11_minValue.cpp

class Solution {
public:
    int minStartValue(vector<int>& nums) {
        // We use "total" for current step-by-step total, "minVal" for minimum 
        // step-by-step total among all sums. Since we always start with 
        // startValue = 0, therefore the initial current step-by-step total is 0, 
        // thus we set "total" and "minVal" be 0. 
        int minVal = 0;
        int total = 0;

        // Iterate over the array and get the minimum step-by-step total.
        for (int num : nums) {

            total += num;
            minVal = min(minVal, total);
        }
        
        // We have to let the minimum step-by-step total equals to 1, 
        // by increasing the startValue from 0 to -minVal + 1, 
        // which is just the minimum startValue we want.
        return -minVal + 1;
    }
};