Minimum Value to Get Positive Step by Step Sum

Problem 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.

Key Insights

• The goal is to ensure that at every step of the summation, the cumulative sum remains at least 1.
• If the cumulative sum dips below 1, it indicates that the initial startValue is insufficient.
• The problem can be solved by calculating the minimum cumulative sum during the iterations and determining how much more startValue is needed.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we will iterate through the array while maintaining a cumulative sum. We will track the minimum cumulative sum encountered during the iteration. If this minimum sum is less than 1, we will calculate the required startValue to keep the cumulative sum positive. The required startValue will be the difference between 1 and the minimum cumulative sum, ensuring that we also start with a positive value.

Code Solutions