It's the next greater element problem with a twist in the story.
Clarify the problem and constraints, then propose an efficient monotonic stack solution that processes the array in O(n) time. Explain how the stack maintains indices of days with decreasing readings, and when a higher reading is encountered, pop and compute waiting days. Finally, discuss edge cases and complexity.
Pro tip: Mention that the monotonic stack approach is optimal and can be easily adapted to find the next greater element to the left or right, showing versatility. Also, emphasize handling duplicates correctly by using strictly greater comparison.
Restate the problem in your own words and ask clarifying questions about input size, duplicates, and expected output format.
Mention the naive O(n^2) approach of checking each future day, and explain why it's inefficient for large inputs.
Explain that a stack can keep track of days with unresolved higher readings, maintaining a decreasing order of readings.
Iterate through the array; while the stack is not empty and current reading is greater than the reading at the top index, pop and set the result for that index. Push the current index.
State that each index is pushed and popped at most once, giving O(n) time and O(n) space. Discuss cases like strictly increasing, decreasing, and all equal readings.
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