Took me a while to even understand what they were asking.
First, clarify that adding x to a subarray means increasing each element in that range by x, and x must be non-negative. Then, model the problem as finding the minimum total increment to make the array non-decreasing, which can be solved by computing the difference array and summing the negative differences.
Pro tip: Mention that the problem reduces to summing the absolute values of negative differences between consecutive elements, and that this can be computed in O(n) time. Also, note that the order of operations doesn't matter, so a greedy approach works.
Confirm that x is a non-negative value added to a contiguous subarray, and the goal is to minimize the sum of all x used. Ensure that the final array must be non-decreasing.
Realize that adding x to a subarray increases the difference between the element before the subarray and the first element of the subarray, and decreases the difference between the last element of the subarray and the element after it. This affects the non-decreasing condition.
Show that the minimum total sum of x is the sum of the absolute values of all negative differences between consecutive elements in the original array. That is, for each i from 1 to n-1, if arr[i] < arr[i-1], add (arr[i-1] - arr[i]) to the total.
Iterate through the array once, compute the difference between each pair of consecutive elements, and accumulate the positive part of (arr[i-1] - arr[i]). Return the total.
State that the algorithm runs in O(n) time and O(1) space. Discuss edge cases: already non-decreasing array (answer 0), single element, and large values.
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