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The idea is to simulate the step by step summation of the start value with the elements of the array. We maintain a running sum and adjust the start value such that this sum never drops below 1. At each step, if the running sum is less than 1, we calculate and update the new minimum start value needed to keep the running sum at least 1.
Time Complexity: O(n), where n is the length of nums.
Space Complexity: O(1), as we are using a constant amount of space.
1#include <stdio.h>
2
3int minStartValue(int* nums, int numsSize) {
4 int min_sum = 0, current_sum = 0;
5 for (int i = 0; i < numsSize; i++) {
6 current_sum += nums[i];
7 if (current_sum < min_sum) {
8 min_sum = current_sum;
9 }
10 }
11 return 1 - min_sum;
12}
13
14int main() {
15 int nums[] = {-3, 2, -3, 4, 2};
16 printf("%d\n", minStartValue(nums, 5)); // Output: 5
17 return 0;
18}We iterate over the nums array, maintaining a cumulative running sum. We track the minimum value of this sum as min_sum. After processing all elements, the start value must be greater than or equal to 1 minus this minimum sum in order to ensure the step by step sum never falls below 1.
This approach is similar to the first but conceptualized through using prefix sums and adjusting the needed start value based on the lowest prefix sum reached. We cumulatively add each number and check if the prefix sum dips below a certain threshold, indicating the minimal adjustment needed for the start value.
Time Complexity: O(n).
Space Complexity: O(1).
This approach in JavaScript employs prefix summation to dictate where negative incursions on the cumulative sum require a larger starting value, guaranteeing positivity at every step.