Formatted question description: https://leetcode.ca/all/1413.html

# 1413. Minimum Value to Get Positive Step by Step Sum (Easy)

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


Constraints:

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

Related Topics:
Array

## Solution 1.

This problem is similar to finding the minimum prefix sum of nums. Once we find that minimum prefix sum m, we return 1 - min(0, m) where min(0, m) returns 0 for positive m.

// OJ: https://leetcode.com/problems/minimum-value-to-get-positive-step-by-step-sum/

// Time: O(N)
// Space: O(1)
class Solution {
public:
int minStartValue(vector<int>& nums) {
partial_sum(begin(nums), end(nums), begin(nums));
int m = *min_element(begin(nums), end(nums));
return 1 - min(0, m);
}
};


Java

class Solution {
public int minStartValue(int[] nums) {
int min = 0;
int sum = 0;
int length = nums.length;
for (int i = 0; i < length; i++) {
sum += nums[i];
min = Math.min(min, sum);
}
int minStart = min >= 0 ? 1 : -min + 1;
return minStart;
}
}