The code itself is basically five lines once you see it: just sum up the drops between consecutive elements where a[i-1] > a[i].
First, clarify the problem and constraints, then derive the optimal strategy by analyzing the effect of operations. The key insight is to process the array from right to left, maintaining the minimum required value for each position, and using a stack or greedy approach to compute the minimal total increment.
Pro tip: Emphasize that the optimal solution involves only adding to suffixes, and the minimal total sum equals the sum of positive differences between the required minimum and the original value when traversing from right to left. This shows deep insight and avoids overcomplicating with interval operations.
Ask about input size, value ranges, and whether the array can be modified in place. Confirm that operations can be applied multiple times and that we want to minimize the total sum of added values.
Observe that adding to a closed interval is equivalent to adding to a contiguous subarray. To make the array non-decreasing, we need to ensure each element is at least as large as the previous one.
Process from right to left: maintain the minimum value that the current element must have to keep the suffix non-decreasing. If the current element is less than this minimum, we must add the difference; otherwise, update the minimum to the current element.
Sum all positive differences between the required minimum and the original value. This sum is the minimal total added value, achievable by adding to suffixes ending at each position where a difference occurs.
Test with small arrays, strictly increasing/decreasing arrays, and arrays with equal elements. Confirm that the computed sum matches the result of applying the operations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.