Prefix Sum Questions

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1413. Minimum Value to Get Positive Step by Step Sum

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:

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:

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

Example 3:

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

Suppose the array nums is:
[a,b,c,d]
If we iterate the array with startValue = 0 (There are other values we can use, but 0 is the most convenient), the first step-by-step total will be 0, and we can have a list of all step-by-step sums (we call it List):