Took me a while to see that this reduces to summing up the drops between adjacent elements after accounting for whatever increases you've already applied going left to right.
Reframe the problem by considering the differences between adjacent elements. The minimum number of operations equals the sum of positive differences between consecutive elements, as each operation can fix a deficit by incrementing a suffix. Explain this insight and provide a simple O(n) algorithm.
Pro tip: Mention that this is equivalent to the total 'upward slope' needed, and note that the operation is like adding 1 to a suffix, so each positive difference requires at least that many operations. This shows deep understanding and efficiency.
Recognize that incrementing a contiguous subarray by 1 can be used to raise elements to meet non-decreasing constraints. The key is to think about how to fix violations efficiently.
A violation occurs when an element is greater than the next element (a[i] > a[i+1]). To fix it, we need to increment a[i+1] and possibly subsequent elements.
The minimum operations equal the sum of positive differences between consecutive elements: sum(max(0, a[i] - a[i+1])) for i from 0 to n-2. This is because each operation can reduce one positive difference by 1.
Test with simple arrays like [3,2,1] (answer 3) and [1,2,3] (answer 0) to confirm the formula. Explain why it works: each operation increments a suffix, effectively reducing the deficit at the start of the suffix.
State that the algorithm runs in O(n) time and O(1) space, as it only requires a single pass through the array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.