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1 <= nums.length <= 100
-100 <= nums[i] <= 100

Solution

The smallest positive integer is required.
We can get the smallest negative sum, and the answer is the opposite of the negative number + 1

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# O(n) time | O(1) space
class Solution:
    def minStartValue(self, nums: List[int]) -> int:
        ans = 0
        cur = 0
        for i in nums:
            cur += i
            if cur < ans:
                ans = cur
        return -ans + 1